text stringlengths 148 4.25k | __index_level_0__ int64 0 97.5k |
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<|im_start|>user
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Answer Choices: (A) 40 sec (B) 42 sec (C) 45 sec (D) 48 sec (E) 50 sec<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Formula for converting from km/hr to m/s: X km/hr =(X x 5/8)m/s.
Th... | 6,907 |
<|im_start|>user
If we have 12 people in a meeting, in how many ways they can sit around a table?
Answer Choices: (A) 11*10! (B) 9*8! (C) 8*7! (D) 7*6! (E) 6*5!<|im_end|>
<|im_start|>assistant
<think>
</think>
If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=12
(n-1)!=11!=11*1... | 30,101 |
<|im_start|>user
Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 12% vinegar, dressing P comprises what percentage of the new dressing?
Answer Choices: (A) 50% (B) 40% (C) 30% (D) 20% (E)... | 58,808 |
<|im_start|>user
If in a certain sequence of consecutive multiples of 100, the median is 650, and the greatest term is 1000, how many terms that are smaller than 650 are there in the sequence?
Answer Choices: (A) 6 (B) 4 (C) 8 (D) 12 (E) 13<|im_end|>
<|im_start|>assistant
<think>
</think>
Since the median is 650 we k... | 68,074 |
<|im_start|>user
A boat having a length 4 m and breadth 3 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Answer Choices: (A) 12 kg (B) 120 kg (C) 72 kg (D) 96 kg (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Volume of water displaced = (... | 64,509 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
The atmosphere is the layer of air that surrounds Earth. Both weather and climate tell you about the atmosphere.
Weather is what the atmosphere is like at a certain place and time. Weather can change quickly. For example, th... | 4,030 |
<|im_start|>user
Which of the following is closest in value to (9^8)-(9^2)?
Answer Choices: (A) 9^9 (B) 9^8 (C) 9^7 (D) 9^6 (E) 9^5<|im_end|>
<|im_start|>assistant
<think>
</think>
9^8 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^8)-(9^2) = ~9^8... | 74,644 |
<|im_start|>user
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time... | 5,326 |
<|im_start|>user
Carol spends 1/4 of her savings on a stereo and 1/6 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
Answer Choices: (A) 1/4 (B) 2/7 (C) 5/12 (D) 1/2 (E) 11/24<|im_end|>
<|im_start|>assistant
<think>
</think>
Total Savings = ... | 19,610 |
<|im_start|>user
In a convention where they distributes prizes. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any number of prizes?
Answer Choices: (A) 58 (B) 60 (C) 64 (D) 68 (E) 90<|im_end|>
<|im_start|>assistant
<think>
</think>
In this case, repetitions are allowed, so all the three pr... | 81,282 |
<|im_start|>user
The average weight of a group of boys is 20 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Answer Choices: (A) 12 (B) 14 (C) 18 (D) 24 (E) 10<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the n... | 7,808 |
<|im_start|>user
n a contest, a bowl contains 10 keys, one of which will open a treasure chest and nine of which will not. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first con... | 17,501 |
<|im_start|>user
here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 80 and 92 respectively. the average of the whole class is 86, what is the value of x?
Answer Choices: (A) a) 6 (B) b) 7 (C) c) 8 (D) d) 10 (... | 20,362 |
<|im_start|>user
In a consumer survey, 65% of those surveyed liked at least one of three products: 1, 2, and 3. 40% of those asked liked product 1, 35% liked product 2, and 15% liked product 3. If 7% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than ... | 23,030 |
<|im_start|>user
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Answer Choices: (A) 4:5 (B) 3:5 (C) 6:8 (D) 3:5 (E) 5:4<|im_end|>
<|im_start|>assistant
<think>
</think>
third number be x.
first no = 120% of x = 6x/5
second no = 150% of x = 3x/2
ratio in first two n... | 41,465 |
<|im_start|>user
If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 10000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years la... | 49,494 |
<|im_start|>user
Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Answer Choices: (A) 9:36 (B) 9:31 (C) 9:35 (D) 9:37 (E) 9:32<|im_end|>
<|im_start|>assistant
<think>
</think>
1/4 : 3/4 = (1:... | 63,016 |
<|im_start|>user
When positive integer x is divided by positive integer y, the result is 59.32. What is the sum R of all possible 2-digit remainders for x/y?
Answer Choices: (A) 560 (B) 616 (C) 672 (D) 728 (E) 784<|im_end|>
<|im_start|>assistant
<think>
</think>
ans B 616...
remainders = .32=32/100=8/25=16/50 and so ... | 73,632 |
<|im_start|>user
A person bought 118 glass bowls at a rate of Rs. 12 per bowl. He sold 102 of them at Rs. 15 and the remaining broke. What is the percentage gain for A?
Answer Choices: (A) 40 (B) 300/11 (C) 243/7 (D) 475/59 (E) 279/8<|im_end|>
<|im_start|>assistant
<think>
</think>
CP=118*12=1416 and SP=102*15=1530
G... | 17,865 |
<|im_start|>user
Sandy is younger than Molly by 10 years. If their ages are in the respective ratio of 7:9, how old is Molly?
Answer Choices: (A) 27 (B) 36 (C) 45 (D) 54 (E) 63<|im_end|>
<|im_start|>assistant
<think>
</think>
S = M - 10
S / M = 7/9
9S = 7M
9(M-10) = 7M
M = 45
The answer is C<|endoftext|> | 83,881 |
<|im_start|>user
John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam two years ago?
Answer Choices: (A) 2 (B) 4 (C) 6 (D) 8 (E) 16<|im_end|>
<|im_start|>assistant
<think>
</think>
j= 3s
after 6 years
j +6 = 2(s+6)
j= 2s+6
2s +6 = 3s
s= 6
two years ago
s= 6-2= 4
B is
Th... | 62,986 |
<|im_start|>user
2.08 can be expressed in terms of percentage as
Answer Choices: (A) 2.08% (B) 20.8% (C) 208% (D) 0.208% (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
While calculation in terms of percentage we need to multiply by 100, so
2.08 * 100 = 208
The answer is C<|endoftext|> | 79,918 |
<|im_start|>user
A line of 24 children walk single file down the 54-meter hallway of their school at a speed of 20 meter/min. If each child takes up 1/4 meter of space in line, how long does it take for all of them to traverse the full length of the hallway?
Answer Choices: (A) 1 min (B) 2 min (C) 3 min (D) 4 min (E) 5... | 20,126 |
<|im_start|>user
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Answer Choices: (A) 15 kmph (B) 40 kmph (C) 18 kmph (D) 19 kmph (E) 10 kmph<|im_end|>
<|im_start|>assistant
<think>
</think>
Speed downstream = 60 + 20
= 80 kmph
Speed upstream... | 7,401 |
<|im_start|>user
The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
Answer Choices: (A) 27 (B) 33 (C) 54 (D) 81 (E) 162<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation... | 71,470 |
<|im_start|>user
The sum of four consecutive even numbers is 52, Find the third number ?
Answer Choices: (A) 14 (B) 10 (C) 12 (D) 16 (E) 20<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the first number be n
Let the second number be n + 2
Let the third number be n + 4
Let the third number be n + 6
n + n + 2 + ... | 49,969 |
<|im_start|>user
Chytridiomycota are considered the most primitive of what kingdom?
Answer choice: (A) animals (B) fungi (C) plants (D) protists<|im_end|>
<|im_start|>assistant
<think>
</think>
24.2 Classifications of Fungi Chytridiomycota (chytrids) are considered the most primitive group of fungi. They are mostly a... | 2,819 |
<|im_start|>user
Cellular respiration and photosynthesis are important parts of which cycle?
Answer choice: (A) vapor cycle (B) greenhouse effect (C) carbon cycle (D) water cycle<|im_end|>
<|im_start|>assistant
<think>
</think>
Cellular respiration and photosynthesis are important parts of the carbon cycle. The carbo... | 10,604 |
<|im_start|>user
In a class of 79 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Answer Choices: (A) 6 (B) 15 (C) 25 (D) 33 (E) 54<|im_end|>
<|im_start|>assistant
<think>
</think>
Formula for... | 9,939 |
<|im_start|>user
A fort of 2000 soldiers has provisions for 50 days. After 10 days some of them left and the food was now enough for the same period of 40 days as before. How many of them left?
Answer Choices: (A) 100 (B) 0 (C) 200 (D) 400 (E) 500<|im_end|>
<|im_start|>assistant
<think>
</think>
2000 ---- 50
2000 ---... | 52,818 |
<|im_start|>user
Two sets A and B consists only of positive integers such that mean of set A is 55 . If set R consist of all the elements of both A and B such that mean of R is 80 then the mean of set B is =>
Answer Choices: (A) [A] 65 (B) [B] 60 (C) [C] 70 (D) [D] 55 (E) [E] cannot be determined<|im_end|>
<|im_start|>... | 83,782 |
<|im_start|>user
Where is gabbro found?
Answer choice: (A) volcanoes (B) forest floor (C) oceanic crust (D) wetlands<|im_end|>
<|im_start|>assistant
<think>
</think>
Gabbro is a dark dense rock that can be found in oceanic crust.
The answer is C<|endoftext|> | 7,853 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
A force is a push or a pull.
A force can make an object start moving or stop an object that is moving. A force can also make an object speed up, slow down, or change direction.
Forces can be different sizes.
Think about tryi... | 5,077 |
<|im_start|>user
A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
Answer Choices: (A) 17 6/7 km/hr (B) 25 km/hr (C) 30 km/hr (D) 35 km/hr (E) 40 km/hr<|im_end|>
<|im_start|>assistant
<think>
</think>
Time taken = 1 hr 40 min 48 sec = 1 hr40 4/5min = 1 51/... | 62,141 |
<|im_start|>user
Find remainder if (67^67 +67) is divided by 68
Answer Choices: (A) 60 (B) 62 (C) 66 (D) 72 (E) 78<|im_end|>
<|im_start|>assistant
<think>
</think>
=> (6767 + 1) is divisible by (67 + 1)
=> (6767 + 1) is divisible by 68
=> (6767+1) ÷ 68 gives a remainder of 0
=> [(6767+1) + 66] ÷ 68 gives a remainder ... | 95,869 |
<|im_start|>user
Mr.Jones gave 40% of the money he had to his wife. he also gave 20% of the remaining amount to his 3 sons. half of the amount now left was spent on miscellaneous items and the remaining amount of Rs.12000 was deposited in the bank. how much money did Mr.jones have initially?
Answer Choices: (A) 100000 ... | 85,028 |
<|im_start|>user
A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Answer Choices: (A) 253m (B) 239m (C) 236m (D) 240m (E) 230m<|im_end|>
<|im_start|>assistant
<think>
</think>
Relat... | 10,621 |
<|im_start|>user
In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Answer Choices: (A) 6 sec (B) 7 sec (C) 8 sec (D) 9 sec (E) 2 sec<|im_end|>
<|im_start|>assistant
<think>
</think>
T = 60/36 * 18/5
= 6 sec
The answer is A<|endoftext|> | 59,498 |
<|im_start|>user
If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
Answer Choices: (A) 4:3 (B) 4:8 (C) 4:1 (D) 4:2 (E) 4:7<|im_end|>
<|im_start|>assistant
<think>
</think>
a1:a2 = 4:3
d1:d2 = 4:3
The answer is A<|endoftext|> | 63,975 |
<|im_start|>user
A can do a piece of work in 5 days and B can do it in 4 days how long will they both work together to complete the work?
Answer Choices: (A) 6/11 (B) 8/11 (C) 7/9 (D) 2/9 (E) 10/11<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
A’s one day work = 1/5
B’s one day work = 1/4
(A+B)’s one ... | 66,050 |
<|im_start|>user
A cube has a volume of 125 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Answer Choices: (A) 24 (B) 48 (C) 64 (D) 80 (E) 1000<|im_end|>
<|im_start|>assistant
<think>
</think>
Volume = 125 = side^3
i.e. Side of Cube = ... | 91,098 |
<|im_start|>user
What is it called when two waves in the same medium pass one another?
Answer choice: (A) accumulation (B) frequency (C) interference (D) synchrony<|im_end|>
<|im_start|>assistant
<think>
</think>
Any two waves in the same medium undergo wave interference as they pass each other. At the location where... | 828 |
<|im_start|>user
The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Bren 10 years from now?
Answer Choices: (A) 17 (B) 25 (C) 27 (D) 35 (E) 50<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the present ages of A... | 49,474 |
<|im_start|>user
In how many different number of ways 5 boys and 3 girls can sit on a bench such that girls always sit together.
Answer Choices: (A) A) 720 (B) B) 730 (C) C) 4230 (D) D) 4320 (E) E) 790<|im_end|>
<|im_start|>assistant
<think>
</think>
4320
Option 'D'
The answer is D<|endoftext|> | 95,496 |
<|im_start|>user
The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 2 years is
Answer Choices: (A) s.9621 (B) s.6921 (C) s.8820 (D) s.6261 (E) s.6361<|im_end|>
<|im_start|>assistant
<think>
</think>
c.i=p(1+r/100)^n
=8000(1+5/100)^2
=Rs8820
The answer is C<|endoftext|> | 88,744 |
<|im_start|>user
10 men can prepare 20 toys in 12 days working 15 hours a day. Then in how many days can 24 men prepare 32 toys working 20 hrs a day?
Answer Choices: (A) 4 days (B) 10 days (C) 20 days (D) 25 days (E) 26 days<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
10*12*15/20 = 24*20*x/32
X=4
Th... | 75,757 |
<|im_start|>user
Analyze the number square carefully and find out what number fits in place of question mark.
2 4 6
3 6 9
4 8 ?
Answer Choices: (A) 2 (B) 8 (C) 4 (D) 14 (E) 20<|im_end|>
<|im_start|>assistant
<think>
</think>
20 fits in place of question mark.
This is because (number in first column) / (number in seco... | 9,646 |
<|im_start|>user
Out of three consecutive odd numbers eleven times the first number is equal to addition of thrice the third number and adding 16 to four times the second . What is the first number?
Answer Choices: (A) 5 (B) 6 (C) 7 (D) 8 (E) 9<|im_end|>
<|im_start|>assistant
<think>
</think>
Description :
=> 11x=4(x... | 77,906 |
<|im_start|>user
If r is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Answer Choices: (A) √n + 1 (B) n + 1 (C) n^2 + 1 (D) r + 2√r + 1 (E) n^2 + 2n + 1<|im_end|>
<|im_start|>assistant
<think>
</think>
If r is the square of a positive integer, which... | 30,694 |
<|im_start|>user
If a positive integer n is divisible by both 3 and 7, then n must also be divisible by which of the following?
I. 21
II. 10
III. 63
Answer Choices: (A) None (B) I only (C) II only (D) I and II (E) II and III<|im_end|>
<|im_start|>assistant
<think>
</think>
A multiple of 3 and 7 is also a multiple of ... | 79,135 |
<|im_start|>user
If 5 machines can produce 20 units in 10 hours, how long would it take 10 to produce 80 units?
Answer Choices: (A) 63 (B) 20 (C) 42 (D) 65 (E) 84<|im_end|>
<|im_start|>assistant
<think>
</think>
5 machines would produce 80 units in 40 hours. Increasing the amount of machines by 2 would mean dividing ... | 89,331 |
<|im_start|>user
Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $250, what were her original savings?
Answer Choices: (A) $500 (B) $600 (C) $700 (D) $800 (E) $1000<|im_end|>
<|im_start|>assistant
<think>
</think>
If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 ... | 90,722 |
<|im_start|>user
Find the simple interest on $10000 at 4% per annum for 12 months?
Answer Choices: (A) $400 (B) $500 (C) $650 (D) $710 (E) $1000<|im_end|>
<|im_start|>assistant
<think>
</think>
P = $10000
R = 4%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*4*1/100 = $400
The answer is A<|endoftext|> | 15,872 |
<|im_start|>user
If 1 is added to the denominator of fraction, the fraction becomes
1/2. If 1 is added to the numerator, the fraction becomes 1. The fraction is
Answer Choices: (A) 4/7 (B) 5/9 (C) 2/3 (D) 10/11 (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Let the required fraction b... | 24,804 |
<|im_start|>user
Breaking a window with a baseball is an example of what kind of change in matter?
Answer choice: (A) unusual (B) chemical (C) physical (D) sudden<|im_end|>
<|im_start|>assistant
<think>
</think>
You hit a baseball out of the park and head for first base. You’re excited. The score is tied, and now you... | 9,359 |
<|im_start|>user
Silk and cotton are examples of what type of fibers?
Answer choice: (A) natural (B) mechanical (C) artificial (D) coral<|im_end|>
<|im_start|>assistant
<think>
</think>
Many of the fibers that compose the materials for our clothes are naturally occurring. Silk and cotton are examples of natural fiber... | 9,553 |
<|im_start|>user
Which type of electromagnetic radiation is used in medical imaging to visualize bones and soft tissues?
Answer choice: (A) Ultraviolet rays. (B) X-rays. (C) Infrared radiation. (D) Radio waves.<|im_end|>
<|im_start|>assistant
<think>
</think>
X-rays are used in radiography for medical imaging.
The an... | 222 |
<|im_start|>user
Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 45%. What fraction of the original paint was replaced?
Answer Choices: (A) 1/30 (B) 1/5 (C) 2/3 (D) 3/4 (E) 4/5<|im_end|>
<|im_start|>assistant
<think>
</think>
45% is 20%-points above 25% ... | 94,431 |
<|im_start|>user
Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
Answer Choices: (A) 7/125 (B) 4/125 (C) 4/25 (D) 3/25 (E) 2/25<|im_end... | 25,215 |
<|im_start|>user
One packet contains 2 black, 3 white and 2 red rubbers. 2 rubbers are drawn at random. What is the probability that none of the rubbers drawn is red?
Answer Choices: (A) 10/21 (B) 21/23 (C) 23/25 (D) 21/20 (E) None<|im_end|>
<|im_start|>assistant
<think>
</think>
Total number of rubbers = (2 + 3 + 2)... | 93,671 |
<|im_start|>user
Find the cost of fencing around a circular field of diameter 14 m at the rate of Rs.2.50 a meter?
Answer Choices: (A) 288 (B) 110 (C) 772 (D) 592 (E) 261<|im_end|>
<|im_start|>assistant
<think>
</think>
2 * 22/7 * 7 = 44
44 * 2.5 = Rs.110
The answer is B<|endoftext|> | 36,461 |
<|im_start|>user
If a sum of money borrowed at 5 percent/annum SI amounts to Rs.1020 in 4 yrs, then the sum of money borrowed is?
Answer Choices: (A) Rs. 850 (B) Rs. 980 (C) Rs. 990 (D) Rs. 1000 (E) Rs. 1100<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol We have, A : Rs.1U2D
Let the pr xnpal be R5 x
Then mteres... | 19,891 |
<|im_start|>user
A customer went to a shop and paid a total of $30, out of which 90 cents was for sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Answer Choices: (A) $12.70 (B) $13.20 (C) $14.10 (D) $15.60 (E) $16.80<|im_end|>
<|im_start|>assistant
<think>
</think>... | 17,842 |
<|im_start|>user
Which of the following is equal to 1(1/6)%?
Answer Choices: (A) 0.012/100 (B) 0.12/100 (C) 1.1/100 (D) 12/100 (E) 12/10<|im_end|>
<|im_start|>assistant
<think>
</think>
This notation may be confusing for some, since it looks like we're multiplying 1 and 1/6
How about adding a space:Which of the follo... | 3,968 |
<|im_start|>user
W is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of W, and y is the minimum value of the sum of k distinct members of W, what is x + y?
Answer Choices: (A) kn (... | 55,048 |
<|im_start|>user
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II. Regine
III. Brian
Answer Choices: (A) I only (B) II only (C) III (D) only I or II on... | 67,801 |
<|im_start|>user
Elements are defined by their atomic number, a number that describes the amount of what in the element?
Answer choice: (A) bonds (B) electrons (C) protons (D) neutrons<|im_end|>
<|im_start|>assistant
<think>
</think>
Rutherford’s nuclear model of the atom helped explain why atoms of different element... | 9,040 |
<|im_start|>user
From 5 positive numbers and 5 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
Answer Choices: (A) 720 (B) 110 (C) 30 (D) 960 (E) 255<|im_end|>
<|im_start|>assistant
<think>
</think>
The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of w... | 69,415 |
<|im_start|>user
What is the remainder when 43*49 is divided by 8?
Answer Choices: (A) 1 (B) 3 (C) 4 (D) 5 (E) 7<|im_end|>
<|im_start|>assistant
<think>
</think>
we can make use of the rule :
Remainder of { (a * b)/n}} = Remainder of (a/n) * Remainder of (b/n)
Here
Remainder of { 43 * 49)/8}} = Remainder of (43/... | 83,896 |
<|im_start|>user
A wheel that has 4 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Answer Choices: (A) 49 (B) 4 (C) 12 (D) 6 (E) 27<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the required number of rev... | 45,932 |
<|im_start|>user
At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.60000?
Answer Choices: (A) 19860 (B) 3277 (C) 2688 (D) 2998 (E) 2789<|im_end|>
<|im_start|>assistant
<think>
</think>
A = 60000(11/10)3
= 79860
= 60000
----------
19860
The answer is A<|endoftext|> | 22,991 |
<|im_start|>user
A man's speed with the current is 18 km / hr and the speed of the current is 2 km / hr. The man's speed against the current is
Answer Choices: (A) 8.5 km / hr (B) 9 km / hr (C) 14 km / hr (D) 12.5 km / hr (E) None<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
Man's rate in still in water = (1... | 39,725 |
<|im_start|>user
A college has classes from 10:00 AM until 1:40 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?
Answer Choices: (A) 38 min (B) 41 min (C) 40 min (D) 42 min (E) 52 min<|im_end|>
... | 67,170 |
<|im_start|>user
In a simultaneous throw of 2 dice, what is the probability of getting a total of 10 or 11?
Answer Choices: (A) 2/7 (B) 1/4 (C) 1/2 (D) 7/36 (E) 5/36<|im_end|>
<|im_start|>assistant
<think>
</think>
n(S) = 6*6 = 36
E = event of getting a total of 10 or 11 = {(4,6),(5,5),(6,4),(5,6),(6,5)}
probability ... | 78,466 |
<|im_start|>user
14, 35, 56, 63, 91, 126
In the sequence above, each term is related with the others. Which of the following could not be a term in the sequence?
Answer Choices: (A) 402 (B) 259 (C) 322 (D) 686 (E) 847<|im_end|>
<|im_start|>assistant
<think>
</think>
Simplifying the question into easier words we just ... | 53,014 |
<|im_start|>user
If you roll 2 dice, what is the probability of rolling a 5?
Answer Choices: (A) 1/9 (B) 1/12 (C) 1/3 (D) 5/12 (E) 2/13<|im_end|>
<|im_start|>assistant
<think>
</think>
The answer is A<|endoftext|> | 27,169 |
<|im_start|>user
Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent is 5time of years , then the Time is:
Answer Choices: (A) 6 1/2 years. (B) 5 1/2 years. (C) 4 1/2 years. (D) 2 1/2 years. (E) 3 1/2 years.<|im_end|>
<|im_start|>assistant
<t... | 30,213 |
<|im_start|>user
At a loading dock, each worker on the night crew loaded 1/2 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Answer Choices: (A) 1/2 (B) 2/5 (C) 3/5 (D) 4/5 (E) 5/7<|im_... | 40,418 |
<|im_start|>user
Out of first 28 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
Answer Choices: (A) 1/2 (B) 16/19 (C) 4/5 (D) 22/28 (E) 3/5<|im_end|>
<|im_start|>assistant
<think>
</think>
n(S) = 28
n(Even no) = 14 = n(E)
n(Prime no) = 9 = n... | 1,860 |
<|im_start|>user
The remainder when Q=1+3+3^2+3^3+..........+3^200 is divided 13.
Answer Choices: (A) 12 (B) 7 (C) 0 (D) 5 (E) 3<|im_end|>
<|im_start|>assistant
<think>
</think>
Q=1+3+3^2+3^3+..................+3^200
Is a Geometric progression having common ratio as '3' and number of terms as '201'.
Since Sum to n te... | 59,504 |
<|im_start|>user
There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 10 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
Answer Choices: (A) 20 (B) 31 (C) 42 (D) 47 (E) 64<|im_end|>
<|im_start|>assistant
<think>
</think>
x ... | 14,202 |
<|im_start|>user
If a quarter kg of potato costs 60 paise, how many paise does 200 gm cost?
Answer Choices: (A) 65 paise (B) 70 paise (C) 52 paise (D) 48 paise (E) 75 paise<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
(Chain Rule)
Let 200 gm potato costs x paise
Cost of 14 Kg potato = 60 Paise
=> Cos... | 21,308 |
<|im_start|>user
Factory X's bulbs work for over 5000 hours in 79% of cases, whereas factory Y's bulbs work for over 5000 hours in 85% of cases. It is known that factory X supplies 80% of the total bulbs available. What is the chance that a purchased bulb will work for longer than 5000 hours?
Answer Choices: (A) 80.2% ... | 70,046 |
<|im_start|>user
What is the sum of all the prime numbers from 20 to 40?
Answer Choices: (A) 279 (B) 100 (C) 278 (D) 120 (E) 191<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
23 + 29 + 31 + 37 = 120
The answer is D<|endoftext|> | 72,603 |
<|im_start|>user
How many even integers from 1 to 50 (both inclusive) have even number of factors?
Answer Choices: (A) 3 (B) 14 (C) 5 (D) 6 (E) 7<|im_end|>
<|im_start|>assistant
<think>
</think>
Integers having even number of factors will be perfect squares. even numbers will have even perfect squares. Thus, the poss... | 55,610 |
<|im_start|>user
A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Answer Choices: (A) 48 Kmph (B) 50 Kmph (C) 52 Kmph (D) 56 Kmph (E) 60 Kmph<|im_end|>
<|im_start|>assistant
<think>
</think>
Time = 6
Distence ... | 92,771 |
<|im_start|>user
Through which process is the human gene for insulin placed into bacteria?
Answer choice: (A) migration (B) transformation (C) mutation (D) absorption<|im_end|>
<|im_start|>assistant
<think>
</think>
Through the process of transformation, the human gene for insulin is placed into bacteria. The bacteri... | 359 |
<|im_start|>user
If a * b = 2a - 3b + ab, then 3 * 5 + 5 * 3 is equal to :
Answer Choices: (A) 22 (B) 37 (C) 38 (D) 398 (E) 72<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)
= (6 + 10 - 9 + 15) = 22.
The answer is A<|endoftext|> | 97,206 |
<|im_start|>user
A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?
Answer Choices: (A) 1/4 (B) 2/4 (C) 1/2 (D) 1/3 (E) 2/3<|im_end|>
<|im_start|>assistant
<think>
</think>
Out of the 6 possible numbers that may rolled, 3 are even: 2, 4 and 6 BUT only 4 an... | 73,514 |
<|im_start|>user
If two numbers are in the ratio 4:7. If 10 is added to both of the numbers then the ratio becomes 6:10 then find the largest number?
Answer Choices: (A) 80 (B) 40 (C) 140 (D) 100 (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
4:7
4x + 10 : 7x + 10 = 6 : 10
10[4x + 10]... | 8,585 |
<|im_start|>user
When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?
Answer Choices: (A) 22 (B) 56 (C) 78 (D) 112 (E) 175<|im_end|>
<|im_start|>assistant
<think>
</think>
1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.08, the ... | 65,566 |
<|im_start|>user
In x-y plane, there is a right triangle ABC (∠B=90o). If the length of AC is 25 and the slope of line segment AC is 4/3, what is the length of AB?
Answer Choices: (A) 12 (B) 18 (C) 24 (D) 20 (E) 40<|im_end|>
<|im_start|>assistant
<think>
</think>
Slope = Change in Vertical Direction/Change in Horizon... | 68,838 |
<|im_start|>user
What is the sum of 60 consecutive integers from -30 inclusive, in a increasing order?
Answer Choices: (A) -29 (B) 29 (C) -30 (D) 30 (E) 60<|im_end|>
<|im_start|>assistant
<think>
</think>
From -39 to -1 --> 30 nos.
zero --> 1 number
from +1 to +29 --> 29 nos.
When we add up nos. from -30 to +29 sum w... | 32,093 |
<|im_start|>user
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Answer Choices: (A) 14009 (B) 14409 (C) 14006 (D) 14000 (E) 14001<|im_end|>
<|im_start|>assi... | 22,441 |
<|im_start|>user
The difference between a two-digit number and the number after interchanging the position of the two digits is 45. What is the difference between the two digits of the number?
Answer Choices: (A) 4 (B) 6 (C) 5 (D) Cannot be determined (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
... | 8,467 |
<|im_start|>user
12+6=792
10+2=110
1+9=9
2+7=16
11+4=??
Solve it?
Answer Choices: (A) 100 (B) 120 (C) 190 (D) 160 (E) 154<|im_end|>
<|im_start|>assistant
<think>
</think>
x+y=x[y+(x-1)]=x^2+xy-x
12+6=12[6+(12-1)]=792
10+2=10[2+(10-1)]=110
1+9=1[9+(1-1)]=9
2+7=2[7+(2-1)]=16
11+4=11[4+(11-1)]=154
The answer is E<|endof... | 11,160 |
<|im_start|>user
A class consists of 100 students, 30 of them are girls and 70 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Answer Choices: (A) 3/125 (B) 1/59 (C) 1/56 (D) 1/54 (E) 1/53<|im_end|>
<|im_start|>assistant
<thin... | 58,056 |
<|im_start|>user
161?85?65?89=100
then use + or - in place of ? and take + as m,- as n then find value of m-n
Answer Choices: (A) 3 (B) -1 (C) 1 (D) -3 (E) 2<|im_end|>
<|im_start|>assistant
<think>
</think>
161-85-65+89=100
so m=1, n=2 => (m-n)=-1
The answer is B<|endoftext|> | 48,448 |
<|im_start|>user
In covering a distance of 42 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Answer Choices: (A) 5 km/h (B) 7 km/h (C) 10 km/h (D) 15 km/h (E) 25 km/h<|im_end|>
<|im_start|>assistant
<think>
</think>
Let A's speed be X km/hr.
Then, 42/x - ... | 77,054 |
<|im_start|>user
A is thrice as good a workman as B and therefore is able to finish a job in 40 days less than B. working together, they can do it in
Answer Choices: (A) days (B) ½ days (C) days (D) days (E) days<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
B = 3A
3A – A =40 days
A = 20days
Then, B =... | 38,108 |
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