mathewhe/aqua_rat huggingface dataset:
Question: Winners will be announced the following day at 11 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?
(A) 13
(B) 21
(C) 22
(D) 24
(E) 25
Rationale: The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. Thus wrong
C) is the correct answer because Y>xwill give 2 digit numbermiddle digit is Y
C
Answer: (C) 22
Question: If x and y are positive odd integers, then which of the following must also be an odd integer?
I. x^(y+1)
II. x(y+1)
III. (y+1)^(x-1) + 1
(A) I only
(B) II only
(C) III only
(D) I and III
(E) None of the above
Rationale: I. x^(y+1)>> (odd)^even=odd
II. x(y+1)>>(odd)*even=even
III. (y+1)^(x-1) + 1>>(even)^even+1>>even+1>> odd if x is not equal to 1 and if x=1 then its (even)^0+1=1+!=2 even.
answer A
Answer: (A) I only
Question: Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 0.5% more. She would get how much?
(A) 9320
(B) 96288
(C) 26667
(D) 1662
(E) 2882
Rationale: (8000*3*0.5)/100 = 120
9200
--------
9320
Answer:A
Answer: (A) 9320
Question: Car A runs at the speed of 100km/hr & reaches its destination in 5hr. Car B runs at the speed of 80 km/h & reaches its destination in 6h. What is the respective ratio of distances covered by Car A & Car B?
(A) 11 : 5
(B) 11 : 8
(C) 13 : 7
(D) 25 : 24
(E) 16 : 9
Rationale: Sol. Distance travelled by Car A = 100 × 5 = 500 km
Distance travelled by Car B = 80 × 6 = 480 km
Ratio = 500/480 = 25 : 24
Answer : D
Answer: (D) 25 : 24
Question: The average of first 14 even numbers is?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Rationale: Sum of 14 even numbers = 14 * 15 = 210
Average =210/14= 15
ANSWER:E
Answer: (E) 15
Question: Sarah is driving to the airport. After driving at 40 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 50 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
(A) 140
(B) 340
(C) 210
(D) 245
(E) 280
Rationale: After driving at 40 miles per hourfor one hour, this distance left to cover is d-40. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 40 miles per hour and 50 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/40 - x/50 = 3/2 --> 5x/200 - 4x/200 = 3/2 --> x/200 = 3/2 --> x = 300.
Total distance = x + 40 = 340 miles.
Answer: B
Answer: (B) 340
Question: Find the odd man out. 187, 264, 386, 473, 682, 781
(A) 386
(B) 187
(C) 781
(D) 682
(E) 264
Rationale: Explanation :
In all numbers except 386, the middle digit is the sum of other two digits.
Answer : Option A
Answer: (A) 386
Question: The speed of a train is 110 kmph. What is the distance covered by it in 11 minutes?
(A) 15 kmph
(B) 11 kmph
(C) 88 kmph
(D) 20 kmph
(E) 12 kmph
Rationale: 110 * 11/60
= 20 kmph
Answer:D
Answer: (D) 20 kmph
Question: If (-6)^(2x) = 6^(7 + x) and x is an integer, what is the value of x ?
(A) 5
(B) 4
(C) 3
(D) 8
(E) 7
Rationale: Since x is an integer, (-6)^2x is always positive.
So, 6^2x = 6^(7 + x)
2x = 7 + x
x = 7
Answer: E
Answer: (E) 7
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 288
(B) 240
(C) 88
(D) 66
(E) 812
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240
Question: 150 is what percent of 60 ?
(A)  250%
(B)  20%
(C)  50%
(D)  200%
(E)  500%
Rationale: 60*x=150 --> x=2.5 -->2.5 expressed as percent is 250%.
Answer: A.
Answer: (A)  250%
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 2.5
(B) 1.5
(C) 1.7
(D) 1.2
(E) 1.9
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2
= 1.5
Answer: B
Answer: (B) 1.5
Question: UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 8:2. If 80% of the Toyota bought and 20% of the Honda bought were SUVâ€™s. How many SUVâ€™s did UBA capital buy in the aforementioned purchase?
(A) 66%
(B) 64%
(C) 68%
(D) 69%
(E) 72%
Rationale: let total no of Vehicles bought be 100, Toyota 80 and Honda 20, so total number of SUV's bought for Toyota and Honda respectively 80* 80/100=64 and 20* 20/100=4
so total 68 SUV's were bought out of 100 Vehicles bought..so required % is 68%
ANSWER:C
Answer: (C) 68%
Question: When Rahul was born, his father was 32 years older than his brother and his mother was 27 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
(A) 10 years
(B) 9 years
(C) 8 years
(D) 7 years
(E) 11 years
Rationale: When Rahul was born, his brother's age = 6 years; his father's age = (6 + 32) years = 38 years,
his mother's age = (38 - 3) years = 35 years;
his sister's age = (35 - 27) years = 8 years.
Answer: Option C
Answer: (C) 8 years
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 176 m
(B) 187 m
(C) 175 m
(D) 150 m
(E) 167 m
Rationale: Speed=(60 * 5/18) m/sec
= (50/3) m/sec Length of the train
= (Speed x Time)
= (50/3 * 9) m
= 150 m.
Answer: D
Answer: (D) 150 m
Question: A man covers a distance of 180 Km at 72 Kmph and next 190km at 88 Kmph. what is his average speed For his whole journey of 370 Km?
(A) 77 Kmph
(B) 77.15 Kmph
(C) 77.25 Kmph
(D) 79 Kmph
(E) 80 Kmph
Rationale: Formula = 2*F.S*S.P/F.S+S.P
= 2*72*88/88+72
=79.2 Kmph
Option 'C'
Answer: (C) 77.25 Kmph
Question: In a college the ratio of the numbers of boys to the girls is 8:5. If there are 160 girls, the total number of students in the college is?
(A) 562
(B) 356
(C) 452
(D) 416
(E) 512
Rationale: Let the number of boys and girls be 8x and 5x
Then , 5x = 160
x= 32
Total number of students = 13x = 13*32 = 416
Answer is D
Answer: (D) 416
Question: Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 10 on the two dice?
(A) 5/9
(B) 11/18
(C) 19/36
(D) 23/36
(E) 25/36
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 10 is 3.
We need to subtract the outcomes that have both an even number on the first die and a sum of 10 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 10 is 18+3-2=19.
The probability is 19/36.
The answer is C.
Answer: (C) 19/36
Question: Three friends A, B and C run around a circular track of length 120 metres at speeds of 5 m/s, 7 m/sec and 15 m/sec, starting simultaneously from the same point and in the same direction. How often will the three of them meet ?
(A) Every 60 seconds
(B) Every 120 seconds
(C) Every 30 seconds
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
A and B will meet for the first time in:
=>(Circumference of track/relative speed) seconds
=>120/2 = 60 seconds.
This also means that A and B will continue meeting each other every 60 seconds.
When B and C will meet for the first time.
B and C will meet for the first time in 120/8=15 seconds.
This also means that they will meet every 15 seconds after they meet for the first time i.e. A and B meet every 60 seconds and multiples of 60 seconds and B and C meet every 15 seconds and multiples of 15 seconds.
The common multiples to both these time, will be when A and B and B and C will meet i.e. when A, B and C will meet.
The common multiple of 60 and 15 will be 60,120,180 etc. i.e. they will meet every 60 seconds.
Answer : A
Answer: (A) Every 60 seconds
Question: The speed of a car is 100 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 12
(B) 75
(C) 80
(D) 54
(E) 15
Rationale: S = (100 + 60)/2
= 80 kmph
Answer: C
Answer: (C) 80
Question: If the sum of two numbers is 24 and the sum of their squares is 400, then the product of the numbers is
(A) 40
(B) 44
(C) 80
(D) 88
(E) 48
Rationale: according to the given conditions x+y = 24
and x^2+y^2 = 400
now (x+y)^2 = x^2+y^2+2xy
so 24^2 = 400 + 2xy
so xy = 176/2 = 88
ANSWER:D
Answer: (D) 88
Question: If Rosé reads at a constant rate of 3 pages every 5 minutes, how many seconds will it take her to read N pages?
(A) 100
(B) 2N
(C) 5/2*N
(D) 24N
(E) 150
Rationale: Rose would read 1 page in 5/3 min
Rose would read N page in (5/3)*N min i.e. (5/3)*N*60 Seconds = 100N Seconds.
Option A is the correct Answer.
Answer: (A) 100
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg. What is the weight of the new person?
(A) 90
(B) 65
(C) 85
(D) 95
(E) 80
Rationale: Total increase in weight = 8 × 2.5 = 20
If x is the weight of the new person, total increase in weight = x−70
=> 20 = x - 70
=> x = 20 + 70 = 90
Answer is A.
Answer: (A) 90
Question: When Rahul was born, his father was 30 years older than his brother and his mother was 24 years older than his sister. If Rahul's brother is 6 years older than him and his mother is 3 years younger than his father, how old was Rahul's sister when he was born ?
(A) 10 years
(B) 7 years
(C) 8 years
(D) 9 years
(E) 12 years
Rationale: When Rahul was born, his brother's age = 6 years; his father's age = (6 + 30) years = 36 years,
his mother's age = (36 - 3) years = 33 years;
his sister's age = (33 - 24) years = 9 years.
Answer: Option D
Answer: (D) 9 years
Question: Arun and Tarun can do a work in 10 days.After 4 days tarun went to his village.How many days are required to complete the remaining work by Arun alone.Arun can do the work alone in 50 days.
(A) 16 days.
(B) 17 days.
(C) 18 days.
(D) 30 days.
(E) 20 days.
Rationale: They together completed 4/10 work in 4 days.
balance 6/10 work will be completed by Arun alone in 50*6/10 = 30 days.
ANSWER:D
Answer: (D) 30 days.
Question: Excluding stoppages, the average speed of a bus is 100 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
(A) 15 min
(B) 18 min
(C) 16 min
(D) 20 min
(E) 36 min
Rationale: In 1hr, the bus covers 100 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (100 - 40) km i.e 60 km at 100 km/hr.
stoppage time = 60/100 hrs
= 36 min
Answer: E
Answer: (E) 36 min
Question: Which of the following is a prime number ?
(A) 33
(B) 81
(C) 97
(D) 93
(E) 10
Rationale: C
97
Clearly, 97 is a prime number.
Answer: (C) 97
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 40, what is the compound interest on the same sum at the rate and for the same time?
(A) s. 41.00
(B) s. 51.22
(C) s. 51.219
(D) s. 41.18
(E) s. 51.11
Rationale: Explanation:
Sum = (40 * 100) / (2 * 5) = Rs. 400
Amount = [400 * (1 + 5/100)2] = Rs. 441
C.I. = (441 - 400) = Rs. 41
Answer:A
Answer: (A) s. 41.00
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) 6620
(B) 3378
(C) 2768
(D) 2999
(E) 2771
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: (A) 6620
Question: (1/5)^e * (1/4)^18 = 1/(2(10)^35). What is e?
(A) 17
(B) 18
(C) 34
(D) 35
(E) 36
Rationale: We need to arrive at a common base. -->
(5)^(-e) * 2^(-36) = 2^(-36)*5^(-35)
5^(-e)=5^(-35)
-e=-35
e=35=D
Answer: (D) 35
Question: An integer is said to be “diverse” if no two of its digits are the same. For example, 327 is “diverse” but 404 is not. How many “diverse” two digit numbers are there ?
(A) 70
(B) 72
(C) 81
(D) 90
(E) 91
Rationale: A two digit number has to be formed from digits 0 to 9 such that unit's digit and ten's digit are not same.
The unit's digit can have 10 values from 0 to 9.
Ten's digit can have 9 values from 1 to 9
So total number of two digit numbers will be 9 x 10 = 90
But there are 9 numbers which are not diverse.
11,22,33,44,55,66,77,88,99
so, the number of diverse two digit numbers will be 90-9 = 81
Answer:- C
Answer: (C) 81
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 3 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 15
(B) 30
(C) 43
(D) 45
(E) 80
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 3 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 3 x 5 = 15 ways
Answer: (A) 15
Question: 200 is what percent of 40?
.
(A) 0.2%
(B) 2%
(C) 5%
(D) 20%
(E) 500%
Rationale: 200= x*40/100
x = 500%
Ans; E
Answer: (E) 500%
Question: If m is 3 more than a multiple of 5 and 2 more than a multiple of 6, which of the following could be m?
(A) 14
(B) 28
(C) 58
(D) 68
(E) 74
Rationale: m is 3 more than a multiple of 5 i.e. m = 5a+3
m is 2 more than a multiple of 6 i.e. m = 6b+2
Just check option
A. 14 when divided by 5 leaves remainder 4 instead of 3 hence incorrect option
B. 28 when divided by 5 leaves remainder 3 and when divided by 6 leaves remainder 4 instead of 2 hence Incorrect option
C. 58 when divided by 5 leaves remainder 3 and when divided by 6 leaves remainder 4 instead of 2 hence Incorrect option
D. 68 when divided by 5 leaves remainder 3 and when divided by 6 leaves remainder 2 hence Correct option
E. 74
Answer: Option D
Answer: (D) 68
Question: Sakshi can do a piece of work in 25 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
(A) 15
(B) 20
(C) 18
(D) 25
(E) 10
Rationale: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 25 : x ⇒ x = (25x4/5) ⇒ x = 20 days.
Hence,Tanya takes 16 days is complete the work.
Answer B
Answer: (B) 20
Question: In a college, 71 percent of students Play Football, 76 percent of students Play Hockey, 86 percent Play Basket Ball and 81 percent Play Volleyball.
Can you find out the percentage of students who study all 4 Games?
(A) 14%
(B) 10%
(C) 16%
(D) 18%
(E) 19%
Rationale: A
14% of student Play all four Games.
Answer: (A) 14%
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 16 seconds
(B) 18 seconds
(C) 19 seconds
(D) 27 seconds
(E) 36 seconds
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 400 / (15 + 25)5/18 = 400* 18 / 40 * 5
= 36 seconds.
Answer:E
Answer: (E) 36 seconds
Question: At a game of billiards, A can give B 15 points in 60 and A can give C to 20 points in 60. How many points can B give C in a game of 90?
(A) 30 points
(B) 20 points
(C) 10 points
(D) 12 points
(E) 22 points
Rationale: a:b=60:45
a:c=60:40
b/a *a/c=45/60 *60/45=45/40=90/80 so 10 points
ANSWER:C
Answer: (C) 10 points
Question: How many different positive integers exist between 10^7 and 10^8, the sum of whose digits is equal to 2?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 10000001
10000010
10000100
10001000
10010000
10100000
11000000
20000000
E
Answer: (E) 8
Question: 12 is subtracted from 95% of a number, the result is 178. Find the number?
(A) 200
(B) 240
(C) 198
(D) 190
(E) 322
Rationale: (95/100) * X â€“ 12 = 178
9.5X = 1900
X = 200
Answer:A
Answer: (A) 200
Question: A invested $50 in a business and B invested $100 in a business. At the end of the year they got $150 as the profit. Find their share?
(A) $50,$100
(B) $150,$250
(C) $210,$130
(D) $120,$150
(E) $50,$200
Rationale: A:B = 50:100
A:B = 1:2
A's share = 150*1/3 = $50
B's share = 150*2/3 = $100
Answer is A
Answer: (A) $50,$100
Question: The sum of two consecutive number is 115. Which is the larger number?
(A) 42
(B) 58
(C) 44
(D) 45
(E) 46
Rationale: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=115
2x+1=115
2x=114
x=57
Therefore larger number is x+1=58
ANSWER:B
Answer: (B) 58
Question: Of the three numbers, the first is twice as second and three times the third. The average of the three numbers is 77, and the three numbers in order are?
(A) 116,58,36
(B) 98,49,33
(C) 126,63,42
(D) 108,54,36
(E) None of these
Rationale: Explanation :
Solution: Let A =x,
B =x/2, C = x/3.
=x + x/2 + x/3 / 3 = 77
By solving we will get x = 126.
Hence A= 126
B= 126/2= 63
C= 126/3 = 42
Answer : C
Answer: (C) 126,63,42
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.22050/- in 3 years at the same rate of interest. Find the rate percentage?
(A) 5%
(B) 7%
(C) 9%
(D) 11%
(E) 25%
Rationale: Explanation:
The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.
S.I = 22050/- - 17640/- = Rs. 4410/-
Rate of interest = (4410/17640) × (100/1) => 25%
Answer: Option E
Answer: (E) 25%
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
(A) 3 dm
(B) 4 dm
(C) 5 dm
(D) 6 dm
(E) 7 dm
Rationale: 33 + 43 + 53 = a3 => a = 6
ANSWER:D
Answer: (D) 6 dm
Question: If u r genius solve it:-
60 * 16 = 15
50 * 15 = 12
40 * 14 = ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 11
Rationale: Logic :
60*16=960=9+6+0=15
50*15=750=7+5+0=12
40*14=560=5+6+0=11
Answer : E
Answer: (E) 11
Question: IF
1= N
2= W
3= H
4= O
5= I
THEN 6=?
(A) I
(B) J
(C) K
(D) L
(E) M
Rationale: IF
1= N... Second letter of ONE.
2= W.... Second letter of TWO.
3= H
4= O
5= I
THEN 6=I ... Second letter of SIX.
ANSWER:A
Answer: (A) I
Question: The average of first 10 even numbers is?
(A) 8
(B) 92
(C) 83
(D) 11
(E) 12
Rationale: Explanation:
Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11
Answer: Option D
Answer: (D) 11
Question: I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?
(A) 800
(B) 237
(C) 2765
(D) 288
(E) 161
Rationale: Let xx be the number I chose, then
x5−154=6x5−154=6
x5=160x5=160
x=800
Answer:A
Answer: (A) 800
Question: A train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds. The length of the train (in metres) is:
(A) 182
(B) 176
(C) 175
(D) 96
(E) None of these
Rationale: Explanation:
Let the length of train be L m.
Acc. to question
(273+L)/20 = L/8
2184+8L=20L
L= 2184/12 = 182 m
Answer A
Answer: (A) 182
Question: Two trains of length 120 m and 300 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 21 sec
(B) 32 sec
(C) 82 sec
(D) 20 sec
(E) 89 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 300 = 420m.
The time required = d/s = 420/20 = 21 sec.
Answer:A
Answer: (A) 21 sec
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 30 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
(A) 33 1/3%
(B) 40%
(C) 53 11/13%
(D) 62 1/2%
(E) 75%
Rationale: P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
30% of (70-x) = x => 21 - 0.3x = x => x = 16 2/13% so only P = 70 -x = 53 11/13%
Answer C
Answer: (C) 53 11/13%
Question: An air-conditioning unit costs $470. On December there was a discount for Christmas of 16%. Six months later, the holiday season was over so the company raised the price of the air-conditioning by 15%. How much will an air-conditioning unit cost in November?
(A) $454
(B) $470
(C) $472
(D) $484
(E) $491
Rationale: if its previous November (before discount) then price is $470.
but if its November of next year then
16% discount on $470=470(1-16/100)=$394.8
again a corrected raised price of 15% over $394.8=394.8(1+15/100)=454.02~$454
Ans A
Answer: (A) $454
Question: The salaries of A and B together is Rs. 14,000. A spend 80% of his salary and B spends 85% of his salary. What is the salary of B if their savings are equal?
(A) Rs. 6,000
(B) Rs. 8,000
(C) Rs. 7,500
(D) Rs. 6,500
(E) Rs. 8,500
Rationale: Let the salaries of A and B are X and Y respectively
X + Y = 14,000
Savings of A = 20X/100 = Savings of B = 15Y/100
X = ¾ Y
3/4Y + Y = 14,000, 7Y/4 =14,000, Y =8,000
ANSWER:B
Answer: (B) Rs. 8,000
Question: A sum of Rs. 2040 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
(A) Rs. 120
(B) Rs. 160
(C) Rs. 240
(D) Rs. 360
(E) None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 2040
=> 17x/12 =2040
=> 2040 x 12/ 17 = Rs.1440
Hence, B’s share = Rs. (1440/4) = Rs. 360.
Answer D
Answer: (D) Rs. 360
Question: Each student at a certain business school is assigned a 8-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
(A) 9,000
(B) 3,600
(C) 36,000,000
(D) 2,592
(E) 1,944
Rationale: The identification number is of the form _ _ _ _
1. First digit cannot be 0
2. Middle digits can be anything
3. Last digit has to be prime - 2, 3, 5, 7
We can have the following number of possibilities for each space
__ __ __ __
9 10 10 10 10 10 10 4
Total cases = 36,000,000
Option C
Answer: (C) 36,000,000
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1350 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) Rs. 4500
(B) Rs. 4800
(C) Rs. 5250
(D) Rs. 7380
(E) None of these
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1350
45k = 1350 => k = 30
246k = 246(30) = Rs. 7380
Thus the total rent paid by all the four agencies is Rs. 7380.
ANSWER:D
Answer: (D) Rs. 7380
Question: The average of 10 numbers is 23. If each number is increased by 2, what will the new average be?
(A) 36
(B) 25
(C) 72
(D) 29
(E) 22
Rationale: Sum of the 10 numbers = 230
If each number is increased by 2, the total increase =
2 * 10 = 20
The new sum = 230 + 20 = 250 The new average = 250/10
= 25.
Answer:B
Answer: (B) 25
Question: A train 180 m in length crosses a telegraph post in 20 seconds. The speed of the train is?
(A) 37 kmph
(B) 35 kmph
(C) 32 kmph
(D) 38 kmph
(E) 36 kmph
Rationale: S = 180/20 * 18/5
= 32 kmph
Answer: C
Answer: (C) 32 kmph
Question: The speeds of three motor bikes are in the ratio 6 : 5 : 4. The ratio between the time taken by them to travel the same distance is :
(A) 10 : 12 : 15
(B) 12 : 10 : 8
(C) 15 : 12: 10
(D) 10 : 15 : 12
(E) 13 : 15 : 12
Rationale: Ratio of time taken :
1/6 :1/5 : 1/4 = 10 : 12 : 15
ANSWER:A
Answer: (A) 10 : 12 : 15