text stringlengths 148 4.25k | __index_level_0__ int64 0 97.5k |
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<|im_start|>user
Find the odd man out. 1, 3, 9, 12, 19, 29
Answer Choices: (A) 12 (B) 9 (C) 1 (D) 3 (E) 4<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation :
12 is an even number. All other given numbers are odd..
The answer is A<|endoftext|> | 59,582 |
<|im_start|>user
The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 35 what is the value of a1 ?
Answer Choices: (A) 1 (B) 6 (C) 15 (D) 16 (E) 21<|im_end|>
<|im_start|>assistant
<think>
</think>
Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest w... | 75,720 |
<|im_start|>user
Pressure is defined as the force per unit area on?
Answer choice: (A) weight (B) gravity (C) speed (D) surface<|im_end|>
<|im_start|>assistant
<think>
</think>
Pressure is defined as the force per unit area on a surface.
The answer is D<|endoftext|> | 7,954 |
<|im_start|>user
In how much time will a train of length 100 m, moving at 54 kmph cross an electric pole?
Answer Choices: (A) sec (B) sec (C) sec (D) sec (E) sec<|im_end|>
<|im_start|>assistant
<think>
</think>
Convert kmph to mps. 54 kmph = 54 * 5/18 = 15 mps.
The distance to be covered is equal to the length of the... | 33,499 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
A sentence is a group of words that expresses a complete thought.
The band I'm in has been rehearsing daily because we have a concert in two weeks.
A sentence fragment is a group of words that does not express a complete tho... | 6,004 |
<|im_start|>user
How long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length?
Answer Choices: (A) 22 sec (B) 20 sec (C) 15 sec (D) 23 sec (E) 16 sec<|im_end|>
<|im_start|>assistant
<think>
</think>
D = 100 + 245 = 345 m
S = 54* 5/18 = 15
T = 345 * 1/15 = 23 sec
The answer is D<|e... | 61,538 |
<|im_start|>user
Find the 10th and 12th term of the series 1, 3.5, 6, 8.5,...? And their ratio is?
Answer Choices: (A) .98 (B) 2.5 (C) 1.21 (D) 3.4 (E) 2<|im_end|>
<|im_start|>assistant
<think>
</think>
common difference = d = 3.5 - 1 = 2.5 ,, n = 10, a = first term = 1-----
By using arithmetic progression , t10 = a ... | 60,495 |
<|im_start|>user
A train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds. What is the length of the train?
Answer Choices: (A) 100 m (B) 125 m (C) 130 m (D) 150 m (E) 165 m<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the length of the train be x meters.
The speed of the train is... | 12,407 |
<|im_start|>user
If the price has fallen by 11% what percent of its consumption be: increased so that the expenditure may be the same as before?
Answer Choices: (A) A) 11/89% (B) B) 10% (C) 1/9 % (D) 1/11 % (E) %<|im_end|>
<|im_start|>assistant
<think>
</think>
100 – 11 = 89
89------11
100------? => 11/89%
The answer... | 64,010 |
<|im_start|>user
0.01 is what percent of 0.1?
Answer Choices: (A) 1% (B) 10% (C) 100% (D) 50% (E) 25%<|im_end|>
<|im_start|>assistant
<think>
</think>
Required percentage = 0.01*100/0.1 = 100/10 = 10%
The answer is B<|endoftext|> | 36,021 |
<|im_start|>user
When the integer n is divided by 8, the remainder is 5. Which of the following is NOT an even number?
Answer Choices: (A) n + 3 (B) n/2 + 3.5 (C) n – 3 (D) 3n + 1 (E) 5n + 2<|im_end|>
<|im_start|>assistant
<think>
</think>
Given number = N =8p+5 ---> the number N is odd.
Thus ,
A. n + 3
n+3 = odd + o... | 2,734 |
<|im_start|>user
Triangle STV has sides ST = TV = 5, and SV = 6. What is the area?
Answer Choices: (A) 8 (B) 10 (C) 12 (D) 14 (E) 16<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the base B of the triangle be SV = 6. Then we need to find the height H.
H^2 = 5^2 - 3^2 = 16 and then H = 4.
The area is (1/2)*B*H ... | 13,556 |
<|im_start|>user
If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much will he reduce the quantity of petrol purchased?
Answer Choices: (A) 10% (B) 12% (C) 8% (D) 16% (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation :
Let the price... | 38,381 |
<|im_start|>user
What are named for major physical or climatic features and for their predominant vegetation?
Answer choice: (A) terrestrial substrates (B) terrestrial biomes (C) geological formations (D) celestial bodies<|im_end|>
<|im_start|>assistant
<think>
</think>
The answer is B<|endoftext|> | 2,898 |
<|im_start|>user
A machine puts d caps on bottles in m minutes. How many hours will it take to put caps on b bottles?
Answer Choices: (A) 60bm/d (B) b/60dm (C) bd/60m (D) 60b/dm (E) bm/60d<|im_end|>
<|im_start|>assistant
<think>
</think>
A machine puts d caps on bottles in m minutes.
So, the machine puts 1 cap in m/c... | 72,495 |
<|im_start|>user
A sum of Rs. 2900 amounts to Rs. 3422 in 3 years. Had the rate of interest be 3% higher then what would the sum amount in the same time period?
Answer Choices: (A) Rs. 4465 (B) Rs. 3683 (C) Rs. 3596 (D) Data inadequate (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
3422=2900+(2900... | 76,986 |
<|im_start|>user
A shopkeeper sold an article at $100 with 15% profit. Then find its cost price?
Answer Choices: (A) $120 (B) $100 (C) $91 (D) $87 (E) $69<|im_end|>
<|im_start|>assistant
<think>
</think>
cost price = selling price *100/(100+profit)
C.P. = 100*100/115 = $87(approximately)
The answer is D<|endoftext|> | 15,425 |
<|im_start|>user
The denominator of a fraction is 15 greater than the numerator. If the numerator and the denominator are increased by 3, the resulting fraction is equal to 3â„4. What is the value of the original fraction?
Answer Choices: (A) 23/38 (B) 29/44 (C) 33/48 (D) 38/53 (E) 42/57<|im_end|>
<|im_start|>assistan... | 24,965 |
<|im_start|>user
In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (6, 0), (0, -3.5), (-6, 0)?
Answer Choices: (A) 42 (B) 56 (C) 88 (D) 112 (E) 116<|im_end|>
<|im_start|>assistant
<think>
</think>
Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 6+6= ... | 79,273 |
<|im_start|>user
A woman named Ranjani started a business investing Rs. 5,000. Roja joined him after six months with an amount of Rs. 5,000 and Sachin joined them with Rs. 10,000 after another six months. The amount of profit earned should be distributed in what ratio among Ranjani, Roja and Sachin respectively, 3 year... | 57,197 |
<|im_start|>user
The perimeters of two squares are 44 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
Answer Choices: (A) 22 cm (B) 24 cm (C) 26 cm (D) 30 cm (E) 29 cm<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
We know perim... | 24,765 |
<|im_start|>user
What lies between the continental shelf and the abyssal plain?
Answer choice: (A) successive slope (B) continental slope (C) continental belt (D) equator<|im_end|>
<|im_start|>assistant
<think>
</think>
The continental slope lies between the continental shelf and the abyssal plain. It has a steep slo... | 729 |
<|im_start|>user
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back, how far is the place?
Answer Choices: (A) 2 km (B) 2.4 km (C) 2.5 km (D) 3.4 km (E) None<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
Speed downstream = (5+1) ... | 81,105 |
<|im_start|>user
A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Answer Choices: (A) 299 (B) 150 (C) 267 (D) 551 (E) 121<|im_end|>
<|im_start|>assistant
<think>
</think>
Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15... | 53,135 |
<|im_start|>user
A person plans to start a business with x% of a list of 10,000 products in his inventory. Next year after a business loss, the person wants to reduce the list by (x − 4)%. In terms of x, how many products will be in the inventory?
Answer Choices: (A) x*x – 4x (B) (x) (104 – x) (C) (100) (104 – x) (D)... | 11,187 |
<|im_start|>user
Six years ago Ram was P times as old as Shyam was. If Ram is now 17 years old, how old is Shyam now in terms of P ?
Answer Choices: (A) 11/P + 6 (B) P/11 +6 (C) 17 - P/6 (D) 17/P (E) 11.5P<|im_end|>
<|im_start|>assistant
<think>
</think>
let's call Shyam's age six years ago is x
so six years ago Ram ... | 13,954 |
<|im_start|>user
If e is a positive integer, Which of the following options must be divisible by 2?
Answer Choices: (A) (e−1) *e*(e+1) (B) e^2*(e−5) (C) e^2*(e−5) (D) (e^2−2) (E) e(e+2) ^3<|im_end|>
<|im_start|>assistant
<think>
</think>
option A) (e−1)*e*(e+1) which represents the product of three consecutive in... | 53,799 |
<|im_start|>user
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?
Answer Choices: (A) 7 years (B) 9 years (C) 6 years (D) 4 years (E)... | 81,335 |
<|im_start|>user
If a, x, y, and z are positive integers and (x)×(y)×(z)=a^2, which of the following could be the values of x, y, and z?
Answer Choices: (A) 3, 16, 25 (B) 9, 25, 24 (C) 2, 36, 32 (D) 2, 9, 16 (E) 8, 16, 36<|im_end|>
<|im_start|>assistant
<think>
</think>
As it contains every no. 2 times
2
36=6*6
32=4*... | 30,305 |
<|im_start|>user
The area of a triangle is with base 4m and height 5m?
Answer Choices: (A) 10 (B) 20 (C) 30 (D) 15 (E) 11<|im_end|>
<|im_start|>assistant
<think>
</think>
The area of a triangle=1/2*bh
=1/2 * 4 * 5 = 10 m^2
The answer is A<|endoftext|> | 52,807 |
<|im_start|>user
If 135*s is a perfect square then s can be which of the following numbers?
Answer Choices: (A) 15 (B) 35 (C) 54 (D) 105 (E) 150<|im_end|>
<|im_start|>assistant
<think>
</think>
My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 135 are 3 *3 *... | 47,335 |
<|im_start|>user
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 55?
Answer Choices: (A) 3944 (B) 3740 (C) 7290 (D) 6928 (E) 3729<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Let the side of the square plo... | 37,205 |
<|im_start|>user
Divide $900 among A,B in the ratio 1:2. How many $ that A get?
Answer Choices: (A) $50 (B) $300 (C) $150 (D) $250 (E) $600<|im_end|>
<|im_start|>assistant
<think>
</think>
Sum of ratio terms = 1+2 = 3
A = 900*1/3 = $300
The answer is B<|endoftext|> | 57,168 |
<|im_start|>user
Many hydrocarbons are cyclic and adopt specific three-dimensional structures that influence their physical and what properties?
Answer choice: (A) liquid (B) electrical (C) radiation (D) chemical<|im_end|>
<|im_start|>assistant
<think>
</think>
Many hydrocarbons are cyclic and adopt specific three-di... | 186 |
<|im_start|>user
If Henry were to add 5 gallons of water to a tank that is already 3/4 full of water, the tank would be 7/8 full. How many gallons of water would the tank hold if it were full?
Answer Choices: (A) 25 (B) 40 (C) 64 (D) 80 (E) 96<|im_end|>
<|im_start|>assistant
<think>
</think>
7/8x-3/4x=5 galls
1/8*x=5... | 45,955 |
<|im_start|>user
X and Y put in 3,000 and 4,000 respectively into a business. X reinvests into the business his share of the first year?s profit of 2,100 whereas Y does not reinvest. In what ratio should they share the second year?s profit?
Answer Choices: (A) 39 : 40 (B) 3 : 4 (C) 3 : 7 (D) 40 : 79 (E) None of these<|... | 20,108 |
<|im_start|>user
20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 11:10 in the morning?
Answer Choices: (A) 32. (B) 75. (C) 42. (D) 46. (E) 50.<... | 25,141 |
<|im_start|>user
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Answer Choices: (A) 388 (B) 190 (C) 277 (D) 288 (E) 261<|im_end|>
<|im_start|>assistant
<think>
</think>
L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec .
... | 64,866 |
<|im_start|>user
A jogger running at 9 km/hr along side a railway track is 250 m ahead of the engine of a 100 m long train running at 99 km/hr in the same direction. In how much time will the train pass the jogger?
Answer Choices: (A) 14 sec (B) 67 sec (C) 98 sec (D) 36 sec (E) 23 sec<|im_end|>
<|im_start|>assistant
<t... | 81,723 |
<|im_start|>user
In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
Answer Choices: (A) 10 (B) 12 (C) 30 (D) 40 (E) 20<|im_end|>
<|im_start|>assistant
<think>
</think>
Dist = (100/45*9) = 20 m
The answer is E<|endoftext|> | 89,628 |
<|im_start|>user
What is studied to understand gene expression patterns in cells?
Answer choice: (A) rna (B) dna (C) protein (D) mutations<|im_end|>
<|im_start|>assistant
<think>
</think>
RNA is studied to understand gene expression patterns in cells. RNA is naturally very unstable because enzymes that break down RNA... | 7,465 |
<|im_start|>user
What are mid-wavelength electromagnetic waves commonly referred to as?
Answer choice: (A) light (B) gamma rays (C) x-rays (D) electricity<|im_end|>
<|im_start|>assistant
<think>
</think>
Mid-wavelength electromagnetic waves are commonly called light. This range of electromagnetic waves has shorter wa... | 7,713 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Organisms, including people, have both inherited and acquired traits. Inherited and acquired traits are gained in different ways.
Inherited traits are passed down through families. Children gain these traits from their paren... | 1,299 |
<|im_start|>user
A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 14 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Answer Choices: (A) 2,060 (B) 1,320 (C) ... | 81,247 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
Overall supply is the total amount of a good or service that producers make and sell. There are several things that can make overall supply go up or down. The table below shows how changes to these things might affect overal... | 4,080 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
All solids, liquids, and gases are made of matter. Matter is made up of tiny particles that are always moving. The energy from the motion of these particles is called thermal energy.
Temperature measures how hot or cold matt... | 4,554 |
<|im_start|>user
At a dinner party, 7 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
Answer Choices: (A) 5 (B) ... | 48,385 |
<|im_start|>user
An oil cylinder was 3/4th full. When SIX bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?
Answer Choices: (A) 120 (B) 115 (C) 140 (D) 130 (E) 135<|im_end|>
<|im_start|>assistant
<think>
</think>
(4/5 -3/4) cylinder is filled by 6 bottles
0.8 -0.7... | 1,992 |
<|im_start|>user
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Answer Choices: (A) 33 (B) 77 (C) 20 (D) 99 (E) 71<|im_end|>
<|im_start|>assistant
<think>
</think>
M = 15
S = 5
DS = 15 + 5 = 20
The answer is C<|endoftext|> | 73,603 |
<|im_start|>user
Use the following context to help answer a multiple choice question.
Context:
When you review a fellow student's writing, try to make your feedback clear and specific. You can use questions such as the following to guide your feedback:
Ideas and development: Does the writer express a clear main idea a... | 2,739 |
<|im_start|>user
he number of sequences in which 3 players can throw a ball, so that the youngest player may not be the last is?
Answer Choices: (A) 81 (B) 10 (C) 4 (D) 6 (E) 8<|im_end|>
<|im_start|>assistant
<think>
</think>
x Not younger_______ ↑
The last ball can be thrown by any of the remaining 2 players. The fi... | 62,642 |
<|im_start|>user
Susan, John, Peter, Jack, Daisy, Tim, Matt and Kim need to be seated in 8 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Answer Choices: (A) 22360 (B) 21120 (C) 21800 (D) 21060 (E) 20160<|im_end|>
<|im_start|>assistant
<think>
</... | 59,316 |
<|im_start|>user
sum of the digits of 5^2010*8^673
Answer Choices: (A) 7 (B) 8 (C) 9 (D) 10 (E) 11<|im_end|>
<|im_start|>assistant
<think>
</think>
5^2010 * 8^673 (2^3=8) therefore 673*3=2019
=5^2010 * 2^2019
=10^2010 * 2^9 (2^9=512)
=10^2010 * 512= 512000..... upto 2010 zeroes.So the sum is 8.
The answer is B<|endof... | 62,265 |
<|im_start|>user
In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 360 vote’s majority. What is the total number of votes polled?
Answer Choices: (A) 750 (B) 700 (C) 900 (D) 850 (E) None of these<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Note: majo... | 8,253 |
<|im_start|>user
Three hoses work to fill a tub at at different rate. Hose W and B, working together, can fill the tub in 6/5 of an hour. Hoses W and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution
An... | 80,091 |
<|im_start|>user
If (5^13)(9^7)=3(15^x), what is the value of x?
Answer Choices: (A) 7 (B) 9 (C) 11 (D) 13 (E) 15<|im_end|>
<|im_start|>assistant
<think>
</think>
(5^13)(9^7)=3(15^x)
=> 5^13 * 3^14 = 3 * 3^x * 5^x
=> 5^13 * 3^14 = 3^(x+1) * 5^x
Value of x = 13
The answer is D<|endoftext|> | 6,386 |
<|im_start|>user
Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for r dollars each. What is th... | 3,392 |
<|im_start|>user
P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
Answer Choices: (A) 1:8 (B) 1:6 (C) 2:1 (D) 1:1 (E) 1:7... | 28,939 |
<|im_start|>user
A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred.
Answer Choices: (A) Rs. 5750 (B) Rs. 6000 (C) Rs. 5500 (D) Rs. 5000 (E) Rs. 7000... | 59,009 |
<|im_start|>user
What is type of substance is formed when water vapor condenses or when ice melts?
Answer choice: (A) toxic water (B) chemical water (C) gaseous water (D) liquid water<|im_end|>
<|im_start|>assistant
<think>
</think>
Liquid water is formed when water vapor condenses (i. e. , H 2 O(g) → H 2 O(l) or whe... | 6,317 |
<|im_start|>user
In a corporation, 50 percent of the male employees and 40 percent of the female employees are at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corporation are females?
Answer Choices: (A) 3/5 (B) 2/3 (C) 3/4 (D) 4/5 (E) 5/6<|im_e... | 29,104 |
<|im_start|>user
If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is?
Answer Choices: (A) 4/16 (B) 4/19 (C) 4/12 (D) 4/13 (E) 4/11<|im_end|>
<|im_start|>assistant
<think>
</think>
P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52... | 12,140 |
<|im_start|>user
If an investor puts $700 in a savings account that earns 10 percent annual interest compounded semiannually, how much money will be in the account after one year?
Answer Choices: (A) $769.75 (B) $771.75 (C) $773.75 (D) $775.75 (E) $777.75<|im_end|>
<|im_start|>assistant
<think>
</think>
1.05*1.05*700... | 59,653 |
<|im_start|>user
In what ratio should a variety of rice costing Rs. 5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Answer Choices: (A) 1/2 (B) 5/9 (C) 5/1 (D) 5/3 (E) 7/6<|im_end|>
<|im_start|>assistant
<think>
</think>
Let us say the ratio of the q... | 71,059 |
<|im_start|>user
A certain collage has total of 600 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
Answer C... | 7,486 |
<|im_start|>user
A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
Answer Choices: (A) 4/9 (B) 5/9 (C) 7/9 (D) 8/9 (E) 1/3<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
Two balls can be picked from nin... | 3,049 |
<|im_start|>user
Through what form of energy transfer does the sun's energy travel?
Answer choice: (A) solar burst (B) convection (C) Fusion (D) radiation<|im_end|>
<|im_start|>assistant
<think>
</think>
Radiation is the transfer of energy by waves. Energy can travel as waves through air or empty space. The Sun's ene... | 2,494 |
<|im_start|>user
A positive integer, which when added to 1000, gives a sum which is greater than when it is multiplied by 1000. This positive integer is
Answer Choices: (A) 1 (B) 3 (C) 5 (D) 7 (E) 9<|im_end|>
<|im_start|>assistant
<think>
</think>
Solution
(1000 + N) > (1000N)
Clearly, N=1.
The answer is A<|endoftext... | 77,124 |
<|im_start|>user
R is the set of positive even integers less than 50, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Answer Choices: (A) None (B) Two (C) Three (D) Five (E) Seven<|im_end|>
<|im_start|>assistant
<think>
</think>
squares < 50 {1,4,9,16... | 36,086 |
<|im_start|>user
x =2.5 3.5 1.5
y= 25 49 9 then what is the relation between x and y
Answer Choices: (A) Y=(2*X) ^2 (B) Y=(2*X) ^3 (C) Y=(2*X) ^4 (D) Y=(3*X) ^2 (E) Y=(4*X) ^2<|im_end|>
<|im_start|>assistant
<think>
</think>
Y=(2*X)^2
25=(2*2.5)^2
The answer is A<|endoftext|> | 66,459 |
<|im_start|>user
The difference between simple and compound interest on Rs. 1500 for one year at 10% per annum reckoned half-yearly is?
Answer Choices: (A) 8.0 (B) 3.0 (C) 9.5 (D) 3.75 (E) 2.15<|im_end|>
<|im_start|>assistant
<think>
</think>
S.I. = (1500 * 10 * 1)/100 = Rs. 150
C.I. = [1500 * (1 + 5/100)2 - 1500]
= ... | 6,859 |
<|im_start|>user
In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 6 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
Answer Choices: (A) 4 (B) 6 (C) 8 (D) 9 (E) 12<|im_end|>
<|im_start|>assistant
<think>
</think>
... | 44,178 |
<|im_start|>user
Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $550, how many sales has Matt made?
Answer Choices: (A) 3 (B) 4 (C) 5 (D) 6 (E) 7<|im_end|>
<|im_start|>assistant
<think>
</think>
Let, Average Commission = x
... | 87,105 |
<|im_start|>user
If the average (arithmetic mean) of five consecutive negative integers is 4k – 1, what is the difference between the greatest and least of the five integers?
Answer Choices: (A) 4K (B) 4k^2 -4k (C) 4-4k (D) 4 (E) 4k+4<|im_end|>
<|im_start|>assistant
<think>
</think>
(n-2 + n - 1 + n + n + 1 + n + 2)/... | 85,089 |
<|im_start|>user
In a 1000 m race, A beats B by 90 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Answer Choices: (A) 145 m (B) 176 m (C) 181 m (D) 159 m (E) 218 m<|im_end|>
<|im_start|>assistant
<think>
</think>
By the time A covers 1000 m, B covers (1000 - 90) = 910 m.
By the time B c... | 10,215 |
<|im_start|>user
If A =x% of y and B =y% of x, then which of the following is true?
Answer Choices: (A) None of these (B) A is smaller than B (C) Relationship between A and B cannot be determined (D) If x is smaller than y, then A is greater than B (E) A is greater than B<|im_end|>
<|im_start|>assistant
<think>
</thin... | 89,606 |
<|im_start|>user
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the24 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
Answer Choices: (A) 48 (B) 72 (C) 76 (D) 78 (E) 90<|im_end|>
<|im_start|>assistant
<think>
</think>
Number of arrangements... | 86,398 |
<|im_start|>user
the numbers 272738 and 232342,when divided by n, a 2 digit number leave a remainder 13 and 17 respectively.Find the sum of digits of n?
Answer Choices: (A) 4 (B) 5 (C) 6 (D) 7 (E) 8<|im_end|>
<|im_start|>assistant
<think>
</think>
We have to find the h.c.f of both
1.272738-13
2.232325-17
H.c.f is 25
... | 41,741 |
<|im_start|>user
Amit and Sumit started a business with initial investments in the ratio 2 : 3, after some months Sumit withdrawn his investment, and their share in the annual profits were in the ratio 8 : 7. Then how long Sumit was in the business ?
Answer Choices: (A) 6 months (B) 8 months (C) 9 months (D) 5 months (... | 34,660 |
<|im_start|>user
Ira and Jake will throw three dice each. The score is the sum of points on all three dice. If Ira scores 4 in her attempt, what is the probability that Jake will outscore Ira in his attempt?
Answer Choices: (A) 5/6 (B) 17/18 (C) 26/27 (D) 35/36 (E) 53/54<|im_end|>
<|im_start|>assistant
<think>
</think... | 51,599 |
<|im_start|>user
If a = -0.6, which of the following is true?
Answer Choices: (A) a < a^2 < a^3 (B) a < a^3 < a^2 (C) a^2 < a < a^3 (D) a^3 < a < a^2 (E) a^2 < a^3 < a<|im_end|>
<|im_start|>assistant
<think>
</think>
a=-0.6;
a^2=0.36;
a^3=-0.216;
The answer is B<|endoftext|> | 94,471 |
<|im_start|>user
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Answer Choices: (A) (a) 7/16 (B) (b) ... | 10,307 |
<|im_start|>user
Dew point is the temperature at which what occurs?
Answer choice: (A) combustion (B) fermentation (C) condensation (D) precipitation<|im_end|>
<|im_start|>assistant
<think>
</think>
When air is very humid, it doesn’t have to cool very much for water vapor in the air to start condensing. The temperatu... | 6,524 |
<|im_start|>user
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly three elements each?
Answer Choices: (A) 24 (B) 42 (C) 54 (D) 72 (E) 84<|im_end|>
<|im_start|>assistant
<think>
</think>
nC2 = 36
=> n*(n-1)/2 = 36
=> n = 9
nC3 = 9C3 = 84
So,
T... | 35,758 |
<|im_start|>user
The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is
Answer Choices: (A) 124345 m (B) 233234 m (C) 153600 m (D) 123567 m (E) 168999 m<... | 16,284 |
<|im_start|>user
There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Answer Choices: (A) 12 (B) 15 (C) 16 (D) 13 (E) 18<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = ... | 27,837 |
<|im_start|>user
What is the ratio R of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Answer Choices: (A) 1/4 (B) 3/8 (C) 1/2 (D) 3/5 (E) 2<|im_end|>
<|im_start|>assistant
<think>
</think>
Let X be the side of the cube.... | 53,188 |
<|im_start|>user
When E is divided by 9, the remainder is 4. All of the following are possible values of E, except for which of the following?
Answer Choices: (A) 13 (B) 31 (C) 49 (D) 57 (E) 67<|im_end|>
<|im_start|>assistant
<think>
</think>
The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
b... | 62,011 |
<|im_start|>user
y = x^2 + bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
Answer Choices: (A) -512 (B) -257 (C) -256 (D) -513 (E) 128<|im_end|>
<|im_start|>assistant
<think>
</think>
As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of ... | 73,102 |
<|im_start|>user
If l / r is an integer, which of the following statements must be true?
Answer Choices: (A) both l and r are integers (B) r / l is an integer (C) r is an integer (D) l = nr where n is an integer (E) either l or r is negative<|im_end|>
<|im_start|>assistant
<think>
</think>
Let l = 1/4; r = 1/8 --> l/... | 82,983 |
<|im_start|>user
In 1979 approximately 1/3 of the 37.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 5 times the number that used Logan Airport, approximately how many mill... | 27,096 |
<|im_start|>user
A FAIR AND LOVELY manufacturer produces 100 units of a certain model each month at a cost to the manufacturer of £10 per unit and all of the produced units are sold each month. What is the minimum selling price per unit that will ensure that the monthly profit (revenue from sales minus production costs... | 52,470 |
<|im_start|>user
The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 145, what is the difference between the ages of Patrick and Monica?
Answer Choices: (A) 27 (B) 48 (C) 45 (D) 72 (E) 18<|im_end|>
<|im_start|>assistant
<think>
... | 64,648 |
<|im_start|>user
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first flip but not on the last 4 flips?
Answer Choices: (A) 1/4 (B) 1/8 (C) 1/16 (D) 1/32 (E) 1/64<|im_end|>
<|im_start|>assistan... | 30,608 |
<|im_start|>user
The difference between the place values of 9 and 4 in the number 927435 is
Answer Choices: (A) 899600 (B) 856200 (C) 875200 (D) 896200 (E) None<|im_end|>
<|im_start|>assistant
<think>
</think>
Sol.
= (Place value of 9) – (place Value of 4)
= (900000 - 400)
= 899600
The answer is A<|endoftext|> | 47,272 |
<|im_start|>user
Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
Answer Choices: (A) 1/6 (B) 5/8 (C) 3/8 (D) 5/6 (E) 7/8<|im_end|>
<|im_start|>assistant
<think>
</think>
Explanation:
P(at least one graduate) = 1 - P(no... | 34,443 |
<|im_start|>user
A and B run a 1 km race. If A gives B a start of 50m, A wins by 14 seconds and if A gives B a start of 22 seconds, B wins by 20 meters. Find the time taken by A to run 1 km.
Answer Choices: (A) 222 (B) 100 (C) 287 (D) 2976 (E) 111<|im_end|>
<|im_start|>assistant
<think>
</think>
To solve these type o... | 41,503 |
<|im_start|>user
In a class of boys and girls Vikas's rank is 9th and Tanvi's rank is 17th . Vikas's rank among the boys in that class is 4th from the top and 18th from the bottom and Tanvi's rank among the girls is 8th from top and 21st from bottom. In the order of rank, how many girls are there between Tanvi and Vika... | 84,227 |
<|im_start|>user
If the average (arithmetic mean) of a and b is 100, and the average of b and c is 160, what is the value of a − c?
Answer Choices: (A) −120 (B) −100 (C) 100 (D) 135 (E) It cannot be determined from the information given<|im_end|>
<|im_start|>assistant
<think>
</think>
Question: a - c = ?
(a + b)/ 2 =... | 92,252 |
<|im_start|>user
A corporation paid $7 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $100 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the n... | 91,179 |
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