mathewhe/aqua_rat huggingface dataset:
Question: A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B
(A) Rs. 3400
(B) Rs. 2700
(C) Rs. 1720
(D) Rs. 7200
(E) Rs. 8200
Rationale: Explanation:
Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y
Then, savings of A = 5x-3y = 1800—?(1)
Savings of B = 6x-4y = 1600—?(2)
By solving equations (1) and (2)
y = 1400
Monthly income of B = Expenses of B + savings of B
= 4y+1600 = 4(1400) + 1600 = Rs. 7200
Answer: D
Answer: (D) Rs. 7200
Question: John has 10 pairs of matched socks. If he loses 9 individual socks, what is the greatest number of pairs of matched socks he can have left?
(A)  7
(B)  6
(C)  5
(D)  4
(E)  3
Rationale: Because we have to maximize the pair of matched socks, we will remove 4 pairs(8 socks) out of 10 pairs 1 sock from the 5th pair.
Thus the no of matching socks pair remaining = 10 -5 = 5
Answer C
Answer: (C)  5
Question: Jim takes a seconds to swim d meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?
(A) c(b-a)/ a+b
(B) d(a-b)/a+b
(C) c(a+b)/a-b
(D) ab(a-b)/a+b
(E) ab(b-a)/a+b
Rationale: Both JimRoger are travelling at constant speedin opposite direction:
So, speed of Jim = d/a speed of Roger = d/b
Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (c-x) from point Q
[x would be less than (c-x) as Jim is travelling slow]
From above, time taken by Jim to travel x = xa/d....................... (1)
Also, time taken by Roger to travel (c-x) = (d-x)b/d.....................(2)
Time taken by both JimRoger is same, so (1) = (2)
xa/d = (d-x)b/d,
Solving further, x = bd/(a+b).................... (3)
We require to find how many fewer meters will Jim have swum i.e
additional distance travelled by Roger = (d - x) - x
= d-2x
Substituting value of x from (3)solving the equation further, we get Answer = d(a-b)/a+b
Answer = (B)
Answer: (B) d(a-b)/a+b
Question: In the first 10 overs of a cricket game, the run rate was only 3.4. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 4.25
(B) 5
(C) 6.2
(D) 7
(E) 7.5
Rationale: Required run rate = 282 - (3.4 x 10) =	248
248/40 = 6.2
C)
Answer: (C) 6.2
Question: Which of the following equations describes a line that is perpendicular to y=x-7?
(A) y = x + 7
(B) y = −5 − x
(C) y = 7x
(D) y = 7x+1
(E) y = 1/x - 7
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x-7 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
Answer: (B) y = −5 − x
Question: A taxi company with a fleet of 50 taxis, plans to replace all their taxis with electric cars. Every year it retires 10 of their old taxis and buys 12 electric cars to replace them. How many years will it take to reduce their old taxi fleet to below 50% of their entire fleet if they started in 2003.
(A) 3
(B) 4
(C) 1
(D) 2
(E) 10
Rationale: Total fleet--50
End of year 2003 -- (retires 10 and buys 12) total fleet--52(40 old 12 new).
End of year 2004 -- (retires 10 and buys 12) total fleet--54(30 old 24 new).
End of year 2005 -- (retires 10 and buys 12) total fleet--56(20 old 36 new).
Answer is A--after 3 years the company has a total of 56 taxis (20 old 36 new), the old taxis are already less than 50% of its fleet.
Answer: (A) 3
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
(A) 628 ways
(B) 600 ways
(C) 767 ways
(D) 762 ways
(E) 672 ways
Rationale: Two men, three women and one child can be selected in 4C2 * 6C3 * 5C1 ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5
= 600 ways.
Answer:B
Answer: (B) 600 ways
Question: If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
(A) 10 km
(B) 8 km
(C) 6km
(D) 4km
(E) 7 km
Rationale: Sol. Let the required distance be x km
Difference in the time taken at two speeds=1 min =1/2 hr
Hence x/5-x/6=1/5<=>6x-5x=6
x=6
Hence, the required distance is 6 km
Option C
Answer: (C) 6km
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
(A) 5 to 4
(B) 3 to 2
(C) 2 to 1
(D) 5 to 1
(E) 6 to 1
Rationale: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6
# of 4 letter code words:
nPr = 10! / (10 – 4)! = 10*9*8*7
# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7) = 6 = 6/1
Answer is E.
Answer: (E) 6 to 1
Question: A husband and wife can complete a certain task in 1 and 3 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
(A) a)15:46
(B) b)3:10
(C) c)12:23
(D) d)5:16
(E) e)10:3
Rationale: couples one hour work=1/1+1/3=4/3
so total time=3/4.
now, kids one hour work=1/4+1/6=5/12
so total time=12/5..
ratio=3/4:12/5=5:16
ans D
Answer: (D) d)5:16
Question: How many different committees each composed of 2 Republicans and 3 Democrats can be formed from a group of 4 Republicans and 5 Democrats?
(A) 12
(B) 24
(C) 60
(D) 72
(E) 120
Rationale: Let's take the Republicans. How many combinations of 2 can be created.
There are four total so: 4!/2!2! = 6
Democrats: 5!/3!2! = 10
6 x 10 = 60
ANSWER:C
Answer: (C) 60
Question: 10^25 - 260 is divisible by all of the following except:
(A) A.10
(B) B.8
(C) C.5
(D) D.4
(E) E.2
Rationale: The last three digits ( 1000 - 260 ) 740
740 is divisible by 10,4,2,5
740 is not evenly divisible by 8 so the answer is B) 8
Answer: (B) B.8
Question: M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 2, 3}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
(A) 0
(B) 1/3
(C) 2/5
(D) 1/2
(E) 3/5
Rationale: Answer C.
Total # of outcomes: 5*5= 25
# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 10
Probability: 10/25 = 2/5
Answer: (C) 2/5
Question: A train 600 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is:
(A) 45 km/hr
(B) 149 km/hr
(C) 54 km/hr
(D) 55 km/hr
(E) 56 km/hr
Rationale: Speed of the train relative to man = (600/15) m/sec = 40 m/sec. [40 * (18/5)] km/hr = 144 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 144 ==> x = 149 km/hr.
ANSWER: B
Answer: (B) 149 km/hr
Question: 3/4th of a number exceeds its 2/3rd by 8. What is the number?
(A) 96
(B) 36
(C) 72
(D) 144
(E) 146
Rationale: Explanation:
Let the number be x.
3/4x = 2/3x + 8
Multiply by 12
9x = 8x + 96
x = 96
ANSWER :A
Answer: (A) 96
Question: If p/q =4/5, then the value of 18/7 + {(2q - p) / (2q + p)} is ?
(A) 3 / 7
(B) 34
(C) 1
(D) 2
(E) 3
Rationale: Answer
Given Exp. = 18 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 18/7 + {2-p/q) / (2 + p/q)}
= 18/7 + {(2 - 4/5) / (2 + 4/5)}
= 18/7 + 6/14
= 18/7 + 3/7
=21/7
=3
Correct Option: E
Answer: (E) 3
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A?
(A) 13
(B) 24
(C) C is elder than A
(D) Data inadequate
(E) None
Rationale: Solution
[(A+B) - (B+C)]	= 13
â€¹=â€ºA - C
= 13.
Answer A
Answer: (A) 13
Question: A group consists of 7 men, 7 women and 6 children. In how many ways can 2 men , 1 woman and 2 child selected from the given group?
(A) 2210
(B) 2205
(C) 2215
(D) 2230
(E) 2245
Rationale: Two men, one woman and two child can be selected in 7C2 * 7C1 * 6C2 ways
7*6/2*1*7*6*5/2*1
=2205 ways
Answer : B
Answer: (B) 2205
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 45%?
(A) 600
(B) 887
(C) 256
(D) 654
(E) 725
Rationale: Cost price = Rs.500
profit = 45% of 500 = Rs.225
Selling price = Cost price + Profit
= 500 + 225 = 725
Answer: E
Answer: (E) 725
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3795. What is the difference between Rohan’s and Sudhir’s share in the profit?
(A) s.345
(B) s.350
(C) s.352
(D) s.362
(E) s.368
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3795 × 1/11 = Rs.345.
A
Answer: (A) s.345
Question: The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ?
(A) 31 kg
(B) 63 kg
(C) 61 kg
(D) 62 kg
(E) 91 kg
Rationale: let c=coach's avg. weight
original total weight=(30 friends)(30 kg avge)=900kg
(900+3c)/(30+3)=33 kg avg.
c=63 kg
Answer B
Answer: (B) 63 kg
Question: Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?
(A) 20 years
(B) 22 years
(C) 25 years
(D) 27 years
(E) 29 years
Rationale: let varuns age =x
x+1=2(x-12)
der4 x=25..
ANSWER:C
Answer: (C) 25 years
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 120 different possible selections of the 2 members, how many members does the club have?
(A) 20
(B) 27
(C) 16
(D) 57
(E) 95
Rationale: I have done this problem by substituting numbers
We have n!/2!(n-2)! = 120
or n(n-1)/2 = 120 or n^2-n =240 or (n-16)(n+15)
n=16 satisfies the equation
C
Answer: (C) 16
Question: In covering a distance of 15 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
(A) 5 km/h
(B) 8 km/h
(C) 10 km/h
(D) 15 km/h
(E) 2.5 km/h
Rationale: Let A's speed be X km/hr.
Then, 15/x - 15/2x = 3
7.5/x = 3
x = 2.5 km/hr.
Answer : E
Answer: (E) 2.5 km/h
Question: If x = 8 and y = −2, what is the value of (x − 2y)^y?
(A) −100
(B) 0.007
(C) 0.25
(D) 4
(E) 8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.007
Answer: B
Answer: (B) 0.007
Question: When 12 + 10 = 1205, 11 + 8 = 885, then 16 + 15 = ?
(A) 2405
(B) 3205
(C) 2463
(D) 2631
(E) 3425
Rationale: A
2405
12 + 10 => 12 × 10 = 120 => 120 × 10 + 5 = 1205
11 + 8 => 11 × 8 = 88 => 88 × 10 + 5 = 885
16 + 15 => 16 × 15 = 240 => 240 × 10 + 5 = 2405
Answer: (A) 2405
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different Y ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
(A) 5
(B) 6
(C) 9
(D) 12
(E) 18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible Y is 2*6=12.
Answer: D.
Answer: (D) 12
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long Q would it have taken for him to walk both ways.
(A) 8 h 45 min
(B) 7 h 45 min
(C) 6 h 45 min
(D) 5 h 30 min
(E) None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back Q=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: (A) 8 h 45 min
Question: I. a2 + 11a + 30 = 0,
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
(A) If a < b
(B) If a ≤ b
(C) If the relationship between a and b cannot be established
(D) If a > b
(E) If a ≥ b
Rationale: I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b
ANSWER:B
Answer: (B) If a ≤ b
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 2
(B) 8
(C) 9
(D) 1
(E) 6
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: (B) 8
Question: What is the highest integer that is the sum of 2 distinct prime integers, each lesser than 60 ?
(A) 107
(B) 112
(C) 113
(D) 129
(E) 136
Rationale: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
Immediate two prime numbers before 60 are - 59 and 53
Sum = 59 + 53 = 112
Answer - B
Answer: (B) 112
Question: What is the angle between the minute and the hour hand of the clock which shows 12:24?
(A) 115
(B) 120
(C) 124
(D) 130
(E) 132
Rationale: At 12:24
-minute hand will be at 24*6 = 144 degrees from position of 12.
- Hour hand will move by 2*6 = 12 degree during the same time
So the difference between the two hands will be 144-12 = 132 degrees. ANSWER:E
Answer: (E) 132
Question: In a certain game there are 10 steps, referred to as step 1, step 2, and so on with the final step being step 10. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Mary played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?
(A) 25
(B) 28
(C) 24
(D) 32
(E) 30
Rationale: There are two conditions:
1. Mary got at least one score of each of 1, 2, 3, 4, and 5.
2. She never got the same score in consecutive steps.
Taking that into account, the greatest possible score that Mary could have gotten is 5 + 1 + 5 + 2 + 5 + 3 + 5 + 4 = 30.
Answer: E
Answer: (E) 30
Question: The only items of clothing at Michelle’s Boutique are 4 shirts, 8 pairs of pants and 18 ties. What is the probability of randomly selecting 2 ties out of all the items in Michelle’s Boutique?
(A) 51/145
(B) 9/25
(C) 3/5
(D) 94/145
(E) 5/6
Rationale: We have 4 shirts, 8 pairs of pants and 18 ties. i.e 30 items
Total ways of picking two items out of all = 30C2 = 435
Total ways of picking two items out of all TIES = 18C2 = 153
Required Probability = 153/435 = 51/145
Answer: Option A
Answer: (A) 51/145
Question: If 20 liters of chemical X are added to 80 liters of a mixture that is 15% chemical X and 85% chemical Y, then what percentage of the resulting mixture is chemical X?
(A) 30%
(B) 32%
(C) 35%
(D) 38%
(E) 40%
Rationale: The amount of chemical X in the solution is 20 +0.15(80) = 32 liters.
32 liters / 100 liters = 32%
The answer is B.
Answer: (B) 32%
Question: If d is the standard deviation a, b, and c, what is the standard deviation of a +2, b + 2, c + 2 ?
(A) 2d
(B) d
(C) 2d+2
(D) 8d
(E) 2d+4
Rationale: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.
1) It depends on the separation between the successive terms of the set
2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant
e.g.{1, 2, 3, 4, 5} will have same standard Deviation as {1+10, 2+10, 3+10, 4+10, 5+10}
3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number
e.g. {0.7, 1.4, 2.1, 2.8, 3.5} will have Standard Deviation = 0.7* Standard deviation of set {1, 2, 3, 4, 5}
When 2 is added in each term of set {a, b,c} then the new set {a+2, b+2, c+2} will remain same as the previous standard deviation i.e. d
Answer: B
Answer: (B) d
Question: Of the 150 employees at company X, 80 are full-time, and 100 have worked at company X for at least a year. There are 10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
(A) 10
(B) 30
(C) 50
(D) 80
(E) 100
Rationale: Full time employee who have NOT worked for at least one year = a
Full time employee who have worked for at least one year = b
NON Full time employee who have worked for at least one year = c
NON Full time employee who have NOT worked for at least one year = d
a+b+c+d = 150
a+b = 80
i.e. c+d = 70
b+c = 100
i.e. a+d = 50
d = 20
i.e. c = 70-20 = 50
i.e. b = 100-50 = 50
i.e. a = 80-50 = 30
b = 10
Answer: Option A
Answer: (A) 10
Question: Simplify
16âˆ’[2âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))]
(A) 23
(B) 25
(C) 28
(D) 30
(E) 32
Rationale: Explanation:
=16âˆ’[2âˆ’(6+2(7âˆ’8+5))]
(Please check due to overline, sign has been changed)
=16âˆ’[2âˆ’(6+2Ã—4))]
=16âˆ’[âˆ’12]=16+12=28
Option C
Answer: (C) 28
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 2,000, how much money did investors B and C earn in total?
(A) $4,000
(B) $6,000
(C) $5,600
(D) $9,500
(E) $10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 2000
5x = 2000=>x=400
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 15*400= 6,000
Answer B
Answer: (B) $6,000
Question: Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of seven 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) 5
(B) 8
(C) 10
(D) 12
(E) 15
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 7 - 1 = 6 rounds per hour.
The time required to complete one round at this speed is 1/6 hours = 10 minutes.
The answer is C.
Answer: (C) 10
Question: In each term of a sequence, 5 is added to get the next term. If the first term is 3, what is the seventy-first term?
(A)  332
(B)  353
(C)  312
(D)  360
(E)  387
Rationale: 1rst term + 70 terms = 3 + 5+5+5+5+5+5+5+...+5 (70 times)
3 + (5 x 70) = 3 + 350 = 353
Answer B
Answer: (B)  353
Question: If the positive integer x leaves a remainder of 2 when divided by 8, what will the remainder be when x + 9 is?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: x = 8q +2
x +9 =8q+2+9
8q+11 this can be furthur written as 8q +8 +3 = 8(q+1)+3
Remainder 3. Ans D.
Answer: (D) 3
Question: 8 x 2.25- 5 x 0.85/2.5= ?
(A) 3.8
(B) 10
(C) 5
(D) 5.5
(E) 7.5
Rationale: Given Expression
= (18-4.25/2.5
= 13.75/2.5= 137.5/25
= 5.5
Answer is D.
Answer: (D) 5.5
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same Job.How long should it take both A and B, working together but independently, to do the same job?
(A) 70 hours
(B) 40/9 hours
(C) 9 hours
(D) 16 hours
(E) 20 hours
Rationale: A’s 1 hour's work = 1/8
B's 1 hour's work = 1/10
(A + B)'s 1 hour's work = (1/8) +(1/10)=9/40
Both A and B will finish the work in 40/9 days.
Option B is answer
Answer: (B) 40/9 hours
Question: David bought 4 pens with the average cost of $2. If David also buys the fifth pen with the price of $ 3, what is the average (arithmetic mean) price of those 5 pens?
(A) $2.2
(B) $2
(C) $3.2
(D) $4
(E) $5.2
Rationale: 4 pens -> Total cost = 4 * Avg cost = 4*2 = 8
Fifth pen cost = 3
Total cost for 5 pens= 8+3 = 11
AM = 11/5 = 2.2
Hence B
Answer: (B) $2
Question: What is the true discount on a bill of Rs.2916 due in 3 years hence at 8% C.I.?
(A) rs.600
(B) rs.601
(C) rs.602
(D) rs.603
(E) None of these
Rationale: Explanation:
PW = Amount/(1+R100)T.
Answer: C
Answer: (C) rs.602
Question: The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 hours, then the speed of the first train is:
(A) 47.4 km/hr
(B) 57.19 km/hr
(C) 68.13 km/hr
(D) 96.25 km/hr
(E) 89.16 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Hence, speed of first train = (7 x 13.75) km/hr = 96.25 km/hr.
Answer : D
Answer: (D) 96.25 km/hr
Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 2 strokes ?
(A) 3/4
(B) 7/8
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
So removed = 1- 1/4 = 3/4
Answer: (A) 3/4
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 126
(B) 278
(C) 281
(D) 280
(E) 219
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: (D) 280
Question: The speed of the boat in still water is 12km/hr. and the speed of the stream is 3km/hr. Find the distance travelled downstream in 12 minutes.
(A) 160 km
(B) 180 km
(C) 190 km
(D) 170 km
(E) 140 km
Rationale: speed of the boat in downstream =speed of the water + speed of the boat
=12+3 =15km/hr Distance travelled in 12 minutes =15 *12 = 180km. Answer : B
Answer: (B) 180 km
Question: If 64(8^x) = 1 then x=
(A) 2
(B) –1
(C) 0
(D) 1
(E) -2
Rationale: 8^x = 1/64
8^x = 1/8^2
8^x= 8^-2
x = -2
E
Answer: (E) -2
Question: What will be the cost of building a fence around a square plot with area equal to 64 sq ft, if the price per foot of building the fence is Rs. 58?
(A) 3944
(B) 2882
(C) 2999
(D) 1856
(E) 2121
Rationale: Let the side of the square plot be a ft.
a2 = 64 => a = 8
Length of the fence = Perimeter of the plot = 4a = 32 ft.
Cost of building the fence = 32 * 58 = Rs. 1856.
Answer: D
Answer: (D) 1856
Question: John is filling out the office space for his employees. There are 8 people in his office, and he must assign 8 employees to the following positions: 2 next to his cabin, 2 near the gate, 2 in center, and 2 near coffee machine. Only 2 employees are secretary and can sit next to his cabin, and they cannot sit anywhere else. The other employees can sit anywhere they like. How many different groupings are possible?
(A) 100
(B) 90
(C) 80
(D) 70
(E) 60
Rationale: Secretary can sit in 2C2 ways = 1
Near the gate we can have 6C2 combinations (2 secretaries are already having a place)
In the center we can have 4 C2 employees as 4 already have a place
Near coffee machine we can have 2C2 employees as all other place are taken
Number of selection = 2C2 * 6C2 * 4C2 * 2C2 = 90
Ans: B
Answer: (B) 90
Question: What least number should be subtracted from 13605 such that the remainder is divisible by 87 ?
(A) 27
(B) 29
(C) 28
(D) 30
(E) 33
Rationale: 13605 ÷ 87 = 156, remainder = 33
Hence 33 is the least number which can be subtracted from 13605 such that the remainder
is divisible by 87
Answer is E
Answer: (E) 33
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 7/19
(B) 7/11
(C) 7/10
(D) 7/21
(E) 7/15
Rationale: Explanation:
Drawing two balls of same color from seven green balls can be done in ways.
Similarly from eight white balls two can be drawn in ways.
P = 7C2/15C2 + 8C2/15C2 = 7/15
Answer:E
Answer: (E) 7/15