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<|im_start|>user
Cathy and Jim begin running at the same time and they start at the same place on a straight path. Cathy runs at 10 miles per hour, and Jim runs at 6 miles per hour. After 18 minutes, Cathy stops to stretch. If it takes Cathy 27 minutes to stretch and Jim continues to run during this time, how many minutes will it take Cathy to catch up to Jim?
Answer Choices: (A) 20.5 (B) 21.5 (C) 22.5 (D) 23.5 (E) 24.5<|im_end|>
<|im_start|>assistant
<think>
</think>
In 18 minutes, Cathy runs 3 miles.
In 45 minutes, Jim runs 4.5 miles.
Cathy can catch Jim at a rate of 4 miles per hour.
Since Jim is ahead by 1.5 miles, it will take Cathy 1.5 / 4 hours = 22.5 minutes to catch Jim.
The answer is C<|endoftext|>
| 19,485
|
<|im_start|>user
There are two numbers. If 50% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Answer Choices: (A) 5/9 (B) 5/7 (C) 5/3 (D) 5/8 (E) 2/1<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the two numbers be x and y.
50/100 * x + y = 5/4y
=> 1/2 x = 1/4 y => x/y
= 2/1
The answer is E<|endoftext|>
| 325
|
<|im_start|>user
How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr
Answer Choices: (A) 1 1/5min (B) 2 1/5min (C) 3 1/5min (D) 4 1/5min (E) 5 1/5min<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
We know that,
Time=Distance/Speed
Speed=20 km/hr=20∗5/18m/sec=50/9m/sec
Time =(400∗9/50)=72sec=1 1/5min
Option A
The answer is A<|endoftext|>
| 995
|
<|im_start|>user
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 50% profit on the first article and 50% loss on second article. Find the net profit or loss percent?
Answer Choices: (A) 500 (B) 768 (C) 276 (D) 280 (E) 279<|im_end|>
<|im_start|>assistant
<think>
</think>
Profit on first article = 50% of 1000 = 500.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
The answer is A<|endoftext|>
| 30,817
|
<|im_start|>user
What takes both the shape and the volume of their container?
Answer choice: (A) solids (B) tissues (C) fluids (D) gases<|im_end|>
<|im_start|>assistant
<think>
</think>
Solids have a fixed volume and a fixed shape. Liquids have a fixed volume but take the shape of their container. Gases take both the volume and the shape of their container.
The answer is D<|endoftext|>
| 1,678
|
<|im_start|>user
A basket contains 4 blue, 4 red and 4 yellow marbles. If 4 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Answer Choices: (A) 2/21 (B) 3/25 (C) 1/6 (D) 9/28 (E) 16/55<|im_end|>
<|im_start|>assistant
<think>
</think>
12/12*8/11*4/10 = 384/1320 = 16/55
The answer is E<|endoftext|>
| 17,648
|
<|im_start|>user
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
Answer Choices: (A) 18 (B) 68 (C) 67 (D) 55 (E) 56<|im_end|>
<|im_start|>assistant
<think>
</think>
S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162
= 18
The answer is A<|endoftext|>
| 97,126
|
<|im_start|>user
What is the number in the unit place in (729)59?
Answer Choices: (A) 9 in the unit place. (B) 1 in the unit place. (C) 6 in the unit place. (D) 7 in the unit place. (E) none of these<|im_end|>
<|im_start|>assistant
<think>
</think>
When 729 is multiplied twice, the numbers in the unit place in 1.
In other words, if 729 is multiplied an even number of times, the number
in the unit place will be 1. Thus, the number is the place in (729)^58 is 1.
Thus, (729)59 = (729)^58 x (729) = (.....1) x (729)
= 9 in the unit place.
The answer is A<|endoftext|>
| 68,350
|
<|im_start|>user
In what time will a railway train 90 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Answer Choices: (A) 8 sec (B) 1 sec (C) 9 sec (D) 6 sec (E) 2 sec<|im_end|>
<|im_start|>assistant
<think>
</think>
T = 90/36 * 18/5
= 9 sec
The answer is C<|endoftext|>
| 85,857
|
<|im_start|>user
What population on earth is already harming the environment due to less resources to go around?
Answer choice: (A) humans (B) whales (C) rats (D) insects<|im_end|>
<|im_start|>assistant
<think>
</think>
Bundles of vascular tissue run through the ground tissue of a stem and transport fluids. Plants may vary in how these bundles are arranged.
The answer is A<|endoftext|>
| 11,173
|
<|im_start|>user
What type of image is formed when light rays diverge in front of a mirror?
Answer choice: (A) fake (B) large (C) reversed (D) virtual<|im_end|>
<|im_start|>assistant
<think>
</think>
When light rays diverge in front of a mirror, a virtual image is formed. A virtual image is formed by your brain tracing diverging rays backwards and is kind of a trick, like the person you see “behind” a mirror’s surface when you brush your teeth (there's obviously no real light focused behind a mirror!). Since virtual images aren’t actually “anywhere,” you can’t place photographic film anywhere to capture them.
The answer is D<|endoftext|>
| 6,124
|
<|im_start|>user
What process, which results because of great pressure at the center of a star, causes stars to shine?
Answer choice: (A) gravitational pull (B) nuclear fusion (C) electric fusion (D) energy fusion<|im_end|>
<|im_start|>assistant
<think>
</think>
Stars shine because of nuclear fusion. Fusion reactions in the Sun's core keep our nearest star burning. Stars are made mostly of hydrogen and helium. Both are very lightweight gases. A star contains so much hydrogen and helium that the weight of these gases is enormous. The pressure at the center of a star is great enough to heat the gases. This causes nuclear fusion reactions.
The answer is B<|endoftext|>
| 10,544
|
<|im_start|>user
Meg and Bob are among the 7 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Answer Choices: (A) 24 (B) 30 (C) 2520 (D) 90 (E) 120<|im_end|>
<|im_start|>assistant
<think>
</think>
Total # of ways the race can be finished is 7!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 7!/2=2520.
The answer is C<|endoftext|>
| 81,080
|
<|im_start|>user
According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 29, by how much does the temperature in degrees Celsius (C) increase?
Answer Choices: (A) 9 (B) 15 (C) 47 (D) 48 3/5 (E) 59<|im_end|>
<|im_start|>assistant
<think>
</think>
You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+29=61 --> C=5/9*29=16.11.
Increase = 16.11 degrees.
The answer is B<|endoftext|>
| 76,643
|
<|im_start|>user
Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 10x boxes?
Answer Choices: (A) 13 minutes (B) 14 minutes (C) 15 minutes (D) 16 minutes (E) 20 minutes<|im_end|>
<|im_start|>assistant
<think>
</think>
Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 4x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10
Now combine Time = combine work needs to be done / Combine Rate = 10x/5x * 10 = 6 Min
The answer is E<|endoftext|>
| 66,330
|
<|im_start|>user
On a purchase of $112, a store offered a payment plan consisting of a $12 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
Answer Choices: (A) 10.7% (B) 11.7% (C) 12.7% (D) 13.7% (E) 14.7%<|im_end|>
<|im_start|>assistant
<think>
</think>
12*10 + 12 = 132
(12/112)* 100 = 10.7
The answer is A<|endoftext|>
| 79,893
|
<|im_start|>user
A father purchased dress for his 3 daughters. The dresses are of same color but diff size and they are kept in dark room. what is probability that all the 3 will not choose their own dress?
Answer Choices: (A) 22 (B) 87 (C) 29 (D) 26 (E) 191<|im_end|>
<|im_start|>assistant
<think>
</think>
The answer is B<|endoftext|>
| 9,928
|
<|im_start|>user
Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/8 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Answer Choices: (A) 24 (B) 35 (C) 39 (D) 60 (E) 65<|im_end|>
<|im_start|>assistant
<think>
</think>
The total number of the people in the room must be a multiple of both 7 and 8 (in order 3/7 and 5/8 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 8, which is 56.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 56 people in the room.
Therefore there are 3/7*56=24 people in the room under the age of 21.
The answer is A<|endoftext|>
| 55,748
|
<|im_start|>user
A rower can row upstream at 7 km/hr and downstream at 15 km/hr. What is the rower's rate in still water?
Answer Choices: (A) 9 km/hr (B) 10 km/hr (C) 11 km/hr (D) 12 km/hr (E) 13 km/hr<|im_end|>
<|im_start|>assistant
<think>
</think>
The rate in still water is 1/2 * (15 + 7) = 11 km/hr
The answer is C<|endoftext|>
| 77,942
|
<|im_start|>user
What is an electrically neutral compound with positive and negative ions?
Answer choice: (A) correlated compound (B) ionic compound (C) isotope (D) neutralized molecule<|im_end|>
<|im_start|>assistant
<think>
</think>
Most of the rocks and minerals that make up the Earth’s crust are composed of positive and negative ions held together by ionic bonding. An ionic compound is an electrically neutral compound consisting of positive and negative ions. You are very familiar with some ionic compounds such as sodium chloride (NaCl). A sodium chloride crystal consists of equal numbers of positive sodium ions (Na + ) and negative chloride ions (Cl − ).
The answer is B<|endoftext|>
| 2,046
|
<|im_start|>user
During a clearance sale, a retailer discounted the original price of its TVs by 25% for the first two weeks of the month, then for the remainder of the month further reduced the price by taking 20% off the sale price. For those who purchased TVs during the last week of the month, what percent of the original price did they have to pay?
Answer Choices: (A) 40% (B) 45% (C) 55% (D) 60% (E) 62.5%<|im_end|>
<|im_start|>assistant
<think>
</think>
As it's a percentage problem, start with $100.
The first discount is 25% of $100, so the sales prices is 75% of $100 = $75.
The second discount is 20% of $75. Move the decimal once to the left and double it = $7.5*2 = $15.
The final sales price is $75-$15 = $60, which is 60% of $100.
The
The answer is D<|endoftext|>
| 42,885
|
<|im_start|>user
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7/10 of its present?
Answer Choices: (A) 61.5 (B) 60.5 (C) 63.5 (D) 35.71429 (E) 64.5<|im_end|>
<|im_start|>assistant
<think>
</think>
Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 7x/10
Hence, number of buckets needed = 25x/(7x/10)=(25×10)/7=35.71429
The answer is D<|endoftext|>
| 52,990
|
<|im_start|>user
A fruit drink is made of grapefruit, lemon, and orange juice, where 25 percent of the drink is grapefruit juice and 35 percent is lemon juice. If the drink is made with 20 ounces of orange juice, how many ounces is the drink total?
Answer Choices: (A) 60 (B) 80 (C) 50 (D) 100 (E) 40<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the total number of ounces in the drink be x
% of orange = 25%
% of watermelon = 35%
% of grape = 100% - 60% = 40%
But this number is given as 20 ounces
so 40% of x = 20 and x = (20)(100/40) = (20)(5/2)
x = 50
Therefore there a total of 50 ounces in the drink.
The answer is C<|endoftext|>
| 57,432
|
<|im_start|>user
Seven people went to a restaurant for dinner. Six of them spent $9 each on their meals and the seventh person spent $12 more than the average expenditure of all seven people. What was the total amount of money that the seven people spent?
Answer Choices: (A) $71 (B) $73 (C) $75 (D) $77 (E) $79<|im_end|>
<|im_start|>assistant
<think>
</think>
Let T be the total amount of money spent.
6*9 + (T/7 + 12) = T
66 = 6T/7
T = (7*66)/6 = 77
The answer is D<|endoftext|>
| 91,069
|
<|im_start|>user
If a and b are unique prime integers, which of the following must be odd?
Answer Choices: (A) a−b (B) 2a+2b (C) 2a−2b (D) 2a / 2b (E) ab^2<|im_end|>
<|im_start|>assistant
<think>
</think>
Any number multiplied by 2 has to be an even number. hence
The answer is A<|endoftext|>
| 96,276
|
<|im_start|>user
A rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares. Through how many of the squares does a diagonal of the rectangle pass?
Answer Choices: (A) 6 (B) 8 (C) 10 (D) 12 (E) 16<|im_end|>
<|im_start|>assistant
<think>
</think>
1)If the two sides are co-prime, SUM of sides -1..
2)and if not co-prime , Sum of sides - HCF of sides..
the difference is related to the diagonal passing through a vertex of squares at some place..
here 6 and 8 are NOT co-primes, so ans =6+8−HCF(6,8)=14−2=12
The answer is D<|endoftext|>
| 58,239
|
<|im_start|>user
Two goods trains each 680 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Answer Choices: (A) 228 (B) 65.28 (C) 48.32 (D) 27 (E) 21.1<|im_end|>
<|im_start|>assistant
<think>
</think>
Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 680 + 680 = 1360 m.
Required time = 1360 * 6/125 = 65.28 sec.
The answer is B<|endoftext|>
| 24,131
|
<|im_start|>user
As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 30%, what is the probability that Karen will be accepted to at least one project?
Answer Choices: (A) 729/1000 (B) 657/1000 (C) 343/500 (D) 123/250 (E) 17/100<|im_end|>
<|im_start|>assistant
<think>
</think>
Since the probability of Karen's being accepted to each individual project is 30%, the probability of her not being accepted to each project is 70%. The probability that she will be accepted to none is, therefore, (7/10)*(7/10)*(7/10)=343/1000.
P(Karen will be accepted to at least one project) = 1 - (343/1000) = 657/1000.
The answer is B<|endoftext|>
| 64,236
|
<|im_start|>user
Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 4 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
Answer Choices: (A) 2 (B) 2.5 (C) 3 (D) 3.25 (E) 3.5<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 4 km/hour
x/3 = 4
x = 12 km
The average speed while climbing = distance/time = 12/4 = 3 km/h
The answer is C<|endoftext|>
| 78,022
|
<|im_start|>user
If the price of a computer were reduced by 14 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
Answer Choices: (A) $844.10 (B) $894.40 (C) $1,053.50 (D) $1,135.20 (E) $1,259.90<|im_end|>
<|im_start|>assistant
<think>
</think>
Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-14/100)------->X(43/50)=A(say)
means X=A*(50/43).....
so initial price to be integer(As per stem) final price must be multiple of 43
if we check options all were divisible by 43 except option (A)..which is Ans.
The answer is A<|endoftext|>
| 21,858
|
<|im_start|>user
A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone can do the whole work in
Answer Choices: (A) 15days (B) 10days (C) 9days (D) 8days (E) 7days<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 time
If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 days
Option A
The answer is A<|endoftext|>
| 18,563
|
<|im_start|>user
The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 3: 14. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is
Answer Choices: (A) 12 kg (B) 6.625 kg (C) 6.25 kg (D) 6.35 kg (E) 6.55 kg<|im_end|>
<|im_start|>assistant
<think>
</think>
sodium chloride in 100 kg = 3/17 x 100 = 17.64 kg
ammonium in 100 kg = 14/17 x 100 = 82.35 kg
Now 82.35 is 25 parts out of (25 + 9) = 34 parts.
Hence 9 parts = 9/25 x 82.35 =29.64
Amount to be added = 29.64 - 17.64= 12 Kg
The answer is A<|endoftext|>
| 31,441
|
<|im_start|>user
A number when divided by 296 leaves 75 as remainder when the same number is divided by 37 then the remainder will be?
Answer Choices: (A) 2 (B) 9 (C) 6 (D) 5 (E) 1<|im_end|>
<|im_start|>assistant
<think>
</think>
let x=296q+75=(37*8q+37*2)+1
37*(8q+2)+1
thus when the number is divided by 37 the remainder is 1
The answer is E<|endoftext|>
| 25,458
|
<|im_start|>user
John is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 10%. What is the approximate interest he pays annually?
Answer Choices: (A) 4000 (B) 9500 (C) 2500 (D) 2000 (E) 4500<|im_end|>
<|im_start|>assistant
<think>
</think>
An easy way too attempt this is by approximation:
For the first quarter, he pays 10% of 10,000 which is $1000.
So for the four quarters in the year, he will approximately play 1000*4=4000 over the entire year.
Because of compound interest it will be more than 4000. Approx. option E is correct.
The answer is E<|endoftext|>
| 78,024
|
<|im_start|>user
What can human facial expressions communicate?
Answer choice: (A) emotions (B) behaviors (C) ideas (D) theories<|im_end|>
<|im_start|>assistant
<think>
</think>
Human facial expressions can communicate a range of emotions.
The answer is A<|endoftext|>
| 6,699
|
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
When writing, make sure to avoid vague pronoun references. A vague pronoun reference occurs when a pronoun could refer to more than one possible antecedent.
When Lisa and Kim finally landed, she breathed a sigh of relief.
The pronoun she could refer to either Lisa or Kim, so the meaning of the sentence is unclear.
Vague pronoun references can be corrected in one of two ways:
1. Replace the pronoun with its correct antecedent:
When Lisa and Kim finally landed, Lisa breathed a sigh of relief.
2. Rewrite the sentence:
Lisa breathed a sigh of relief when she and Kim finally landed.
A vague pronoun reference also occurs when they, them, their, theirs, it, or its is used without its antecedent.
They say that this nail polish dries in less than five minutes.
The pronoun they is used without its antecedent, so the meaning of the sentence is unclear.
This problem can be fixed by replacing the pronoun with its missing antecedent.
The advertisements say that this nail polish dries in less than five minutes.
Question:
Which of the following contains a vague pronoun reference?
Answer Choices: (A) Peter's brother John wondered whether he ran fast enough to qualify for the Boston Marathon. (B) Peter's brother John wondered whether Peter ran fast enough to qualify for the Boston Marathon.<|im_end|>
<|im_start|>assistant
<think>
</think>
The first answer choice contains a vague pronoun reference. The pronoun he could refer to Peter or John.
The second answer choice shows a possible correction for the vague pronoun reference. He has been replaced with Peter.
Peter's brother John wondered whether Peter ran fast enough to qualify for the Boston Marathon.
The answer is A<|endoftext|>
| 3,604
|
<|im_start|>user
A number is trebled and 10 is subtracted. If the resultant is divided by 5, it becomes 35. What is that number?
Answer Choices: (A) 73.5 (B) 185/3 (C) 155/3 (D) None of these (E) Cannot be determined<|im_end|>
<|im_start|>assistant
<think>
</think>
Solution
Let the number be x.
Then, (3x - 10)/5 ‹=› 35
‹=› 3x - 10 = 175
‹=› 3x= 185
x= 185/3.
The answer is B<|endoftext|>
| 19,983
|
<|im_start|>user
The tensor fascia latae acts as what, in relation to the gluteus medius and iliopsoas, for the purpose of flexing and abducting the thigh?
Answer choice: (A) spicule (B) synergist (C) antagonist (D) symbiotic<|im_end|>
<|im_start|>assistant
<think>
</think>
The tensor fascia latae is a thick, squarish muscle in the superior aspect of the lateral thigh. It acts as a synergist of the gluteus medius and iliopsoas in flexing and abducting the thigh. It also helps stabilize the lateral aspect of the knee by pulling on the iliotibial tract (band), making it taut. Deep to the gluteus maximus, the piriformis, obturator internus, obturator externus, superior gemellus, inferior gemellus, and quadratus femoris laterally rotate the femur at the hip. The adductor longus, adductor brevis, and adductor magnus can both medially and laterally rotate the thigh depending on the placement of the foot. The adductor longus flexes the thigh, whereas the adductor magnus extends it. The pectineus adducts and flexes the femur at the hip as well. The pectineus is located in the femoral triangle, which is formed at the junction between the hip and the leg and also includes the femoral nerve, the femoral artery, the femoral vein, and the deep inguinal lymph nodes.
The answer is B<|endoftext|>
| 8,973
|
<|im_start|>user
A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Answer Choices: (A) 5 (B) 6 (C) 7 (D) 54 (E) 3<|im_end|>
<|im_start|>assistant
<think>
</think>
US = 25
DS = 35
M = (35 - 25)/2 = 5.
The answer is A<|endoftext|>
| 28,754
|
<|im_start|>user
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?
Answer Choices: (A) 24 (B) 36 (C) 72 (D) 84 (E) 96<|im_end|>
<|im_start|>assistant
<think>
</think>
The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:
BGB
GBG
and
GBG
BGB
From here, we can use a simple permutation to get to the answer:
Moving from left-to-right....
For the firstspot, there are 3 different boys to choose from
For the secondspot, there are 3 different girls to choose from
For the thirdspot, there then 2 different boys to choose from
For the fourthspot, there are then 2 different girls to choose form
For the fifth and sixthspots, we have the 1 boy and 1 girl that are left
(3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.
(36)(2) = 72
C
The answer is C<|endoftext|>
| 8,293
|
<|im_start|>user
A train covers a distance of 20 km in 10 minutes. If its speed is decreased by 10 km/hr, the time taken by it to cover the same distance will be?
Answer Choices: (A) 20min 15sec (B) 11min 30sec (C) 15min 20sec (D) 12min 10sec (E) 9min 30sec<|im_end|>
<|im_start|>assistant
<think>
</think>
Speed = 20*60/10 = 120 km/hr
new speed = 120-10 = 110 km/hr
time taken = 20/110 = 60*2/11 = 11 min 30 sec
The answer is B<|endoftext|>
| 47,501
|
<|im_start|>user
A train travels from Albany to Syracuse, a distance of 100 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours . What was the average rate of speed of the train on the return trip to Albany?
Answer Choices: (A) 40 (B) 50 (C) 60 (D) 33.33 (E) 45<|im_end|>
<|im_start|>assistant
<think>
</think>
50*T =100 THEREFORE T = 100/50 =2
ON RETURN SPEED * ( 5 -2) =100 THEREFORE T = 100/3 =33.33
D
The answer is D<|endoftext|>
| 71,178
|
<|im_start|>user
During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
Answer Choices: (A) 80% (B) 100% (C) 116.7% (D) 120% (E) 180%<|im_end|>
<|im_start|>assistant
<think>
</think>
Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%.
Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%.
6 is 6/3.33*100 = 180% of 3.33.
The answer is E<|endoftext|>
| 50,257
|
<|im_start|>user
One drier dries certain quantity of material in 24 minutes. Another drier does the same work in 2 minutes how much time will it take to do the same job when both driers are put to work ?
Answer Choices: (A) 1.00 minutes (B) 1.20 minutes (C) 1.50 minutes (D) 1.85 minutes (E) 2.00 minutes<|im_end|>
<|im_start|>assistant
<think>
</think>
By guess it is clear that the time taken will be less than 2 minutes and more than 1.5 mintes Therefore,
The answer is D<|endoftext|>
| 39,685
|
<|im_start|>user
A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
Answer Choices: (A) 10 % (B) 9/2 % (C) 8/4 % (D) 6/12 % (E) 45 5/11 %<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 110 - (60)
= 50.
Required percentage =(50/110*100)%=45 5/11 %
The answer is E<|endoftext|>
| 28,629
|
<|im_start|>user
Find (7x + 6y ) / (x-2y) if x/2y = 3/2 ?
Answer Choices: (A) 24 (B) 25 (C) 26 (D) 27 (E) 29<|im_end|>
<|im_start|>assistant
<think>
</think>
x/2y=3/2
=>x=6y/2=3y
=>(7x+6y)/(x-2y)=((7*(3y))+6y)/(3y-2y)
=>27y/y=27
The answer is D<|endoftext|>
| 76,819
|
<|im_start|>user
There are four members in a family. Their average income is Rs.10000 per month. Three members get Rs.8000, Rs.15000, Rs.6000 respectively. Therefore what is the income of the fourth member of the family?
Answer Choices: (A) Rs. 10000 (B) Rs. 11000 (C) Rs. 12000 (D) Rs. 9000 (E) Rs. 8500<|im_end|>
<|im_start|>assistant
<think>
</think>
EXPLANATION
Total income of 3 members = Rs. (8000 + 15000 + 6000) = Rs. 29000.
Required income = Rs. [ (10000 x 4) – 29000 ]
= Rs. (40000 – 29000)
= Rs. 11000.
The answer is B<|endoftext|>
| 45,041
|
<|im_start|>user
A square, with perimeter 80, is inscribed in a circle. What is the area of the circle?
Answer Choices: (A) 400π (B) 200π (C) 250π (D) 300π (E) 150π<|im_end|>
<|im_start|>assistant
<think>
</think>
Area of circuscribed circle = pi/2*area of square
Area of square = (80/4)^2 = 20^2= 400
Area of circle = pi/2*400=200pi
The answer is B<|endoftext|>
| 41,876
|
<|im_start|>user
A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 4 miles per hour and returns along the same road at an average speed of 5 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
Answer Choices: (A) (a) 24/5 (B) (b) 5 (C) (c) 40/9 (D) (d) 27/5 (E) (e) 28/5<|im_end|>
<|im_start|>assistant
<think>
</think>
from the uphill we can find out the distance = 4*2 = 8
average speed = total distance/total time
= 16/ (2+ (8/5)) = 40/9
The answer is C<|endoftext|>
| 17,185
|
<|im_start|>user
The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
Answer Choices: (A) 22 (B) 18 (C) 12 (D) 66 (E) 99<|im_end|>
<|im_start|>assistant
<think>
</think>
x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
The answer is C<|endoftext|>
| 40,003
|
<|im_start|>user
If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then A and C will be in the ratio
Answer Choices: (A) 3:13 (B) 9:13 (C) 36:13 (D) 13:9 (E) none<|im_end|>
<|im_start|>assistant
<think>
</think>
Solution: (A/B)*(B/C) = (3/4)*(12/13);
Or, A/B = 36/39 = 9:13.
The answer is B<|endoftext|>
| 23,611
|
<|im_start|>user
A bag contains 2 red, 3 green and 2 yellow balls. Two balls are drawn at random. What is the probability that none of the balls drawn is yellow?
Answer Choices: (A) 10/15 (B) 10 (C) 11 (D) 10/21 (E) 10/23<|im_end|>
<|im_start|>assistant
<think>
</think>
Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S) = Number of ways of drawing 2 balls out of 7
= 7C2 `
= (7 x 6)/(2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is yellow.
n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls.
= 5C2
= (5 x 4)/(2 x 1)
= 10.
P(E) = n(E)/n(S) = 10/21
Hence
The answer is D<|endoftext|>
| 32,131
|
<|im_start|>user
Look at this series: 1000, 200, 40, ... What number should come next?
Answer Choices: (A) 8 (B) 10 (C) 15 (D) 20 (E) 25<|im_end|>
<|im_start|>assistant
<think>
</think>
1000/5=200
200/5=40
40/5=8
The answer is A<|endoftext|>
| 21,102
|
<|im_start|>user
A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Answer Choices: (A) $28 (B) $82 (C) $110 (D) $138 (E) $194<|im_end|>
<|im_start|>assistant
<think>
</think>
by the question, the equation would be 150 p - 84*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 194.
The answer is E<|endoftext|>
| 44,072
|
<|im_start|>user
In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 8 women?
Answer Choices: (A) 7C4 8C5 (B) 4C7 5C8 (C) 7C5 8C4 (D) 9C4 7C5 (E) NONE<|im_end|>
<|im_start|>assistant
<think>
</think>
Group consisting of 7 men and 8 women
4 men can be selected from 7 men in 7C4 ways
5 women can be selected from 8 women in 8C5 ways
Therefore, Total number of ways= 7C4 8C5
The answer is A<|endoftext|>
| 90,141
|
<|im_start|>user
The ratio of two numbers is 3 : 4 and their H.C.F. is 3. Their L.C.M. is
Answer Choices: (A) 48 (B) 22 (C) 56 (D) 27 (E) 36<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 3.
So, the numbers 9 and 12.
L.C.M. of 9 and 12 = 36.
The answer is E<|endoftext|>
| 47,359
|
<|im_start|>user
The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Answer Choices: (A) 85 kg (B) 87 kg (C) 90 kg (D) 91 kg (E) 93 kg<|im_end|>
<|im_start|>assistant
<think>
</think>
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
The answer is A<|endoftext|>
| 16,799
|
<|im_start|>user
From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
Answer Choices: (A) 650 (B) 656 (C) 756 (D) 760 (E) 780<|im_end|>
<|im_start|>assistant
<think>
</think>
From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
Hence we have the following 3 options.
We can select 5 men ...(option 1)
Number of ways to do this = 7C5
We can select 4 men and 1 woman ...(option 2)
Number of ways to do this = 7C4 × 6C1
We can select 3 men and 2 women ...(option 3)
Number of ways to do this = 7C3 × 6C2
Total number of ways
= 7C5 + (7C4 × 6C1) + (7C3 × 6C2)
= 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ]
=
7
×
6
2
×
1
+
7
×
6
×
5
3
×
2
×
1
×
6
=7×62×1+7×6×53×2×1×6
+
7
×
6
×
5
3
×
2
×
1
×
6
×
5
2
×
1
+7×6×53×2×1×6×52×1
=
21
+
210
+
525
=756
C)
The answer is C<|endoftext|>
| 69,560
|
<|im_start|>user
The number of waves that pass a fixed point in a given amount of time is called what?
Answer choice: (A) wavelength of a wave (B) spectroscopy of a wave (C) frequency of a wave (D) spread of a wave<|im_end|>
<|im_start|>assistant
<think>
</think>
A photon isn’t a fixed amount of energy. Instead, the amount of energy in a photon depends on the frequency of the electromagnetic wave. The frequency of a wave is the number of waves that pass a fixed point in a given amount of time, such as the number of waves per second. In waves with higher frequencies, photons have more energy.
The answer is C<|endoftext|>
| 8,888
|
<|im_start|>user
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
Answer Choices: (A) Rs.420.20 (B) Rs.319.06 (C) Rs.306.04 (D) Rs.294.75 (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
The answer is C<|endoftext|>
| 31,520
|
<|im_start|>user
The average of first five prime numbers greater than 20 is?
Answer Choices: (A) 32.2 (B) 32.98 (C) 32.3 (D) 32.8 (E) 32.4<|im_end|>
<|im_start|>assistant
<think>
</think>
23 + 29 + 31 + 37 + 41
= 161/5
= 32.2
The answer is A<|endoftext|>
| 82,093
|
<|im_start|>user
which of the following options is the correct value of b, given the equation b^(-2) +b^3 = 64.1?
Answer Choices: (A) 2 (B) 1 (C) 3 (D) 7 (E) 4<|im_end|>
<|im_start|>assistant
<think>
</think>
Plugging in the various option into the equation to find out which is correct:
b^(-2)+b^3 = 64.1
4^(-2)+4^3
The answer is E<|endoftext|>
| 31,721
|
<|im_start|>user
Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 17000, then find his savings?
Answer Choices: (A) 3600 (B) 3400 (C) 3608 (D) 3602 (E) 3603<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 17000 => x = 3400
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3400.
The answer is B<|endoftext|>
| 91,705
|
<|im_start|>user
A cylindrical can has a radius of 3 centimeters and a height of 12 centimeters. What is the area, in square centimeters, of a rectangular label that completely covers the curved surface of the can without over-lapping?
Answer Choices: (A) 16 pi (B) 72 pi (C) 96 pi (D) 192 pi (E) 576 pi<|im_end|>
<|im_start|>assistant
<think>
</think>
They are asking the lateral surface area of the cylinder.
the Lateral surface area = 2* pi * r *h
= 2*pi*3*12=72 pi
The answer is B<|endoftext|>
| 72,901
|
<|im_start|>user
If two times of the daughter’s age in years is included to the mother’s age, the total is 70 and if two times of the mother’s age is included to the daughter’s age, the total is 95. So the Mother’s age is,
Answer Choices: (A) 30 (B) 40 (C) 50 (D) 60 (E) 39<|im_end|>
<|im_start|>assistant
<think>
</think>
B
40
Let daughter’s age = A and mother’s age = B
Given:
2A+B = 70 and,
A+2B = 95
Solving B, we will get B = 40.
The answer is B<|endoftext|>
| 80,785
|
<|im_start|>user
There are three vessels of equal capacity .Vessel A contains Milk and water in the ratio 7:3 ;Vessel B contains Milk and water in the ratio 2:1 and Vessel C contains Milk and water in the ratio 3:2 .If the mixture in all the three vessels is mixed up.What will be the ratio of milk and water ?
Answer Choices: (A) 59:31 (B) 3:2 (C) 118:126 (D) 193:122 (E) 201:132<|im_end|>
<|im_start|>assistant
<think>
</think>
7:3=>7x+3x=10x
2:1=>2y+1y=3y
3:2=>3z+2z=5z
10x=3y=5z
Take LCM of 10,3,5=30
Or simply;
x=3
y=10
z=6
So,
Ratio of Milk:Water= (7x+2y+3z)/(3x+y+2z)=59/31
The answer is A<|endoftext|>
| 65,013
|
<|im_start|>user
n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
Answer Choices: (A) 2 (B) 4 (C) 7 (D) 9 (E) 11<|im_end|>
<|im_start|>assistant
<think>
</think>
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
Option A
The answer is A<|endoftext|>
| 11,192
|
<|im_start|>user
What is the probability of getting a sum 9 from two throws of a dice?
Answer Choices: (A) 1/6 (B) 1/8 (C) 1/9 (D) 1/12 (E) 1/7<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)= 4/36 = 1/9 .
The answer is C<|endoftext|>
| 80,993
|
<|im_start|>user
R and B are integers. The expression (R+1)(B+1) is even. What can be said about R and B?
Answer Choices: (A) They are both even numbers. (B) At least one of them is even. (C) At least one of them is odd. (D) They are both odd. (E) Nothing can be said surly on R and B<|im_end|>
<|im_start|>assistant
<think>
</think>
Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (R+1) or (B+1) needs to be Even
So either R or B needs to be odd
Or Atleast one of them is odd.
Atleast one of them is odd=C
The answer is C<|endoftext|>
| 68,908
|
<|im_start|>user
If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r + s?
Answer Choices: (A) 8 (B) 2 (C) − 2 (D) − 3 (E) − 5<|im_end|>
<|im_start|>assistant
<think>
</think>
We know that given ax^2 + bx + c = 0, Sum of the roots = -b/a and product of the roots = c/a.
The roots here are -r and -s.
-r - s = -(-2)/1 = r + s = -2
(-r)*(-s) = -15/1 = rs
So one of r and s is -5 and the other is 3. So r + s could be -2.
The answer is C<|endoftext|>
| 7,259
|
<|im_start|>user
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
Answer Choices: (A) 33 (B) 77 (C) 12 (D) 88 (E) 91<|im_end|>
<|im_start|>assistant
<think>
</think>
S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205. S.I. for 5 years = Rs. (2205/3) x 5 = Rs. 3675 Principal = Rs. (9800 - 3675) = Rs. 6125. Hence, rate = (100 x 3675)/( 6125 x 5) % = 12%
The answer is C<|endoftext|>
| 19,608
|
<|im_start|>user
If the sides of a triangle are 36 cm, 34 cm and 20 cm, what is its area?
Answer Choices: (A) 320 cm2 (B) 360 cm2 (C) 340 cm2 (D) 310 cm2 (E) 300 cm2<|im_end|>
<|im_start|>assistant
<think>
</think>
The triangle with sides 36 cm, 34 cm and 20 cm is right angled, where the hypotenuse is 36 cm.
Area of the triangle
= 1/2 * 34 * 20
= 340 cm2
The answer is C<|endoftext|>
| 85,078
|
<|im_start|>user
A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 12 years now, the son's age five years back was:
Answer Choices: (A) 3 years (B) 7 years (C) 1 years (D) 6 years (E) 5 years<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the son's present age be x years.
Then, (12 - x) = x
2x = 12 => x = 6
Son's age 5 years back = (6 - 5) = 1 years.
The answer is C<|endoftext|>
| 62,633
|
<|im_start|>user
Of the 700 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 60 percent ?
Answer Choices: (A) 200 (B) 160 (C) 112 (D) 80 (E) 25<|im_end|>
<|im_start|>assistant
<think>
</think>
Original (Long-Term is 70%)
Total = 700
Long-Term = .7(700) = 490
New (Long-Term is 60%)
New Total = 800 - y
New Long-Term =490 - y
490 - y = .6 (800 - y)
y = 25
The answer is E<|endoftext|>
| 12,413
|
<|im_start|>user
A and B together finish a wor in 20 days.They worked together for 15 days and then B left. Afer another 10 days,A finished the remaining work. In how many days A alone can finish the job?
Answer Choices: (A) 30 (B) 40 (C) 50 (D) 60 (E) 70<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
(A+B)'s 15 days work = (1/20 × 15) = ¾
Remaining work = (1 - ¾) = ¼
Now, ¼ work is done by A in 10 days.
Whole work will bedone by A in (10 × 4 = 40) days.
The answer is B<|endoftext|>
| 90,953
|
<|im_start|>user
What least value must be assigned to * so that the number 197*5462 is divisible by 9
Answer Choices: (A) 0 (B) 2 (C) 4 (D) 9 (E) 8<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the missing digit be x.
Sum of digits = (1 + 9 + 7 + x + 5 + 4 + 6 +»2) = (34 + x).
For (34 + x) to be divisible by 9, x must be replaced by 2 .
Hence, the digit in place of * must be 2.
The answer is B<|endoftext|>
| 8,799
|
<|im_start|>user
Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 18 miles, how many miles was Mike's ride?
Answer Choices: (A) 30 (B) 34 (C) 38 (D) 42 (E) 48<|im_end|>
<|im_start|>assistant
<think>
</think>
The cost of Annie's ride was 2.5+5+(0.25*18) = $12
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 12
0.25*x = 9.5
x = 38 miles
The answer is C<|endoftext|>
| 83,610
|
<|im_start|>user
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
Answer Choices: (A) 0.5907 (B) 0.5904 (C) 0.5902 (D) 0.5901 (E) 0.59023<|im_end|>
<|im_start|>assistant
<think>
</think>
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904.
The answer is B<|endoftext|>
| 71,447
|
<|im_start|>user
What the name of the disease where some of the alveoli of the lungs fill with fluid so they can no longer exchange gas?
Answer choice: (A) leukemia (B) pneumonia (C) lung cancer (D) emphysema<|im_end|>
<|im_start|>assistant
<think>
</think>
Pneumonia is a disease in which some of the alveoli of the lungs fill with fluid so they can no longer exchange gas. Symptoms of pneumonia typically include coughing, chest pain, difficulty breathing, and fatigue. Pneumonia may be caused by an infection or an injury to the lungs.
The answer is B<|endoftext|>
| 135
|
<|im_start|>user
Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
Answer Choices: (A) 34778 (B) 26888 (C) 2899 (D) 17600 (E) 12778<|im_end|>
<|im_start|>assistant
<think>
</think>
Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100
= Rs. 17600
The answer is D<|endoftext|>
| 10,594
|
<|im_start|>user
If the numbers 1 to 98 are written on 98 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite?
Answer Choices: (A) 1/50 (B) 1/25 (C) 1/98 (D) 1 (E) 2<|im_end|>
<|im_start|>assistant
<think>
</think>
There are 25 primes, 72 composite numbers from 1 to 98. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/98.
The answer is C<|endoftext|>
| 85,791
|
<|im_start|>user
Two partners in a business (Carol and Ben) invested $500 and $850 in a business respectively. At the end of the year they made a profit of $250. Find share of each partner?
Answer Choices: (A) $92.59,$157.41 (B) $96.59,$157.41 (C) $92.59,$159.41 (D) $92.59,$127.41 (E) $12.59,$157.41<|im_end|>
<|im_start|>assistant
<think>
</think>
A:B = 500:850
A:B = 10 : 17
A's share = 250*10/27 = $92.59
B's share = 250*17/27 = $157.41
The answer is A<|endoftext|>
| 20,922
|
<|im_start|>user
The average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. Find the average age of the women?
Answer Choices: (A) 78 (B) 26 (C) 52 (D) 54 (E) 56<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
36 + 32 + 9 * 4 = 104/2 = 52
The answer is C<|endoftext|>
| 91,011
|
<|im_start|>user
Indu gave Bindu Rs.1875 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Answer Choices: (A) s.10 (B) s.2 (C) s.5 (D) s.3 (E) s.4<|im_end|>
<|im_start|>assistant
<think>
</think>
1875 = D(100/4)2
D = 3
The answer is D<|endoftext|>
| 38,038
|
<|im_start|>user
The C.P of 15 books is equal to the S.P of 19 books. Find his gain% or loss%?
Answer Choices: (A) 16 2/3% (B) 16 2/8% (C) 16 2/5% (D) 21 1/19% (E) 16 1/3%<|im_end|>
<|im_start|>assistant
<think>
</think>
15 CP = 19 SP
19 --- 4 CP loss
100 --- ? => 21 1/19% loss.
The answer is D<|endoftext|>
| 80,288
|
<|im_start|>user
Two numbers are in the ratio 3 : 4. If their L.C.M. is 48. what is sum of the numbers?
Answer Choices: (A) 28 (B) 56 (C) 76 (D) 84 (E) 85<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 48
=> 12x = 48
=> x = 48/12 = 4
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 4 = 28
The answer is A<|endoftext|>
| 10,111
|
<|im_start|>user
60 + 5 * 12 / (180/3) = ?
Answer Choices: (A) 60 (B) 120 (C) 13 (D) 61 (E) 50<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
The answer is D<|endoftext|>
| 39,396
|
<|im_start|>user
A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 25% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?
Answer Choices: (A) $5.60 (B) $7.20 (C) $8.80 (D) $9.60 (E) $15.20<|im_end|>
<|im_start|>assistant
<think>
</think>
The lowest price would have to be calculated by finding the price of the $16 product after the initial 40% reduction, then the final price after 25% was taken off of the already-discounted price. So:
A 40% discount on a $16 product would = 60% of the original $16 price: $16 x .60 = $9.6
Next you have to find the price after an additional 25% had been discounted from the $9.6, which would be 75% of the $9.6: $9.6 x .75 = $7.20
The answer is B<|endoftext|>
| 44,730
|
<|im_start|>user
A sum fetched a total simple interest of $4106.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Answer Choices: (A) $8829 (B) $2840 (C) $6578 (D) $7782 (E) $8927<|im_end|>
<|im_start|>assistant
<think>
</think>
E
8927
Principal
= $100 x 4106.25/9 x 5
= $410625/45
= $8927.
The answer is E<|endoftext|>
| 55,919
|
<|im_start|>user
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity W of the pool?
Answer Choices: (A) 9000 cubic meters (B) 10500 cubic meters (C) 11750 cubic meters (D) 12000 cubic meters (E) 12500 cubic meters<|im_end|>
<|im_start|>assistant
<think>
</think>
D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
The answer is D<|endoftext|>
| 19,114
|
<|im_start|>user
The average age 15 girls of a class is 15 years. Out of these, the average age of 12 girls is 13 years and that of the other 3 girls is 14 years. The age of the 15th girl is?
Answer Choices: (A) 35 (B) 30 (C) 31 (D) 28 (E) 27<|im_end|>
<|im_start|>assistant
<think>
</think>
Age of the 15th girl = 15*15 - (12*13+3*14) = 225-198 = 27 years
The answer is E<|endoftext|>
| 26,416
|
<|im_start|>user
What molecules are usually insoluble in water?
Answer choice: (A) polar (B) acids (C) non-polar (D) ions<|im_end|>
<|im_start|>assistant
<think>
</think>
Non-polar molecules are usually insoluble in water.
The answer is C<|endoftext|>
| 1,256
|
<|im_start|>user
If Sharon's weekly salary increased by 20 percent, she would earn $600 per week. If instead, her weekly salary were to increase by 15 percent, how much would she earn per week?
Answer Choices: (A) Rs.575 (B) Rs.600 (C) Rs.625 (D) Rs.485 (E) Rs.590<|im_end|>
<|im_start|>assistant
<think>
</think>
Soln:-
(600/120)115=575
In this case long division does not take much time.
(5/1)115=Rs.575
The answer is A<|endoftext|>
| 59,584
|
<|im_start|>user
Mr. Mukhambo has two numbers and say that their difference, their sum and their product are to one another as 1:7:24. Mukhambo wants to find out whether you can get him the product of those two numbers:
Answer Choices: (A) 24 (B) 6 (C) 48 (D) 12 (E) 18<|im_end|>
<|im_start|>assistant
<think>
</think>
let the numbers are x and y so according to the given condition
x+y = 7k
x-y = k
and x*y = 24k
on solving 1st and 2nd equations we get x = 4k and y = 3k
so 4k*3k = 24k
or k = 2
so product of the numbers = 12(k^2) = 48
The answer is C<|endoftext|>
| 40,301
|
<|im_start|>user
Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest R?
Answer Choices: (A) 60 (B) 61 (C) 62 (D) 63 (E) 64<|im_end|>
<|im_start|>assistant
<think>
</think>
60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=R
The answer is A<|endoftext|>
| 7,678
|
<|im_start|>user
A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 24 minutes and a model N computer can complete the same task in 12 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?
Answer Choices: (A) 3 (B) 4 (C) 5 (D) 8 (E) 6<|im_end|>
<|im_start|>assistant
<think>
</think>
Let's say 1 work is processing 24 gb of data.
Model M : 1 gb per min
Model N : 2 gb per min
Working together, 1 M and 1 N = 3 gb per min
So, 8 times as many computers would work at 18 gb per min.
So no. of M = 8
The answer is D<|endoftext|>
| 44,247
|
<|im_start|>user
If 0.2 of a number is equal to 0.08 of another number, the ratio of the numbers i
Answer Choices: (A) 2 : 3 (B) 2 : 5 (C) 3 : 20 (D) 20 : 3 (E) None<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
0.2A = 0.08 B ⇔ A / B = 0.08 / 0.20 = 8/20 = 2/5
∴ A : B = 2 : 5.
The answer is B<|endoftext|>
| 74,326
|
<|im_start|>user
What type of tissue covers the outside of a plant?
Answer choice: (A) porous (B) dermal (C) anterior (D) epidermal<|im_end|>
<|im_start|>assistant
<think>
</think>
Dermal tissue covers the outside of a plant in a single layer of cells called the epidermis. It mediates most of the interactions between a plant and its environment.
The answer is B<|endoftext|>
| 4,222
|
<|im_start|>user
An investor bought N shares of company X at $15 per share and N shares of company Y at $20 per share. If a month later the investor sold all the shares at $20 per share and made a profit of $200, then what is the value N?
Answer Choices: (A) 35 (B) 40 (C) 50 (D) 60 (E) 75<|im_end|>
<|im_start|>assistant
<think>
</think>
The investor made a profit of (2∗N∗20)−(15N+20N)=200. This equation simplifies to 5N=200 from where N=40.
The answer is B<|endoftext|>
| 88,985
|
<|im_start|>user
3 machines a,b,c can be used to produce a product. Machine a will take 60 hours to produce a million units. Machine b is twice as fast as machine a. Machine c takes the same amount of time as machine a and b taken together. How much time will be required to produce a million units if all the three machines are used simultaneously?
Answer Choices: (A) 12 hours (B) 10 hours (C) 8 hours (D) 9 hours (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
1 hour capacity of
Machine a =1/60 million
Machine b =2*(1/60)=1/30 million
Machine c =(1/60)+(1/30)=1/20 million
So in 1 hour Machines a,b & c will produce (1/60)+(1/30)+(1/20)=1/10 million
Time taken to produce 1 million units=1/(1/10)=10 hours
The answer is B<|endoftext|>
| 83,754
|
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