mathewhe/aqua_rat huggingface dataset:
Question: the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?
(A) 10
(B) 15
(C) 20
(D) 15/2
(E) 24
Rationale: After passing the hiker the cyclist travels for 5 minutes at a rate of 10 miles/hour.
In those 5 mins the cyclist travels a distance of 5/6 miles.
In those 5 mins the hiker travels a distance of 1/2 miles.
So the hiker still has to cover 1/2 miles to meet the waiting cyclist.
The hiker will need 15/2 mins to cover the remaining 1/2 miles.
So the answer is D.
Answer: (D) 15/2
Question: A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?
(A) 77 years
(B) 88 years
(C) 12 years
(D) 16 years
(E) 17 years
Rationale: 100 ---- 200 ---- 4
400 ---- 4
800 ---- 4
------
12 years
Answer: C
Answer: (C) 12 years
Question: The average of first five prime numbers:
(A) 5.6
(B) 11.2
(C) 12.9
(D) 6.3
(E) 7.4
Rationale: Explanation:
The first five prime numbers is 2, 3, 5, 7, 11
Average = 28/5 = 5.6
Answer: Option A
Answer: (A) 5.6
Question: The daily high temperatures were recorded at an Antarctic weather station. If a temperature of -38.2 degrees Celsius is 2 units of standard deviation below the mean temperature, and a temperature of -22.6 degrees Celsius is 4 units of standard deviation above the mean, which of the following temperatures is 1 unit of standard deviation below the mean?
(A) -35.6 degrees Celsius
(B) -33.0 degrees Celsius
(C) -30.4 degrees Celsius
(D) -27.8 degrees Celsius
(E) -25.2 degrees Celsius
Rationale: Let us suppose mean = M and SD = d.
So, we are given M - 2d = -38.2
and M + 4d = -22.6
solving both the equations, we will get M = -33 an d = 2.6
So, we need to find out M - d = -33 - 2.6 = -35.6. Hence, A
Answer: (A) -35.6 degrees Celsius
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team W. If team A's average speed was 5 mph greater than team W's, what was team W's average mph?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team W's speed was s. Then Team W's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team W. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team W is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Answer: (D) 20
Question: 10% loss on the selling price is what percent loss on the cost price?
(A) 9/55%
(B) 100/11%
(C) 99/110%
(D) 90/11%
(E) 9/11%
Rationale: Let S.P. = $100
Then, loss = $10
C.P. = 100+10 = $110
Loss% = 10/110 * 100 = 9 1/11% = 100/11%
Answer is B
Answer: (B) 100/11%
Question: x - y = 3
2x = -2y + 18
The system of equations above has how many solutions?
(A)  None
(B)  Exactly one
(C)  Exactly two
(D)  Exactly three
(E)  Infinitely many
Rationale: x-y=3 ---------------1
2x=-2y+18 ---------------2
Divide equation 2 by 2:
2x/2=(2y+18)/2
x=-y+3
x+y=9----------------3
Equation 1 and 3 are equal and thus have:
x-y=3
x+y=9
x=6, y=3
Ans:B
Answer: (B)  Exactly one
Question: If a sequence of 8 consecutive odd integers with increasing values has 1 as its 7th term, what is the sum of the terms of the sequence?
(A) -48
(B) -32
(C) -16
(D) 16
(E) 32
Rationale: Let x be the first term.
Then x + 12 = 1 and x = -11
The sum is: x + (x+2) +...+ (x+14) =
8x + 2(1+2+...+7) = 8x + 2(7)(8) / 2 = 8(-11) + 56 = -32
The answer is B.
Answer: (B) -32
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 2/455
(C) 1/91
(D) 4/455
(E) None of these
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455
ANSWER:A
Answer: (A) 1/455
Question: At 30 minutes past 4 O'clock, what is the angle between the two hands?
(A) 22
(B) I8
(C) 99
(D) 17
(E) 181
Rationale: Answer:	E
Answer: (E) 181
Question: Mr X invested an amount for 2 years @ 15 p.c.p.a at simple interest. Had the interest been compounded, he would have earned 450/- more as interest. What was the amount invested?
(A) 22000
(B) 24000
(C) 25000
(D) Data inadequate
(E) None of these
Rationale: 30p/100+450=p+15/100−p
⇒ p = 20,000.
Answer E
Answer: (E) None of these
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $85.0 billion, a year ago. By what percent did the revenue fall?
(A) 20.8
(B) 30.4
(C) 43.5
(D) 32.5
(E) 33.8
Rationale: $85-$48=37$
(37/85)*100=43.5%
ANSWER:C
Answer: (C) 43.5
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag?
(A) 60
(B) 67
(C) 69
(D) 70
(E) 80
Rationale: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 30. Hence
3x = 30
Solve for x
x = 10
The total number of coins is given by
5x + 3x = 8x = 8 × 10 = 80
E
Answer: (E) 80
Question: In how many ways, a committee of 4 members can be selected from 5 men and 4 ladies, consisting of 3 men and 1 lady?
(A) 15
(B) 25
(C) 30
(D) 40
(E) 55
Rationale: (3 men out 5) and (1 lady out of 4) are to be chosen
Required number of ways = 5C3*4C1 = 40
Answer is D
Answer: (D) 40
Question: What is the difference between the C.I. on Rs. 9000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) s.2.04
(B) s.2.08
(C) s.3.67
(D) s.2.83
(E) s.2.42
Rationale: C.I. when interest is compounded yearly
= [9000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 9000 * 26/25 * 51/50 = Rs. 9547.2
C.I. when interest is compounded half-yearly
= [9000 * (1 + 2/100)2]
= (9000 * 51/50 * 51/50 * 51/50)
= Rs. 9550.87 Difference
= (9550.87 - 9547.2)
= Rs.3.67.
Answer: C
Answer: (C) s.3.67
Question: The arithmetic mean of set X is zero. If Y = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of X consisting of all those elements in X which are more than two but less than three standard deviations away from the arithmetic mean of X, what could be equal to the standard deviation of X?
(A) 0.54
(B) 0.77
(C) 0.82
(D) 0.97
(E) 1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and Y = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S
Y consists of all those elements in X that are more than 2 but less than 3 XDs away from the arithmetic mean of X
If an element is 1 XD away from the mean, we can write it as either m + XD or m - XD
Similarly, if an element is 2 XDs away from the mean, we can write it as either m + 2*XD or m - 2*XD
So, if these elements lie within 2 and 3 XDs of mean, m=0
we can find which one of these values of XD satisfies each value within Y
Only XD = 0.77 does
Answer : B
Answer: (B) 0.77
Question: $20000 will become $60000 at 20% P.A. find the time?
(A) 2years
(B) 5years
(C) 7years
(D) 8years
(E) 10years
Rationale: SI = simple interest = A-P = 60000-20000 = $40000
R = 100SI/PT = 100*40000/20000*20 =10 years
Answer is E
Answer: (E) 10years
Question: x is a positive integer of F less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Took me more than 2 mins to solve.
That's how I did it.
x is between 1-499 included.
Smallest number that can be written as 7n+1 (7*0+1) is 1
Largest number that can be written as 7n+1 is (7*71 +1) is 498
So there are total 72 numbers that can be written as 7n+1
Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2
7*0+1 can not be written in the form 3m+2
7*1+1 can be written in the form 3m+2
7*2+1 can not be written in the form 3m+2
7*3+1 can not be written in the form 3m+2
7*4+1 can be written in the form 3m+2
Here we see a sequence that one out of every 4 numbers can be written as 3m+1
72/4= 24 numbers can be written as 3m+1
D is the answer
Answer: (D) 24
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 5
(B) 8
(C) 9
(D) 4
(E) 2
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer: D
Answer: (D) 4
Question: If m+5/n is a prime integer, which of the following must be true?
1.n=5m
2. n is a prime integer
3. m+5/n is ODD.
(A) None
(B) 1 only
(C) 2 only
(D) 1 and 2 only
(E) 2 and 3 only.
Rationale: I would pick up numbers and do .
i hope the question is (m+5)/n....
let m = 3 , n = 4
3+5/4 = 2 = Prime
1. n is not equal to 5m
2.n is not a prime number
3. (m+5)/n is not odd.
hence A
Answer: (A) None
Question: The time on a clock is 20 minutes past 6. What is the angle between the hands of the clock?
(A) 60 degrees
(B) 120 degrees
(C) 90 degrees
(D) 50 degrees
(E) 70 degrees
Rationale: The hour hand rotates 360 degrees in twelve hours.
The hour hand rotates 30 degrees in one hour.
The hour hand rotates 5 degrees in ten minutes.
At this time, the hour hand has rotated 190 degrees.
The minute hand rotates 360 degrees in 60 minutes, or 60 degrees in ten minutes.
At this time, the minute hand has rotated 120 degrees.
The difference is 190 - 120 = 70 degrees.
The answer is E.
Answer: (E) 70 degrees
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
(A) 286 m
(B) 899 m
(C) 200 m
(D) 166 m
(E) 187 m
Rationale: 2(l + 100) = 600 => l
= 200 m
Answer: C
Answer: (C) 200 m
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. If there are 30 5-rupee notes, 20-10-rupee notes, find the number of one-rupee notes.
(A) 180
(B) 150
(C) 130
(D) 200
(E) 170
Rationale: x+150+200=480, x=480-350=130, Ans: C
Answer: (C) 130
Question: After decreasing 56% in the price of an article costs Rs.4400. Find the actual cost of an article?
(A) 12000
(B) 15000
(C) 1200
(D) 1000
(E) 10000
Rationale: CP* (44/100) =4400
CP= 100 * 100 => CP
= 10000
Answer:E
Answer: (E) 10000
Question: The cash difference between the selling prices of an book at a profit of 4% and 8% is $3. The ratio of the two selling prices is:
(A) 55:23
(B) 26:27
(C) 52:53
(D) 45:53
(E) 51:34
Rationale: Let C.P. of the book be $x.
Then, required ratio = 104% of x / 108% of x
= 104/108 = 26/27 = 26:27
B
Answer: (B) 26:27
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/19
(B) 2/19
(C) 2/21
(D) 2/97
(E) 2/18
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer: C
Answer: (C) 2/21
Question: In one alloy there is 12% chromium while in another alloy it is 10%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 8.8%
(B) 9%
(C) 9.2%
(D) 8.6%
(E) 10.6%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.12*15+0.10*35=5.3 kg, so the percentage is 5.3/50*100=10.6%.
Answer: E.
Answer: (E) 10.6%
Question: A car takes 6 hours to cover a distance of 630 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 48 Kmph
(B) 50 Kmph
(C) 52 Kmph
(D) 56 Kmph
(E) 70 Kmph
Rationale: Time = 6
Distence = 630
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 630/9 = 70 Kmph
E
Answer: (E) 70 Kmph
Question: In an election, candidate Smith won 52% of the total vote in Counties A and W. He won 61% of the vote in County A. If the ratio of people who voted in County A to County W is 3:1, what percent of the vote did candidate Smith win in County W ?
(A) A.25%
(B) B.27%
(C) C.34%
(D) D.43%
(E) E.49%
Rationale: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County W
hence answer is A.
Answer: (A) A.25%
Question: In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
(A) 3.5%
(B) 2.4%
(C) 8.3%
(D) 5%
(E) 2.6%
Rationale: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 114*95=10,830, which is 8.3% greater than the actual area.
Answer: C.
Answer: (C) 8.3%
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 4 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 25
(B) 35
(C) 76
(D) 80
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 4 = 72
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 72 + 4 = 76
C
Answer: (C) 76
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive E difference between n and m?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result E will be 8 - 5 = 3
And answer B
Answer: (B) 3
Question: In a fuel station the service costs $2.05 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
(A) 122.6$
(B) 128.9$
(C) 243.7$
(D) 298.85$
(E) 312.12$
Rationale: Mini van cost= 65*0.6+2.05
truck capacity =65(1+120/100)=143 lts.
cost of truck=143+0.6+2.05
Total cost =3* 41.05(car)+2*87.85(truck)=298.85
ANSWER:D
Answer: (D) 298.85$
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 9 units?
(A) 126 sq.units
(B) 170 sq.units
(C) 190 sq.units
(D) 940 sq.units
(E) 149 sq.units
Rationale: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 9 = 126 sq.units
Answer: Option A
Answer: (A) 126 sq.units
Question: A sweet seller sells 3/5th part of sweets at a profit of 10% and remaining at a loss of 5%. If the total profit is Rs 1500, then what is the total cost price of sweets?
(A) Rs 36,500
(B) Rs 37,000
(C) Rs 37,500
(D) Rs 38,500
(E) None of these
Rationale: Assume A be the cost price.
Therefore,
[{(3/5) x A x (10/100)} – {(2/5) x A x 5/100}] = 1500
Or A = Rs 37,500
ANSWER:C
Answer: (C) Rs 37,500
Question: A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 95 on the S scale?
(A) 42
(B) 45
(C) 48
(D) 51
(E) 54
Rationale: A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(95)/5 - 12 = 57-12 = 45
The answer is B.
Answer: (B) 45
Question: Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of four rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.
The relative speed of Sandy and Molly is 4 - 1 = 3 rounds per hour.
The time required to complete one round at this speed is 1/3 hours = 20 minutes.
The answer is B.
Answer: (B) 20
Question: 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?
(A) 6
(B) 9
(C) 8
(D) 12
(E) 2
Rationale: Explanation:
x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer:D
Answer: (D) 12
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 6 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 22 km
(B) 20 km
(C) 65 km
(D) 18 km
(E) 36 km
Rationale: Distance = Relative Speed * Time
= (6 + 3) * 4 = 36 km
[ They are travelling in the opposite direction, relative speed
= sum of the speeds].
Answer: E
Answer: (E) 36 km
Question: A clock loses a minute every three hours for 5 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
(A) 11:54:40 AM
(B) 11:56:24 AM
(C) 12:16:40 PM
(D) 11:54:24 AM
(E) 11:46:24 PM
Rationale: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 40 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;
Net gain in 11 days = 86.40 - 40 = 46.4 minutes.
11AM + 46.4 minutes = 11:46 and 4/10th of a minute or 24 seconds.
Answer: E
Answer: (E) 11:46:24 PM
Question: A retailer sold 2 houses at each $15000. On 1st house he got 20% profit and on 2nd house he loss 5% then find his net profit or loss?
(A) 10%
(B) 9%
(C) 14%
(D) 15%
(E) 12%
Rationale: A = 20%
B = -5%
profit% = 20-5 + (-100/100) = 14%
Answer is C
Answer: (C) 14%
Question: There are six leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
(A) 4 leopard and one sheep
(B) 5 leopard and one sheep
(C) 6 leopard and one sheep
(D) 7 leopard and one sheep
(E) None
Rationale: Solution:
5 leopard and one sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer B
Answer: (B) 5 leopard and one sheep
Question: The red triangle is equilateral with a side of 23 centimetres. Its perimeter is
(A) 68 cm
(B) 69 cm
(C) 70 cm
(D) 71 cm
(E) None
Rationale: Solution:
All three sides of an equilateral triangle are equal. Thus, its perimeter will be 23 × 3 = 69 cm
Answer B
Answer: (B) 69 cm
Question: The simple form of the ratio 9/8:3/4 is?
(A) 5:8
(B) 5:5
(C) 5:9
(D) 3:2
(E) 5:1
Rationale: 9/8 : 3/4 = 3:2
Answer: D
Answer: (D) 3:2
Question: How many even integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?
(A) 37
(B) 38
(C) 39
(D) 40
(E) 46
Rationale: total 51 even integers
out of which 7 will be divided by 7 and 6 will be divided by 9
(for 7..find intervals of 14 as we are taking even numbers
112,126...196
(for 9..find intervals of 18 as we are taking even numbers
108,126...198)
126 is common
so 51-7-6+1 = 39 will not be divided by 7 or 9
ANSWER:C
Answer: (C) 39
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
(A) 98 days
(B) 60 days
(C) 56 days
(D) 76 days
(E) 45 days
Rationale: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
Answer: B
Answer: (B) 60 days
Question: If e=1 and (e-b)/c = 1 which of the following is NOT a possible value of b?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: Equation is:
(e-b)/c = 1 where e = 1
so plug in 1 for e and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Answer: (D) 1
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 34% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
(A) 35.67%
(B) 66.90%
(C) 68.57%
(D) 69.57%
(E) none of these
Rationale: Girls = 900, Boys = 1100
Passed = ( 34% of 1100 ) + ( 32% of 900)
= 374 + 288 = 662
Failed = 2000 - 662 = 1338
Failed % = [(1338/2000) x 100]%
= 66.9%.
ANSWER:B
Answer: (B) 66.90%
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 2
(B) 6
(C) 5
(D) 3
(E) 8
Rationale: 9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer: D
Answer: (D) 3