mathewhe/aqua_rat huggingface dataset:
Question: A wooden box of dimensions 8 m x 10 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 5 cm x 6 cm. The maximum number ofboxes that can be carried in the wooden box, is
(A) 9800000
(B) 1000000
(C) 7500000
(D) 4000000
(E) None of these
Rationale: Explanation: Number = (800*1000*600)/4*5*6 = 4000000 Answer: D
Answer: (D) 4000000
Question: What will be remainder when 17200 is divided by 18 ?
(A) 17
(B) 16
(C) 14
(D) 1
(E) 2
Rationale: When n is even. (xn - an) is completely divisibly by (x + a)
(17200 - 1200) is completely divisible by (17 + 1), i.e., 18.
(17200 - 1) is completely divisible by 18.
On dividing 17200 by 18, we get 1 as remainder.
Option D
Answer: (D) 1
Question: A person travels equal distances with speeds of 7 km/hr, 8 km/hr and 9 km/hr and takes a total time of 47 minutes. The total distance is?
(A) 6 km
(B) 3 km
(C) 7 km
(D) 9 km
(E) 2 km
Rationale: Let the total distance be 3x km.
Then, x/7 + x/8 + x/9 = 47/60
36x/95 = 47/60 => x = 2.07.
Total distance = 3 * 2.07 = 6.2 km.
Answer:A
Answer: (A) 6 km
Question: Pipes A and B can fill a cistern in 20 and 60 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 30
(B) 45
(C) 32
(D) 18
(E) 19
Rationale: :
1/20 + 1/60 = 1/15
15 * 2 = 30.Answer:A
Answer: (A) 30
Question: If 1/(x+1)+1/(x-1)=1/(x-1), what is the value of x?
(A) 2
(B) -2
(C) 1
(D) -1
(E) 5
Rationale: If we solve the question, we get x=1.
Option: C
Answer: (C) 1
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following:
I. 6
II. 4
III. 11
(A) I only
(B) II,III only
(C) III only
(D) I,III only
(E) II only
Rationale: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 3, 4, 5, 6, 7 and 8, then the sum = 33.
33 is divisible by 11
33 is NOT divisible by 4
33 is NOT divisible by 6
There's only one answer that 'fits' with these facts. Answer : C
Answer: (C) III only
Question: The greatest number which on dividing 1557 and 2037 leaves remainders 7 and 5 respectively, is:
(A) 123
(B) 127
(C) 2
(D) 305
(E) 505
Rationale: Explanation:
Required number = H.C.F. of (1557 - 7) and (2037 - 5)
= H.C.F. of 1550 and 2032 = 2. Answer: C
Answer: (C) 2
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 2 kmph
(C) 7 kmph
(D) 8 kmph
(E) 3 kmph
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer:A
Answer: (A) 1 kmph
Question: 1,2,3,4,5,6,7 are arranged such that sum of two successive numbers is a prime number. For example, 1234765 (i.e. 1+2=3, 2+3=5, 3+4=7....)
1. How many such possible combinations occur?
2. How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
3. How many numbers will come on 4th position(xxx_xxx)?
(A) How many such possible combinations occur?
(B) How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
(C) How many numbers will come on 4th position(xxx_xxx)?
(D) W3
(E) 24
Rationale: We have to follow a systematic approach for this question. We know that if at all two consecutive numbers be prime, they should not be even in the first place. So we arrange even numbers in even places, odd numbers in odd places.
2 should not have 7 as its neighbor
4 should not have 5 as its neighbor
6 should not have 3 as its neighbor
Case 1:
__ 2 ____ 4 ____ 6 __
x7 x7,5 x5,3 x3
So fix, 3 or 1 in between 2 and 4. We get the following options with reverse case also.
5234167, 7614325
5234761, 1674325
1234765, 5674321
3214765, 5674123
Case 2:
__ 2 ____ 6 ____ 4 __
x7 x7,3 x3,5 x5
5216743, 3476125
3256147, 7416523
3256741, 1476523
1256743, 3476521
Case 3:
__ 4 ____ 2 ____ 6 __
x5 x5,7 x7,3 x33412567, 7652143
7432165, 5612347
7432561, 1652347
1432567, 7652341
Answer 1: Total possibilities are 24.
Answer 2: 4 possibilities.
Answer 3: 3 possibilities.
Answer:B
Answer: (B) How many possible combination occurs if first number is 1/7 and last number is 7/1 (i.e 1xxxxx7 or 7xxxxx1)?
Question: The length of rectangle is thrice its breadth and its perimeter is 120 m, find the area of the rectangle?
(A) 432 sq m
(B) 356 sq m
(C) 452 sq m
(D) 428 sq m
(E) 675 sq m
Rationale: 2(3x + x) = 120
l = 45 b = 15
lb = 45 * 15 = 675
ANSWER:E
Answer: (E) 675 sq m
Question: The average runs scored by a batsman in 25 matches is 45. In the next 7 matches the batsman scored an average of 15 runs. Find his average in all the 32 matches?
(A) 31355
(B) 38.44
(C) 29.55
(D) 97.66
(E) 45.66
Rationale: Total score of the batsman in 25 matches = 1125.Total score of the batsman in the next 7 matches = 105.Total score of the batsman in the 32 matches = 1230.Average score of the batsman = 1230/32 = 38.44.Answer: B
Answer: (B) 38.44
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 10000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?
(A) $40000
(B) $15000
(C) $12000
(D) $10000
(E) $9000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($10,000*2)*2=$40,000 (after 9 years investment will become $10,000*2=$20,000 and in another 9 years it'll become $20,000*2=$40,000).
Answer: A.
Answer: (A) $40000
Question: Car A leaves the airport at 9:00 am and travels at a constant rate of 30 km per hour. Car B leaves the airport at 9:30 am and travels in the same direction along the same highway at a constant rate of 34 km per hour. At what time will Car B be 12 km ahead of Car A?
(A) 3:45 pm
(B) 4:00 pm
(C) 4:15 pm
(D) 4:30 pm
(E) 4:45 pm
Rationale: At 9:30 am, Car A will be 15 km ahead of Car B.
Car B travels at a rate 4 km per hour faster than Car A.
Car B needs to travel 27 km more than Car A in order to be 12 km ahead.
This will take 27 km/4 km per hour=6.75 hours.
Car B will be 12 km ahead at 4:15 pm.
The answer is C.
Answer: (C) 4:15 pm
Question: Shop Offered 20% offer for every Shirt, Smith bought a shirt at Rs. 560. and What was the shop's original selling Price?
(A) 500
(B) 550
(C) 600
(D) 700
(E) 750
Rationale: SP* (80/100) = 560
SP= 70 * 100 => CP = 700
Answer:D
Answer: (D) 700
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
(A) 15 : 8
(B) 15 : 9
(C) 15 : 5
(D) 15 : 2
(E) 15 : 1
Rationale: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15 : 8
Answer: A
Answer: (A) 15 : 8
Question: Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?
(A) Rs.1104
(B) Rs.1000
(C) Rs.934
(D) Rs.1210
(E) Rs.1110
Rationale: Assume that cost of keeping a cow for 1 day = c ,
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
= 20c + 40g = 46
= 10c + 20g = 23 ---(1)
Given that 5g = c
Hence equation (1) can be written as 10c + 4c = 23 =14c =23
= c=23/14
cost of keeping 50 cows and 30 goats for 1 day
= 50c + 30g
= 50c + 6c (substituted 5g = c)
= 56 c = 56×23/14
= 92
Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104 ANSWER : A
Answer: (A) Rs.1104
Question: Find the average of the series : 312, 162, 132, 142 and 122?
(A) 117
(B) 866
(C) 168
(D) 126
(E) 174
Rationale: Average = (312 + 162 + 132 + 142 + 122)/5 = 870/5
= 174
Answer:E
Answer: (E) 174
Question: Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/11 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
(A) 21
(B) 33
(C) 39
(D) 60
(E) 65
Rationale: The total number of the people in the room must be a multiple of both 7 and 11 (in order 3/7 and 5/11 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 11, which is 77.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 77 people in the room.
Therefore there are 3/7*77=33 people in the room under the age of 21.
Answer: B.
Answer: (B) 33
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what Y percent of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which Y is 40% of 80
hence, D is the answer
Answer: (D) 40
Question: Train X and Y, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train X left at 4 pm traveling at a speed of 60 miles per hour, and train Y left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?
(A) 4.05pm
(B) 5.05pm
(C) 6.05pm
(D) 7.05pm
(E) 9.05pm
Rationale: First, since X has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles
Then remaining distance to be traveled will be 455 - 105 = 350 miles
Now, using relative rates (105)(t) = 350
This gives 10/3 hours
Now 5.45pm + 10/3 hours gives us 9.05pm
Hence answer is E
Answer: (E) 9.05pm
Question: What is the least common multiple of 15, 18, and 34?
(A) 60
(B) 120
(C) 240
(D) 360
(E) 1530
Rationale: Let us first write the numbers in the form of prime factors:
15 = 3*5
18 = 2*3^2
34 = 2 * 17^1
The LCM would be the largest powers of the prime numbers from all these three numbers.
Hence LCM = 1530
Option E
Answer: (E) 1530
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
(A) A)25
(B) B)28
(C) C)20
(D) D)21
(E) E)18
Rationale: M = 15
S = 5
DS = 15 + 10 = 25
Answer:A
Answer: (A) A)25
Question: Let the least number of six digits,which when divided by 4,6,10 and 15 leaves in each case the same remainder of 2, be N. The sum of the digits in N is :
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Solution
Least number of 6 digital is 100000. L.C.M. of 4,6,10 and 15 = 60.
on dividing 100000 by 60, the remainder obtained is 40.
So, least number of 6 digits divisible by 4,6,10 and 15 = 100000 +(60 - 40) = 100020.
So, N = (100020 + 2) = 100022. sum of digits in N = (1 + 2 + 2) = 5. Answer C
Answer: (C) 5
Question: When a natural number N is successively divided by 10,20,30,40. the remainders are 50,60,70,80. What will be the sum of the remainders if the order of the division is reversed?
(A) 16
(B) 14
(C) 28
(D) 11
(E) 9
Rationale: 10 20 30 40
50 60 70 80
leave the top right- most number 8
start with bottom right-most number 5
80*30+70=2470
2470*20+60=49460
49460*10+50=494650
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 28
Hence, the correct option is C
Answer: (C) 28
Question: On a certain plane, 2/5 of the passengers speak Tamil and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?
(A) 12
(B) 75
(C) 80
(D) 94
(E) 96
Rationale: Assume the total members = x
Tamil = .4x
Hebrew = .75x
Tamil + Hebrew = 1.15x, but this is not possible hence 15 people speak both languages.
Only Tamil = .25x, Only Hebrew = .6x, both = .15x
Since these are all people, all of these should be whole numbers.
Checking the options:
A. 12. Only Hebrew = 12*0.6 = 7.2 We do not get the people as whole numbers. INCORRECT
B. 15. Only Tamil = 0.25*15 Again we do not get the people as whole numbers. INCORRECT
C. 80 Only Tamil = .25*80 = 20, Only Hebrew = .6*80 = 48, both = .15*80 = 12. We have the people as whole numbers. CORRECT
D. 94
E.96
Since we have to find the lowest number, no need to calculate for the rest of the options.
Correct Option: C
Answer: (C) 80
Question: A man tosses three coins in the air. When they land, he finds that two of the coins have heads up and one has tails up.
What is the probability that when the coins are tossed again, they will land again with two heads up and one tails up.
Please note that the coins are unbiased.
(A) 50%
(B) 58%
(C) 45%
(D) 61%
(E) 45%
Rationale: A
50%
Explanation:
When the coins are tossed there can be eight possible outcomes (2*2*2)
HHH
HTT
HTH
HHT
TTT
THH
THT
TTH
If you find out, we have only four favorable outcomes. Also, the events here are independent and thus we can calculate the probability by using these only.
Thus the probability is 50 percent.
Answer: (A) 50%
Question: A completes a work in 12 days and B complete the same work in 20 days. If both of them work together, then the number of days required to complete the work will be
(A) 8 days
(B) 9 days
(C) 7.5 days
(D) 12 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 20/ 32 = 7.5 days.
C
Answer: (C) 7.5 days
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
(A) 3.
(B) 1/2.
(C) 2.
(D) 1/3.
(E) 6.
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 24 and L be 8, 24 - 8 = (24 + 8 )/2
A
Answer: (A) 3.
Question: A bag contains 8 red and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 8/15
(B) 2/3
(C) 5/8
(D) 1/4
(E) 5/7
Rationale: Total number of balls = 8+7 = 15
number of white balls = 8
Probability = 8/15
Answer is A
Answer: (A) 8/15
Question: If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
(A) 54
(B) 63
(C) 75
(D) 86
(E) 98
Rationale: (a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)
Therefore, the product should have factors with a difference of 2.
63 = 7*9, so this is a possible value for the original expression.
The answer is B.
Answer: (B) 63
Question: a light flashes every 12 seconds, how many times will it flash in ? of an hour?
(A) 550
(B) 300
(C) 650
(D) 700
(E) 750
Rationale: 1flash=12sec
for 1 min=5flashes
so for 1 hour=5*60=300 flashes.
ANSWER:B
Answer: (B) 300
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum D of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A)  6x
(B)  4x
(C)  5x/3
(D)  3x/2
(E)  3x/5
Rationale: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<D<5x --> only option B fits.
Answer: B.
Answer: (B)  4x
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
(A) 120990
(B) 120950
(C) 120970
(D) 120960
(E) 120980
Rationale: 8!(2!)(2!)=8×7×6×5×4×3×2×1/(2×1)(2×1)
=10080
In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.
Number of ways to arrange these vowels among themselves =4!/2!=4×3×2×12×1=12
Hence, required number of ways
=10080×12=120960
Answer: D
Answer: (D) 120960
Question: How many odd, positive divisors does 440 have?
(A) 3
(B) 8
(C) 12
(D) 15
(E) 24
Rationale: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=3 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: A.
Answer: (A) 3
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability W that each number is different ?
(A) A.18/25
(B) B.4/5
(C) C.81/100
(D) D.9/10
(E) E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability W= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: (A) A.18/25
Question: In a garment industry, 12 men working 8 hours per day complete a piece of work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required is:
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 15 : 8 :: 12 : x
=> 8 x 15 x x = 10 x 8 x 12
=> x = 10 x 8 x 12 / (8 x 15)
=> x = 8
Answer : D
Answer: (D) 8
Question: In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, what part of the total number of students is present ?
(A) 17/25
(B) 18/49
(C) 23/30
(D) 23/36
(E) 29/36
Rationale: Girls = 3/5, boys are 2/5
Absentees are (2/9)*(3/5) + (1/4)*(2/5) = 7/30
Present Students are 23/30
ANSWER:C
Answer: (C) 23/30
Question: For any positive integer b, the sum of the first b positive integers equals b(b+1)/2 . If a and b are positive integers and a > b, what is the sum of all the integers between a and b, inclusive?
(A)  a(a+1)/2 + b(b+1)/2
(B)  a(a+1)/2 - b(b-1)/2
(C)  a(a+1)/2 - b(b+1)/2
(D)  a(a+1)/2 + b(b-1)/2
(E)  a(n+1)/2 - b(a-1)/2
Rationale: The sum of all the integers between a and b,inclusiveis the sum of the first a positive integersminusthe sum of the first b-1 positive integers.
The sum of the first a positive integers is a(a+1)/2;
The sum of the first b-1 positive integers is (b-1)b/2;
Therefore the answer is a(a+1)/2 - (b-1)b/2.
Answer: B.
Answer: (B)  a(a+1)/2 - b(b-1)/2
Question: Two pipes A and B can separately fill a tank in 10 and 15 minutes respectively. A third pipe C can drain off 20 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 150 liters
(B) 540 liters
(C) 200 liters
(D) 560 liters
(E) 580 liters
Rationale: 1/10 + 1/15 - 1/x
= 1/15
x = 10
10 * 20 = 200
Answer:C
Answer: (C) 200 liters
Question: If 2x = 3√32, then x is equal to :
(A) 3/5
(B) 5/3
(C) 15
(D) 25
(E) NOne
Rationale: Sol.
2x = 3√32 ⇔ 2x = (32)1/3 = (25)1/3 = 25/3 ⇔ x = 5/3.
Answer B
Answer: (B) 5/3
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 7:9
(B) 7:3
(C) 7:2
(D) 7:9
(E) 7:1
Rationale: Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3
Answer:B
Answer: (B) 7:3
Question: The speed of a boat in upstream is 30 kmph and the speed of the boat downstream is 50 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 40,10 kmph
(B) 38,10 kmph
(C) 40,70 kmph
(D) 78,10 kmph
(E) 70,12 kmph
Rationale: Speed of the boat in still water
= (30+50)/2
= 40 kmph. Speed of the stream
= (50-30)/2
= 10 kmph.
Answer:A
Answer: (A) 40,10 kmph
Question: An employee identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
(A) 211
(B) 216
(C) 1075
(D) 1080
(E) 2160
Rationale: For the case when the hundreds digit is repeated: XXY or XYX
X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).
Y can take 9 values (10 digits minus the one we used for X).
To account for XXY or XYX case we are multiplying by 2.
So, for this case we'd have 8*9*2.
For the case when the tens and units digits are repeated: XYY
X can take 8 values (2, 3, 4, 5, 6, 7, 8, 9).
Y can take 9 values (10 digits minus the one we used for X).
Now, 8*9 also give number 200 and we need numbers greater than 200, so for this case we'd have 8*9 - 1.
Last step, since there are 5 vowels, then the final answer would be 5*(8*9*2 + 8*9 - 1) = 1,075.
Answer: C.
Answer: (C) 1075
Question: The positive two-digit integers a and b have the same digits, but in reverse order. Which of the following must be a factor of a + b?
(A) 6
(B) 9
(C) 10
(D) 55
(E) 14
Rationale: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9
and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187
55 is multiple of 11
So, Answer D
Answer: (D) 55
Question: A bag contains 3 red, 5 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
(A) 2/7
(B) 3/5
(C) 3/11
(D) 1/4
(E) 7/16
Rationale: Total number of balls = 3+5+4 = 12
n(S) = 12C3 = 12*11*10 / 3*2 = 220
n(E) = 3C1 * 5C1 * 4C1 = 3*5* 4 = 60
Probability = 60/220 = 3/11
Answer is C
Answer: (C) 3/11
Question: By selling 15 pencils for a rupee a man loses 25%. How many for a rupee should he sell in order to gain 25%?
(A) 8
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: 75% --- 15
125% --- ?
75/125 * 15 = 9
Answer: B
Answer: (B) 9
Question: 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
(A) 11
(B) 40
(C) 88
(D) 76
(E) 26
Rationale: Let 1 man's 1 day work = x and 1 woman's 1 day work = y.
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving these two equations, we get:
x = 11/400 and y = 1/400
1 woman's 1 day work = (1/400 * 10) = 1/40.
Hence, 10 women will complete the work in 40 days.
Answer:B
Answer: (B) 40
Question: A and B invest money in the ratio 3:4 and they has loss of Rs.8400 at the end of year. what is the share of loss of B?
(A) Rs.4800
(B) Rs.4700
(C) Rs.4600
(D) Rs.4500
(E) None of the above
Rationale: et ratio of A and B be 3x & 4x
so net loss = 3x+4x= 8400
x=1200
A=3x=3(1200)=3600
B= 4x=4(1200)=4800
so, B= 4800
ANSWER:A
Answer: (A) Rs.4800
Question: A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Then number is
(A) 21
(B) 23
(C) 27
(D) 72
(E) 57
Rationale: Sol.
Let the ten's digit be x and unit's digit be y.
Then, 10x + y = 3(x+y) ⇒ 7x - 2y = 0
10x + y + 45 = 10y + x ⇒ y - x = 5
Solving (i) and (ii), we get : x = 2 and y = 7.
∴ Required number = 27.
Answer C
Answer: (C) 27
Question: The tax on a commodity is diminished by 10% and its consumption increased by 15%. The effect on revenue is?
(A) 2% decrease
(B) 3.5% increase
(C) 9% decrease
(D) 3% decrease
(E) 2% increase
Rationale: 100 * 100 = 10000
90 * 115 = 10350
-----------
10000-----------350
100-----------? => 3.5% decrease
Answer: B
Answer: (B) 3.5% increase