mathewhe/aqua_rat huggingface dataset:
Question: A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is?
(A) 238
(B) 150
(C) 988
(D) 210
(E) 171
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 140)/25 = x/15 => x = 210 m.
Answer: D
Answer: (D) 210
Question: A certain number of machines can do a work in 100days. If there were 10 machines more it could be finished in 10days less. How many machines are there?
(A) 50
(B) 40
(C) 90
(D) 100
(E) 60
Rationale: Original number of machines = 10 * (100-10)/10 = 90 machines
Answer is C
Answer: (C) 90
Question: For which of the following functions f is f(y) = f(1-y) for all y?
(A) f (x) = 1 - x
(B) f (x) = 1 - x^2
(C) f (y) = y^2 - (1 - y)^2
(D) f (y) = y^2*(1 - y)^2
(E) f (y) = y/(1 - y)
Rationale: I remember seeing this problem in a GMATprep test. I think choice D should be F(y)=(y^2) (1-y)^2. If that is true then substituting (1-y) for will give us the same function back and the answer choice is D, where the function is multiplicative
Answer: (D) f (y) = y^2*(1 - y)^2
Question: The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#27?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: First, let's translate the expression 21#27, using the definition given:
21#27 = 21×24×27
We need the prime factorization of this product.
Let's factor out 3 from each multiple.
21#27 = 3^3(7×8×9)
Now let's replace each consecutive integer with its prime factorization:
21#27 = 3^3(7×2^3×3^2)
Let's group the prime bases:
21#27 = 2^3×3^5×7
The sum of the exponents is 3 + 5 + 1 = 9
The answer is D.
Answer: (D) 9
Question: A rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge. If the floor is 12 meters by 10 meters, what is the area of the rug in square meters?
(A) 30
(B) 28
(C) 36
(D) 42
(E) 24
Rationale: A strip of 3 meters is covering the inner rectangular rug for all 4 sides.
Length of inner rug = 12-(2*3)
breadth of inner rug= 10-(2*3)
Area of Rug= 6 * 4 = 24 sq. mt
Ânswer: E
Answer: (E) 24
Question: Of the diplomats attending a summit conference, 14 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?
(A) 72
(B) 96
(C) 108
(D) 120
(E) 180
Rationale: {Total} = {French} + {Russian} - {Both} + {Neither}
{Total} = 14 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}
Solving gives {Total} = 180.
Answer: E.
Answer: (E) 180
Question: Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 9 on the two dice?
(A) 4/9
(B) 5/9
(C) 7/18
(D) 11/18
(E) 7/36
Rationale: There are 36 possible outcomes for two dice.
The number of outcomes with an even number on the first die is 3*6=18.
The number of outcomes with a sum of 9 is 4.
We need to subtract the outcomes that have both an even number on the first die and a sum of 9 because we have counted those outcomes twice. This number of outcomes is 2.
The number of outcomes with either an even number on the first die or a sum of 9 is 18+4-2=20.
The probability is 20/36=5/9.
The answer is B.
Answer: (B) 5/9
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 16 kmph
(B) 18 kmph
(C) 14 kmph
(D) 79 kmph
(E) 27 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3
= 14 kmph.
Answer: C
Answer: (C) 14 kmph
Question: A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: A'S sal = 40% of B =40% Of (25% of C) = 40/100(25/100*100) % Of C = 10%
ANSWER A
Answer: (A) 10
Question: An article is bought for Rs.560 and sold for Rs.340, find the loss percent?
(A) 36%
(B) 38%
(C) 16%
(D) 39%
(E) 12%
Rationale: 560 ---- 220
100 ---- ? => 39%
Answer:D
Answer: (D) 39%
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a odd number written on it?
(A) 1/12
(B) 1/10
(C) 1/8
(D) 1/42
(E) 5/9
Rationale: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)
P(+ on 1st pick) = 5/10
P(+ on 2nd pick) = 4/9
P(+ on 3rd pick) = 3/8
P(+ on 4rd pick) = 2/7
5/10*4/9*3/8*2/7=1/42
D
Answer: (D) 1/42
Question: A chemical tank of capacity 2000m3 which is 65% full is found to be leaking. The chemical in the tank needs to be transported to a new destination using tanker trucks. If the capacity of a truck is 16m3 which can be filled upto 93% full. How many truck loads would be needed to transport the chemical?
(A) 64
(B) 71
(C) 85
(D) 92
(E) 97
Rationale: Volume of chemical in the tank=2000x0.65=1300
Volume of the truck=16x.93=15.36
Number of truck loads needed= 1300/15.36=84.63â‰ˆ85
Answer: C
Answer: (C) 85
Question: The average of 65 numbers is 40. If two numbers, 79 and 60 are discarded, then the average of the remaining numbers is nearly
(A) 28.32
(B) 39
(C) 38.78
(D) 39.06
(E) 30
Rationale: Explanation :
Total sum of 63 numbers = (65*40) - (79 +60) = 2600 - 139 = 2461
Average = 2457/63 = 39.06
Answer : D
Answer: (D) 39.06
Question: If x+y=10z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
(A)  4z-1
(B)  3z
(C)  5z
(D)  z/3
(E)  3z/2
Rationale: Pick any number like X=12, Y=18 and Z= 3 so that X+Y=10Z, now then the arithmetic mean will be (12+18+3)/3=11. Now, just look at the answers and put the value of Z there.
(A) 4.3-1=11,it can be the answer, lets check us the other options
(B) 3.3=6, no
(C) 5.3=15, no
(D) 3/3, no
(E) (3.3)/2=3, no
so the answer will be A..
Answer: (A)  4z-1
Question: In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is theprobability that the extracted ball would turn onto be white, if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ?
(A) 3/5
(B) 5/8
(C) 6/7
(D) 7/8
(E) 6/7
Rationale: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
Answer: (B) 5/8
Question: A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 65 km/hr
(B) 17 km/hr
(C) 55 km/hr
(D) 50 km/hr
(E) 15 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 10) km/hr.
x - 10 = 45 => x = 55 km/hr.
Answer: C
Answer: (C) 55 km/hr
Question: Factor | Percent of Respondents |
User-friendly | 56% |
Fast response time | 48% |
Bargain prices | 42% |
The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,400 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
(A) 312
(B) 336
(C) 364
(D) 384
(E) 420
Rationale: The way I looked at is is as follows:
UserFriendly(UF) + FastResponse (FR) = 30%
UF leftover = 56 - 30 = 26%
FR leftover = 48 - 30 = 18%
Sum these = 74% (ie. 74% were either UF+FR, UF, FR)
26% leftover is the maximum number for Bargain Price
26/100 * 1400 = 26 * 14 = 364 (C).
Answer: (C) 364
Question: A man is trying to climb over a frozen mountain that is sixty feet high. Every minute, he can climb 3 feet, but due to the slippery ice, he slips back 2 feet.
How long will it take him to reach the top of the mountain?
(A) 57 minutes
(B) 58 minutes
(C) 59 minutes
(D) 53 minutes
(E) 54 minutes
Rationale: Solution:
It will take the man 58 minutes to reach the top.
Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.
58 minutes
Answer B
Answer: (B) 58 minutes
Question: The decimal d is formed by writing in succession all the positive, odd integers in increasing order after the decimal point; that is d = 0.1357911131517...
What is the 100th digit of d to the right of decimal point?
(A) 5
(B) 1
(C) 0
(D) 9
(E) 7
Rationale: One-digit odd numbers: There are (1)(10/2) = 5 odd one-digit numbers.
0.13579
5 digits down, 95 remaining. The next 5 odd numbers will be 11, 13, 15, 17, and 19, ... so it follows that: (2)(5) = 10 digits.
Two-digit numbers: 90 digits, which brings us to the number 99.
Three-digit numbers: we only need 5 more digits. The next odd numbers are 101, and 103, thus 0 is the 100th digit.
Answer: C
Answer: (C) 0
Question: There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 68%
(A) 14.11
(B) 19.75
(C) 20.75
(D) 21.75
(E) 22.75
Rationale: 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*68/100=50.40
so x=14.11
ANSWER:A
Answer: (A) 14.11
Question: A sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested?
(A) $340
(B) $360
(C) $380
(D) $400
(E) $420
Rationale: S.I for 5 years = $820 - $520 = $300
The S.I. is $60/year
S.I. for 2 years = $120
Principal = $520 - $120 = $400
The answer is D.
Answer: (D) $400
Question: A cricket bat is sold for $850, making a profit of $215. The profit percentage would be
(A) 24%
(B) 25%
(C) 34%
(D) 36%
(E) 40%
Rationale: 215/(850 - 215) = 215/635 = 43/127 =34%.
Answer: C.
Answer: (C) 34%
Question: 2.2,5.5,8,36,40.5,263.25,?
(A) 269.75
(B) 279.75
(C) 289.75
(D) 299.75
(E) 259.75
Rationale: 5.5/2.2=2.5, 2.5+5.5=8
36/8=4.5, 4.5+36=40.5
263.25/40.5=6.5, 6.5+263.25=269.75
ANSWER:A
Answer: (A) 269.75
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:16
(C) 18:10
(D) 18:14
(E) 14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A
Answer: (A) 18:11
Question: You are gifted a coin that is dated 378 B.C. How much worth the coin is as per your assumption?
(A) 1
(B) 0
(C) 2
(D) 5
(E) 6
Rationale: Solution:
The worth of that coin is zero. This is because the B.C. and A.D. dating system was not empowered till the year 525. So the coin is probably fake.
Answer B
Answer: (B) 0
Question: Dustin's Pizza Shop sells 3 sizes of pizza: Small, Medium, and Large. A Small pizza contains 4 slices, A Medium Pizza contains 6 slices and a Large pizza contains 10 slices. Lisa, a customer having a birthday party, visits the shop with her 2 daughters and 9 friends. To ensure each of the visitors receive an equal amount of pizza with none leftover, which of the following combinations are possible?
(A) 1 Small and 1 Large
(B) 4 Small and 1 Medium
(C) 2 Small and 4 Medium
(D) 4 Medium and 1 Large
(E) 1 Medium and 3 Large
Rationale: There are 12 total customers (Lisa, 2 daughters, and 9 friends) The correct combination must be divisible by 12 with no remainder.
A= 14 Slices (1 slice per guest with 2 slices leftover)
B= 22 Slices (Each kid would have 2 slices, but Lisa would have none)
C= 32 Slices (8 visitors would have 3 slices, but 4 visitors would only have 2)
D= 34 Slices (10 Visitors would have 3 slices, but 2 visitors would only have 2)
E= 36 Slices (Each visitor would have 3 slices, with nothing leftover) *Correct Answer*
The Correct Answer is E
Answer: (E) 1 Medium and 3 Large
Question: If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true?
i. s=0
ii. u is not equal to v
iii.u > v
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers.
Given: 2s=2u+2v --> s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. .
Answer: A
Answer: (A) None
Question: Which of the following equations describes a line that is perpendicular to y = x/2 + 6?
(A) y = x − 6
(B) y = −1 − 2x
(C) y = -3x
(D) y = 6x-1
(E) y = 1/x + 6
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y = x/2 + 6 is 1/2 so the slope of a perpendicular line will be -2.
The answer is B.
Answer: (B) y = −1 − 2x
Question: Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What faction of the bill did Veena pay ?
(A) 1/3
(B) 3/11
(C) 12/13
(D) 5/8
(E) 9/8
Rationale: let veena paid x,
so anita paid 2/3 x,
and tanya paid 2x,
so total bill paid is given by
x+(2/3)x +2x = 1
i.e. x=3/11
ANSWER:B
Answer: (B) 3/11
Question: 40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 60
(B) 70
(C) 80
(D) 90
(E) 100
Rationale: Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 40% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/40 = 60
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (60 + 120)/2 = 90.
ANSWER:D
Answer: (D) 90
Question: An Olympic diver received the following scores: 7, 4, 8, 10, and 6. The standard deviation of her scores is in which of the following ranges?
(A) 0-1.9
(B) 2-3.9
(C) 4 – 6.9
(D) 7 – 7.9
(E) 8 – 9.9
Rationale: 7+4+8+10+6/5 =7
|7-7| = 0 0^2 = 0
|4-7| = 3^2 = 9
|8-7| = 1^2 =1
|10-7| = 3^2 = 9
|6-7| = 1^2 = 1
SD = sqrt 20/5 = 2
Answer : B
Answer: (B) 2-3.9
Question: A 10-by-7 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
(A) The volume of the cylinder with height 10 is 70/pi cubic inches greater than the volume of the cylinder with height 6.
(B) The volume of the cylinder with height 7 is 70/pi cubic inches greater than the volume of the cylinder with height 10.
(C) The volume of the cylinder with height 10 is 70pi cubic inches greater than the volume of the cylinder with height 6.
(D) The volume of the cylinder with height 7 is 70pi cubic inches greater than the volume of the cylinder with height 10.
(E) The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
Rationale: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 7 and 10 are the circumference of the base and not the radius. B is the right answer.
Answer: (B) The volume of the cylinder with height 7 is 70/pi cubic inches greater than the volume of the cylinder with height 10.
Question: In how many different ways can 7 girls and 7 boys form a circle such that the boys and the girls alternate?
(A) 2880211
(B) 3628800
(C) 120000
(D) 36286200
(E) None of these
Rationale: Explanation :
In a circle, 7 boys can be arranged in 6! ways
Given that the boys and the girls alternate.
Hence there are 7 places for girls which can be arranged in 7! ways
Total number of ways = 6! x 7! = 720 x 5040 = 3628800. Answer : Option B
Answer: (B) 3628800
Question: On 8th march,2005,Wednesday falls. What day of the week was it on 8th march,2004?
(A) 28
(B) 00
(C) 27
(D) 01
(E) 8
Rationale: Answer:D
Answer: (D) 01
Question: Two employees X and Y are paid a total of Rs. 638 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.250
(B) s.280
(C) s.290
(D) s.299
(E) s.300
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 638
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 638
⇒ y[12/10 + 1] = 638
⇒ 22y/10 = 638
⇒ 22y = 6380
⇒ y = 6380/22 = 580/2 = Rs.290
C
Answer: (C) s.290
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 2 is subtracted and divided by 13?
(A) 4
(B) 7
(C) 8
(D) 5
(E) 3
Rationale: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 2)/13 = (54 - 2)/13 = 4
Answer: Option A
Answer: (A) 4
Question: An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 8 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.
(A) 8600 litres
(B) 200 litres
(C) 12800 litres
(D) 6400 litres
(E) 13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 8*60 = 480 liters/hour;
Net outflow rate when both pipes operate would be x-480 liters/hour.
Capacity of the tank = x*5 hours = (x-480)*(5+3) hours
5x=(x-480)*8 --> x=1280 --> capacity = 5x = 6400 liters.
Answer: D
Answer: (D) 6400 litres
Question: If the simple interest on a sum of money for 3 years at 7% per annum is Rs. 570, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs. 610.83
(B) Rs. 810.83
(C) Rs. 617
(D) Rs. 618
(E) Rs. 610.83
Rationale: Sum = (570 * 100) / (7 * 3) = Rs. 2,714.29
Amount = [2,714.29 * (1 + 7/100)3] = Rs. 3,325.12
C.I. = (3,325.12 - 2,714.29) = Rs. 610.83.
ANSWER:E
Answer: (E) Rs. 610.83
Question: While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 4 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?
(A) 2
(B) 2.4
(C) 2.7
(D) 3
(E) 3.5
Rationale: Both computers together process files at a rate of 240/12 + 240/4 = 20+60 = 80 files per hour.
The time required to process 240 files is 240/80 = 3 hours
The answer is D.
Answer: (D) 3
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150m
(B) 188m
(C) 267m
(D) 268m
(E) 287m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: (A) 150m
Question: A group of 10 representatives is to be selected out of 15 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
(A) 15C₅ * 10
(B) 15C₇ * 10
(C) 15C10 * ¹⁰C₅
(D) 12 * ¹⁰C₅
(E) None of these
Rationale: Here, five seniors out of 15 seniors can be selected in 15C₅ ways. Also, five juniors out of ten juniors can be selected ¹⁰C₅ ways. Hence the total number of different ways of selection = 15C₅ * ¹⁰C₅ =15C10 * ¹⁰C₅
since 15C₅ = 15C10
ANSWER:C
Answer: (C) 15C10 * ¹⁰C₅
Question: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 10% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
(A) 127%
(B) 120%
(C) 121%
(D) 135%
(E) 140%
Rationale: Since Michelle earns 10% interest compounded semiannually, then she earns 5% interest every 6 months.
Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 5%*5=25%. But, since the interest is compounded every 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 25%, only answer choice A fits.
Answer: A
Answer: (A) 127%
Question: 4.036 divided by 0.04 gives
(A) 1.009
(B) 100.09
(C) 10.9
(D) None of these
(E) cannot be determined
Rationale: Solution
4.036 / 0.04	= 403.6 / 4
= 100.9
Answer A
Answer: (A) 1.009
Question: What will come in place of the x in the following Number series? 18, 22, 30, 46 ,X, 142
(A) 35
(B) 56
(C) 78
(D) 87
(E) 98
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 78
Answer: (C) 78
Question: One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first.
(A) 86
(B) 94
(C) 80
(D) 96
(E) 55
Rationale: Explanation :
When 5th thief entered-1 diamond
When 4th thief entered -(1+2)*2=6 diamonds
When 3rd thief entered -(6+2)*2=16 diamonds
When 2nd thief entered -(16+2)*2=36 diamonds
When 1st thief entered -(36+2)*2=76 diamonds
Hence(D) is the correct answer.
Answer : D
Answer: (D) 96
Question: A train overtakes 2 girls who are walking inthe opposite direction in which the train is going at the rate of 3 km/hour & 6km/hour and passes them completely in 36sec & 30 sec respectively. Find the length of the train is?
(A) 90 m
(B) 120 m
(C) 150 m
(D) 190 m
(E) 210 m
Rationale: Let the length of the train e x meter, and let the speed of train be y km/h, then
\inline x=\left ( y+3 \right )\frac{5}{18}\times 36 ........(1)
and \inline x=\left ( y+6\right )\frac{5}{18}\times 30 ........(2)
From eq (1) and (2), we get
\inline (y+3)\times 36 = ( y+6)\times 30
y = 12 km/h
\inline \therefore \inline x=(y+3)\times \frac{5}{18}\times 36
x= 150 m
C
Answer: (C) 150 m
Question: If 4x + y = 8 and −2x + y = 13, then what is the value of 2x + 2y?
(A) 1/7
(B) 3
(C) 15
(D) 21
(E) 60/7
Rationale: 4x + y = 8
−2x + y = 13
Adding both the equations --> 2x + 2y = 21
Answer: D
Answer: (D) 21
Question: In a 500 m race, the ratio of the speeds of two contestants A and B is 2 : 4. A has a start of 300 m. Then, A wins by:
(A) 60 m
(B) 20m
(C) 43m
(D) 20m
(E) 100 m
Rationale: To reach the winning post A will have to cover a distance of (500 - 300)m, i.e., 200 m.
While A covers 2 m, B covers 4 m.
While A covers 200 m, B covers 4 x 200/2	m	= 400 m.
Thus, when A reaches the winning post, B covers 400 m and therefore remains 100 m behind.
A wins by 100 m.
Answer:	E
Answer: (E) 100 m
Question: The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age?
(A) 20
(B) 21
(C) 22
(D) 25
(E) 18
Rationale: Let the present age of the son =x
Then, present age of the father =(60−x)
Six years ago father's age was 5 times the age of the son
⇒(60−x)−6=5(x−6)⇒84=6x⇒x=846=14
Son's age after 6 years
=x+6=14+6=20
Answer is A.
Answer: (A) 20
Question: A person incures loss for by selling a watch for rs1140.at what price should the watch be sold to earn a 5% profit ?
(A) Rs.1160
(B) Rs.1260
(C) Rs.1200
(D) Rs.1250
(E) Rs.1280
Rationale: let the new sp be Rs x.then
(100-loss%) : (1st sp)=(100+gain%) (2nd sp)
={(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =Rs.1260.
Answer is B.
Answer: (B) Rs.1260