mathewhe/aqua_rat huggingface dataset:
Question: A three-digit number 4a3 is added to another three-digit number 984 to give a four digit number 13b7, which is divisible by 11. What is the value of (a + b)?
(A) 8
(B) 10
(C) 14
(D) 17
(E) 19
Rationale: 4 a 3
9 8 4
13 b 7
=> a + 8 = b ...(1)
13b7 is divisible by 11
=> (1 + b) - (3 + 7) is 0 or divisible by 11
=> (b - 9) is 0 or divisible by 11 ...(2)
Assume that (b - 9) = 0
=> b = 9
Substituting the value of b in (1),
a + 8 = b
a + 8 = 9
=> a = 9 - 8 = 1
If a = 1 and b= 9,
(a + b) = 1 + 9 = 10
10 is there in the given choices. Hence B is the answer.
Answer: (B) 10
Question: If x^2 - 9 = 0 and x > 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 + 5x - 24
Rationale: x^2-9 = 0
x= +3 or x = -3
if we substitute x= 3 in the equation x^2 +5x-24 = 9+15-24 = 0
E is also the answer
Answer: (E)  x^2 + 5x - 24
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 6 2/3%
(B) 6 8/3%
(C) 6 2/6%
(D) 6 3/3%
(E) 6 2/1%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3
= 6 2/3%
Answer: A
Answer: (A) 6 2/3%
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 500-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $200?
(A) 1,108
(B) 4,100
(C) 2,108
(D) 2,124
(E) 2,256
Rationale: We have $200 and we have to maximize the number of hot dogs that we can buy with this amount.
Let's try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money, which in this case is 500 for $22.95.
For the sake of calculation, let's take $23. 23x8 gives 184 ,i.e. a total of 500x8 = 4000 hot dogs . We are left with ~$16. Similarly, let's use $3 for calculation. We can buy 5 20-pack hot dogs (3x5), a total of 20x5 = 100 hot dogs. So we have 4100 hot dogs.
2108 looks far-fetched (since we are not likely to be left with > $1.55). Hence, (b) 4100 (ANSWER B)
Answer: (B) 4,100
Question: A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?
(A) 2 m
(B) 3 m
(C) 4 m
(D) 7 m
(E) 9 m
Rationale: Let radius of the outer circle be R and radius of the inner circle be r.
Circumference of the outer circle =
Circumference of the inner circle =
But,
or, R - r =
Thus, width of the road = 7 m
D
Answer: (D) 7 m
Question: The total of the ages of Amar, Akbar and Anthony is 45 years. What was the total of their ages four years ago ?
(A) 29 years
(B) 24 years
(C) 20 years
(D) 30 years
(E) 21 years
Rationale: Explanation:
Required sum = (45 - 4 x 4) years = (45 - 16) years = 29 years.
Answer: Option A
Answer: (A) 29 years
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 14 minutes, how much time will she spend doing yoga? (rounded to minutes)
(A) 10 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 25 min.
Rationale: The ratio is 2:3 = gym:ride, so (14)(3/2) = 21 minutes at the gym, and 21 + 14 = 35 minutes exercise, so (2/3)(35) = 23 minutes yoga.
Answer: D
Answer: (D) 23 min.
Question: A boy is travelling from his home to school at 3 km/hr and reached 7 min late. Next day he traveled at 6 km/hr and reached 8 min early. Distance between home and school?
(A) 1.2km
(B) 1.3km
(C) 1.4km
(D) 1.5km
(E) 1.6km
Rationale: Let the distance be x
T1 = x/3 hr
T2 = x/6hr
Difference in time = 7+8 = 15 =1/4hr
x/3-x/6 = 1/4
x/6 = 1/4
x = 1.5 km
Answer is D
Answer: (D) 1.5km
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly 7 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
(A) 25/3
(B) 32/3
(C) 35/3
(D) 40/3
(E) 44/3
Rationale: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.
(x+1.5x) = 2.5x = 1/7 of the capacity of the whole pool per hour.
The rate of the fast pump is (1.5/2.5)*1/7 = 3/35 of the whole pool per hour.
The time it takes the faster pump to fill the pool would be 35/3 hours.
The answer is C.
Answer: (C) 35/3
Question: Number A is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that A+K is odd?
(A)  1/2
(B)  2/3
(C)  3/4
(D)  4/7
(E)  5/8
Rationale: All primes except 2 are odd, thus A must be odd. For A + K = odd + K to be odd, K must be even.
There are 7 multiples of 5 between 10 and 40, inclusive: 10, 15, 20, 25, 30, 35, and 40. Out of them 3 (15, 25, and 35) are odd.
Therefore the probability that A + K is odd is 4/7.
Answer: D.
Answer: (D)  4/7
Question: Find the value of (1-(1/3))(1-(1/4))(1-(1/5))….(1-(1/100)).
(A) 1/50
(B) 4/50
(C) 9/50
(D) 7/50
(E) None of them
Rationale: Given expression = (2/3)*(3/4)*(4/5) *…….* (99/100) = 2/100 = 1/50
Answer is A.
Answer: (A) 1/50
Question: On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
Rationale: 30% of 60 will be accommodated at XYZ = 18
70% of 60 will be accommodated at ABC = 42
55% of 60 prefer XYZ = 33
45% of 60 prefer ABC = 27
we were asked to find number of maximum possible people who were accommodated at hotels they dont prefer,
So for 18 XYZ accommodations , we can choose 18 ABC preferring people (so xyz is filled up) Here 18 were given to people who don't prefer XYZ
for 42 ABC accommodations, we can choose 33 ABC preferring people and rest to ABC. Here 33 were given to people who don't prefer ABC.
So total people who were accommodated at hotel they dont prefer = 18+33 = 51
So answer is A.
Answer: (A) 51
Question: Farmer Brown purchased several rabbits (male and female) and bred them on his farm. The rabbit population grew 500% the first year. The population grew 900% the second year. What was the percent, population growth for the two year?
(A)  100%
(B)  5,000%
(C)  2000%
(D)  2500%
(E)  500%
Rationale: Let x be the initial population of rabbits Farmer Brown purchased; then, x + 5x is the rabbit population after the first year, and 5x + 9(5x) = 50x is the rabbit population after the second year.
Now, 50x/x = 50.
So, the percent, population growth is for the two years is 5,000%.
Answer is B
Answer: (B)  5,000%
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 200
(B) 220
(C) 240
(D) 250
(E) 260
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: Option C
Answer: (C) 240
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.0?
(A) 12.6.
(B) 14.4.
(C) 15.8.
(D) 16.2.
(E) 16.4.
Rationale: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.0
= 6*0 + 2*7.2 + 8 - 6.0
= 0 +14.4 +2
16.4
Answer E
Answer: (E) 16.4.
Question: If the sum of a number and its square is 182, what is the number?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Sol.
Let the numbers be x.
Then, x + x2 = 182
⇔ x2 + x - 182 = 0
⇔ (x+14)(x-13) = 0
⇔ x = 13.
Answer A
Answer: (A) 13
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
(A) 20029
(B) 20000
(C) 20289
(D) 20027
(E) 20026
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Answer: (B) 20000
Question: 54671 - 14456 - 35466 = ?
(A) 2449
(B) 5449
(C) 6749
(D) 6449
(E) 4749
Rationale: E
If we calculate we will get 4749
Answer: (E) 4749
Question: A bag contains 6 white and 4 black balls. 2 balls are drawn at random.
Find the probability that they are of same color.
(A) 7/15
(B) 8/15
(C) 6/15
(D) 3/5
(E) 8/5
Rationale: let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10C2=(10*9)/(2*1)=45
Let E=event of getting both balls of same color
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
answer option A)7/15
Answer: (A) 7/15
Question: How many different 4-digit numbers can be written using the digits 1 to 8 without repetition such that the number always contains the digit 2?
(A) 360
(B) 560
(C) 760
(D) 840
(E) 1260
Rationale: The most restrictive case. We should have a two.
No repetition. Numbers range from 1 to 8.
= 1*7*6*5 = 210 ways we can write if '2' is in the first position.
= 4*(210)
=840 ways.
Another method.
Without restriction for 8 digits- 8*7*6*5 = 1680 Ways we can write.
Without restriction for 7 digits- 7*6*5*4 = 840 Ways.
With restriction = 1680 - 840 = 840 Ways.
ANSWER:D
Answer: (D) 840
Question: Six years ago, P was half of Q in age. If the ratio of their present ages is 3:4, what will be the total of their present ages
(A) A)21
(B) B)34
(C) C)45
(D) D)25
(E) E)26
Rationale: Explanation:
Let the present age of P and Q be 3x and 4x respectively.
Six years ago, P was half of Q in age
=> 2(3x – 6) = (4x – 6)
=> 6x – 12 = 4x – 6
=> 2x =6
=> x = 3
7x=7*3=21
Answer: Option A
Answer: (A) A)21
Question: I sold a book at a profit of 10%. Had I sold it for $100 more, 15% would have been gained. Find the cost price?
(A) $2000
(B) $2500
(C) $3000
(D) $3120
(E) $1540
Rationale: 115% of cost - 110% of cost = $100
5% of cost = $100
cost = 100*100/5 = $2000
Answer is A
Answer: (A) $2000
Question: Persons A and B. Person A picks a random no. from 1 to 1000.Then person B picks a random no. from 1 to 1000. What is the probability of B getting no. greater then what A has picked.
(A) 0.3995
(B) 0.4995
(C) 0.5995
(D) 0.6995
(E) 0.7995
Rationale: Probability of A choosing 1 and B greater = (1/1000)*(999/1000);
Probability of A choosing 2 and B greater = (1/1000)*(998/1000);
Probability of A choosing 3 and B greater = (1/1000)*(997/1000); ...;
Probability of A choosing 998 and B greater = (1/1000)*(2/1000);
Probability of A choosing 999 and B greater = (1/1000)*(1/1000);
Total = (1/1000)*(1/1000)*(999+998+997+...+2+1) = (1/1000)*(1/1000)*(999*1000/2) = 0.4995
ANSWER:B
Answer: (B) 0.4995
Question: In a Shop, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 70%
(B) 50%
(C) 100%
(D) 60%
(E) 55%
Rationale: CP.= Rs. 100. => Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Req = (295/420*100) == > 70%
ANSWER A
Answer: (A) 70%
Question: What is the square root of 625, divided by 5?
(A) 9
(B) 36
(C) 5
(D) 6
(E) 1
Rationale: Square root is a number times itself
Square root of 625=25, 25/5=5
(C)5
Answer: (C) 5
Question: In a senior secondary school, 80 students play hockey or football. The number that play football is 5 more than twice the number that play hockey. If the 15 students play both games and every student in the school playsat least one game, find:
The number of students that play football?
(A) 10
(B) 15
(C) 20
(D) 30
(E) 35
Rationale: number who play hockey ---- x
number who play football -- 2x+5
x + 2x+5 = 80
x = 25
so 25 play hockey, 55 play football, and 15 play both
Answer is B
Answer: (B) 15
Question: The average of first 10 prime numbers is?
(A) 12.5
(B) 12.4
(C) 12.9
(D) 12.3
(E) 12.1
Rationale: Sum of 10 prime no. = 129
Average = 129/10 = 12.9
Answer: C
Answer: (C) 12.9
Question: Sandy had $210 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?
(A) $240
(B) $300
(C) $360
(D) $420
(E) $480
Rationale: Let the money Sandy took for shopping be x.
0.7x = 210
x = 300
The answer is B.
Answer: (B) $300
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.65 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 65 sec
(B) 55 sec
(C) 48 sec
(D) 33 sec
(E) 42 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.65 = 1.75 km = 1750 m.
Required time = 1750 * 3/125
= 42 sec.
Answer:E
Answer: (E) 42 sec
Question: 4 apple and 3 mangoes costs rs.34, 2 mangoes and 5 oranges costs 49, 3 oranges and 6 apples costs 54. What is the price of 1 apple?
(A) 151/19
(B) 151/17
(C) 151/18
(D) 151/16
(E) 153/15
Rationale: 4A+3M = 34 -----(1)
2M+5O = 49 -----(2)
3O+6A = 54 -----(3)
from (2) and (3)
30A-6M = 123 -----(4)
from (1) and (4)
A = 191/38
substituting in (1) and (3)
M= 88/19
O = 151/19
ANSWER:A
Answer: (A) 151/19
Question: By how much is three-fifth of 390 greater than four-seventh of 210 ?
(A) 90
(B) 100
(C) 110
(D) 114
(E) 130
Rationale: Explanation:
3/5 of 390 - 4/7 of 210 = 234 - 120 = 114.
Answer: D
Answer: (D) 114
Question: What is the median from the below series
77, 72, 68, 76, 78, 88, 84, 86, and 81
(A) 72
(B) 76
(C) 78
(D) 77
(E) 81
Rationale: Ordering the data from least to greatest, we get:
68, 72, 76, 77, 78, 81, 84, 86, 88
The median numbers was 78. (Four number were higher than 78 and four were lower.)
C
Answer: (C) 78
Question: How many of the integers between 10 and 40 are even ?
(A) 21
(B) 20
(C) 15
(D) 10
(E) 9
Rationale: Number start between 10 to 40 is 30 numbers
half of them is even..which is 15
ANSWER:C
Answer: (C) 15
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 7
(B) 8
(C) 6
(D) 9
(E) 5
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
Answer: D
Answer: (D) 9
Question: If x is an integer, then y(y – 1)(y – l) must be evenly divisible by three when l is any of the following values EXCEPT
(A) -4
(B) -3
(C) -2
(D) 2
(E) 5
Rationale: We have the product of 3 integers: (y-1)y(y-l).
Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to guarantee that at least one integer out of y, (y – 1), and (y – l) is divisible by 3 these numbers must have different remainders upon division by 3, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 3.
Next, if l=-2 then we'll have (y-1)x(y+2)=(y-1)x(y-1+3) --> which means that (y-1) and (y+2) will have the same remainder upon division by 3. Thus for l=-2 we won't be sure whether (y-1)x(y-l) is divisible by 3.
Answer: C.
Answer: (C) -2
Question: A customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 100 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?
(A) (B + 2)/2.
(B) (B + 2)/5.
(C) (2B + 200)/3.
(D) (B + 2)/3.
(E) (B - 2)/6.
Rationale: P = 2w - 100
thus total price in cents as given should be
2w-200 +w = 100B
3w - 200 = 100 B
3w = 100 B+200
3w =b+2 (in dollars)
w/2 = (b+2)/6
Ans:B
Answer: (B) (B + 2)/5.
Question: If a lies in the range (-5,4) then which of the following statements must be true?
(A) a^4 >a^3 > a^2 > a
(B) a > a^2 > a^3 > a^4
(C) a^4 > a^2 > a^3 >a
(D) a^2 > a^4 > a^3 >a
(E) a^2 > a^4 > a > a^3
Rationale: consider any number from the given range (-5, +4)..let a=-1/2
then a^2= 1/4
a^3=-1/8
a^4=1/16
so we have a^2>a^4>a^3>a
Ans D
Answer: (D) a^2 > a^4 > a^3 >a
Question: Choose the missing terms out of the given alternatives.
BY, CX, DW, EV, FU, ?
(A) EF
(B) GH
(C) GT
(D) DW
(E) KN
Rationale: C
GT
The first letter moves one step forward. The second letter moves one step backward.
Answer: (C) GT
Question: If 63 percent of a class answered the first question on a certain test correctly, 50 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A) 24%
(B) 27%
(C) 30%
(D) 33%
(E) 36%
Rationale: 63% answered the first question correctly and 20% answered neither correctly.
Then 17% missed the first question but answered the second question correctly.
Then the percent who answered both correctly is 50% - 17% = 33%.
The answer is D.
Answer: (D) 33%
Question: A bicycle wheel has a diameter of 0.66m. How many complete revolutions does it make in 1km?
(A) 246
(B) 448
(C) 1408
(D) 482
(E) 223
Rationale: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.66m ) = 482.5. Hence 482 complete revolutions.
Answer D
Answer: (D) 482
Question: If the length of an edge of cube M is thrice the length of an edge of cube N, what is the ratio of the volume of cube N to the volume of cube M?
(A) 2/13
(B) 1/27
(C) 1/5
(D) 1/9
(E) 1/8
Rationale: The length of cube N = 1;
The length of cube M = 3;
The ratio of the volume of cube N to the volume of cube M = 1^3/3^3 = 1/27
Answer : B
Answer: (B) 1/27
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12700 after a year?
(A) 3630
(B) 9232
(C) 8828
(D) 2387
(E) 3810
Rationale: 6300:4200:10500
3:2:5
3/10 * 12700 = 3810
Answer: E
Answer: (E) 3810
Question: A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is
(A) 40
(B) 30
(C) 55
(D) 73
(E) 52
Rationale: A
40
Let distance = x km and usual rate = y kmph.
Then, x/y - x/(y+3) = 40/60 --> 2y (y+3) = 9x ----- (i)
Also, x/(y-2) - x/y = 40/60 --> y(y-2) = 3x -------- (ii)
On dividing (i) by (ii), we get: x = 40.
Answer: (A) 40
Question: A Jar contains a mixture of AB in the ratio 3:2. When 20 L of Mixture is replaced with liquid B, ratio becomes 2:3. How many liters of liquid A was present in mixture initially.
(A) 12
(B) 15
(C) 16
(D) 20
(E) 36
Rationale: 20 litres of mixture that is replaced will contain 12 litres of A and 8 litres of B (as A:B = 3:2)
Let the initial volume of the mixture be 3K + 2K = 5K
So by condition ,
[ 3K-12]/ [ 2K-8+20 ] = 2/3 => 9K-36 = 4K-16+40 => 5K= 60
Solve for K which is K = 12
So initial volume of liquid A = 3K = 36 litres
Answer : E
Answer: (E) 36
Question: N is a positive integer. When N + 1 is divided by 9, the remainder is 1. What is the remainder when N is divided by 9?
(A) 0
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: N+1 = 9a+1
i.e. N+1 = 10, 19, 28, 37, ... etc.
i.e. N = 9, 18, 27, 36, ... etc.
When N is divided by 9 Remainder is always 0
Answer: A
Answer: (A) 0
Question: An association of mathematics teachers has 1,260 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 65 percent of the votes cast?
(A) 75%
(B) 58%
(C) 42%
(D) 27.08%
(E) 25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 525
Since , winning candidate received 65 percent of the votes cast
Number of votes for winning candidate = (65/100)*525 = 341.25
Percent of total membership that voted for winning candidate = (341.25/1260)*100 = 27.08%
Answer D
Answer: (D) 27.08%
Question: A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/5-inch increase in the length of the shoe. If the largest size of this shoe is 20% longer than the smallest size, how long, in inches, is the shoe in size 15?
(A) 8.6
(B) 9.8
(C) 10.4
(D) 11.2
(E) 12.6
Rationale: Let x be the length of the size 8 shoe.
Then 0.2x = 9/5
x = 9 inches
The size 15 shoe has a length of 9 + 7/5 = 10.4 inches
The answer is C.
Answer: (C) 10.4
Question: A sealed envelope contains a card with a single digit written on it. Three of the following statements are true and one is false.
I. The digit is 1.
II. The digit is not 2.
III. The digit is not 9.
IV. The digit is 8.
Which one of the following must necessarily be correct?
(A) III
(B) I
(C) IV
(D) II
(E) NONE
Rationale: Three of the given statements are true. So both II and III are correct, and the given number is one of 1 or 8. So option A is correct.
Answer:A
Answer: (A) III
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 24.5
(B) 28.5
(C) 30
(D) Data inadequate
(E) None of these
Rationale: Explanation:
Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer: Option C
Answer: (C) 30
Question: In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 40% of all the employees are men .What % of all the employee went to the picnic?
(A) 32%
(B) 34%
(C) 35%
(D) 36%
(E) 37%
Rationale: total men in company 40% means total women in company 60%(assume total people in company 100%)
no of men employees attended picnic=40x(20/100)=8
no of women employees attended picnic=60x(40/100)=24
total percentage of employees attended the picnic=8+24=32%
ANSWER:A
Answer: (A) 32%
Question: 12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/3 of the same job. How many days will 10 men and 8 women together take to complete the same job?
(A) 6
(B) 13 1â„2
(C) 17
(D) Data inadequate
(E) None of these
Rationale: 12 M Ã— 18 = 12 W Ã— 18 Ã— 3/1
\ w = 1/3 M
10M + 8W = 10M + 8 Ã— 1/3M = 12 2/3 M
\12 2/3 men can complete the same work
in 12Ã—18/12 2/3=17days
Answer C
Answer: (C) 17
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 11
(B) 10
(C) 99
(D) 28
(E) 73
Rationale: Explanation:
7*5: 5*x = 7:10
x = 10
Answer: B
Answer: (B) 10
Question: Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
(A) 1/7
(B) 2/11
(C) 3/10
(D) 4/13
(E) 5/17
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
Answer: (C) 3/10
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
(A) 10
(B) 12
(C) 16
(D) 18
(E) 21
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Answer: (B) 12
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is?
(A) 3/8
(B) 3/2
(C) 3/1
(D) 3/8
(E) 3/9
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y
==> x/y
= 3/2.
Answer:B
Answer: (B) 3/2