mathewhe/aqua_rat huggingface dataset:
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.60 only. Menâ€™s wages are?
(A) 6Rs
(B) 2Rs
(C) 4Rs
(D) 9Rs
(E) 3Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 60 Rs.
5M + 5M + 5M ----- 60 Rs.
15M ------ 60 Rs. => 1M = 4Rs.
Answer: C
Answer: (C) 4Rs
Question: Look at this series: 72, 76, 73, 77, 74, __, 75, ... What number should fill the blank?
(A) 44
(B) 78
(C) 15
(D) 92
(E) 29
Rationale: D
78
This series alternates the addition of 4 with the subtraction of 3.
Answer: (D) 92
Question: The number which exceeds 16% of it by 63 is :
(A) 75
(B) 52
(C) 58
(D) 60
(E) 62
Rationale: Solution
Solution
Let the number be x.
x-16% of x =63
x-16/100x =63
x-4/25x=63
21/25x=63
x=(63x25/21)= 75
Answer A
Answer: (A) 75
Question: The sector of a circle has radius of 21 cm and central angle 108o. Find its perimeter?
(A) 81.6cm
(B) 85.9cm
(C) 90cm
(D) 92cm
(E) 95cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (108/360 * 2 * 22/7 * 21) + 2(21)
= 39.6 + 42 = 81.6 cm
Answer:A
Answer: (A) 81.6cm
Question: 6 3/4 + 7 2/17 - 9 1/15=?
(A) 7 719/1020
(B) 9 817/1020
(C) 9 719/1020
(D) 4 817/1020
(E) None of them
Rationale: Given sum=6+3/4+7+2/17-(9+1/15)
=(6+7-9)+(3/4+2/17-1/15)
=4+(765+120-68/1020
=4 817/1020
Answer is D
Answer: (D) 4 817/1020
Question: One of the longest sides of the triangle is 20 m,the other side is 10 m.Area of the triangle is 80m^2.What is the another side of the triangle?
(A) 2sqrt(61)
(B) 2sqrt(62)
(C) 2sqrt(63)
(D) 2sqrt(64)
(E) 2sqrt(65)
Rationale: base of triangle is 20 and area is 80
therefore height=2*80/20=8.
now one side of triangle is of 10.
so we can get the point were the base is divided by applying Pythagoras therm
so division pt =sqrt(10^2-8^2)=sqrt(36)=6
threfore other half is 14.
now second side=sqrt(14^2+8^2)=sqrt(260)=2sqrt(65)
ANSWER:E
Answer: (E) 2sqrt(65)
Question: Tomy's age 24 years hence will be thrice his age four years ago. Find Tomy's present age?
(A) 12 years
(B) 13 years
(C) 15 years
(D) 17 years
(E) 18 years
Rationale: Let MTomy's present age be 'x' years.
x+ 24 = 3(x- 4)
=> 2x = 36 => x = 18 years.
E
Answer: (E) 18 years
Question: A trader has 50 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
(A) 5 and 45 kg
(B) 10 and 40 kg
(C) 15 and 35 kg
(D) 20 and 30 kg
(E) 40 and 30 kg
Rationale: Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 50/1+9 *1 = 5 kg
Quantity sold at 6% loss = 50/1+9 *9 = 45kg
ANSWER:A
Answer: (A) 5 and 45 kg
Question: In a mixed college 160 students are there in one class. Out of this 160 students 3/8 students are girls. How many boys are there ?
(A) A)40
(B) B)60
(C) C)80
(D) D)100
(E) E)140
Rationale: Total Number of Students :160
Total Girls : 160*3/8 =60
Total Boys : 160-60 = 100
Answer is D
Answer: (D) D)100
Question: A trader expects a gain of 15 % on his cost price. If in a week his sale is of Rs. 580, then what is his profit?
(A) 75.65
(B) 73.26
(C) 72.5
(D) 70.78
(E) 71.62
Rationale: Explanation:
We are given selling price = Rs. 580 and expected profit of 15 %
Therefore, we can easily solve this numerical, considering basic formulae of profit and loss.
Let cost price = x
Selling price = C.P. + Profit
S.P. = C.P. + (15% of C.P.) ---------- (We know that profit is gained on cost price)
580 = x + (0.15 x)
580 = 1.15 x
Therefore,
x = 504.347
Cost Price = Rs. 504.35
Now, we have the cost price and hence,
Profit = S. P. – C.P. = 580 – 504.35 = Rs. 75.65
The trader gets a profit of Rs. 75.65
ANSWER IS A
Answer: (A) 75.65
Question: Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?
(A) 10 years
(B) 38 years
(C) 39 years
(D) 64 years
(E) 67 years
Rationale: current age = 26 years because Nitin's age was equal to square of some number ( 25= 5^2) last year and the following year it would be cube of a number (27= 3^3).
Next cube age will be 64 =4^3 which will come after 64-26 = 38 years.
ANSWER:B
Answer: (B) 38 years
Question: Share Rs.6000 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John?
(A) 900
(B) 980
(C) 1200
(D) 1240
(E) 2000
Rationale: Amount received by sanjay.
4 / 12 X 6000 = 2000= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 2000.
E
Answer: (E) 2000
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
(A) 2777
(B) 2999
(C) 2799
(D) 2781
(E) 10500
Rationale: Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4
Simran's share = 24500 * 3/7 = Rs. 10500.Answer: E
Answer: (E) 10500
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.899] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
(A) 0
(B) 1
(C) 27
(D) 54
(E) 0
Rationale: K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
E
Answer: (E) 0
Question: A freight elevator can carry a maximum load of 1140 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator?
(A) 45
(B) 85
(C) 190
(D) 215
(E) 210
Rationale: The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1140 - 200 - 430 = 510.
allowed per package = 510 / 3 = 170
So difference in average of existing and allowable = 215 - 170 = 45
Hence A
Answer: (A) 45
Question: The product of a and b is equal to 14 more than twice the sum of a and b. If b = 8, what is the value of b - a?
(A) 2
(B) 3
(C) 7
(D) 24
(E) 35
Rationale: ab= 14 + 2(a+b)
8a= 14+2a +16
6a= 30
a=5
b-a= 8-5=3
B is the answer
Answer: (B) 3
Question: A batsman makes a score of 76 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
(A) 36
(B) 28
(C) 42
(D) 45
(E) None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 76 = 17x or x = (76 – 48) = 28.
Answer B
Answer: (B) 28
Question: If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 11 1/8%
(B) 11 1/5%
(C) 11 1/9%
(D) 11 7/9%
(E) 21 1/9%
Rationale: 100 – 10 = 90
90------10
100------? => 11 1/9%
Answer: C
Answer: (C) 11 1/9%
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
(A) 3:6:7
(B) 3:4:7
(C) 9:4:7
(D) 3:4:6
(E) 3:5:7
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
Answer: B
Answer: (B) 3:4:7
Question: Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Both of them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a distance of 50 miles, a housefly starts flying from Suresh Raina's cycle towards Gautam Gambhir at a relative speed of 17 miles per hour with respect to Raina's speed. What will be the time taken by housefly to reach Gambhir?
(A) 37
(B) 10
(C) 27
(D) 36
(E) 19
Rationale: Fly speed is 17 kmph w.r.t to suresh as fly is moving in opposite direction to suresh, its actual speed is 17 - 6 = 11.
Now relative speed of fly and gambhir = 11 - 6 = 5 kmph
So fly takes = 5011−65011−6 = 10 Hrs
Answer:B
Answer: (B) 10
Question: If 5+3+2=151022, 9+2+4=183652, then 7+2+5=?
(A) 223888
(B) 143547
(C) 2607778
(D) 126997
(E) 127811
Rationale: If the given number is a + b + c then a.b | a.c | a.b + a.c - b
⇒⇒ 5+3+2 = 5.3 | 5.2| 5.3 + 5.2 - 3 = 151022
⇒⇒ 9+2+4 = 9.2 | 9.4 | 9.2 + 9.4 - 2 = 183652
7+2+5= 7.2 | 7.5 | 7.2 + 7.5 - 2 = 143547
Answer:B
Answer: (B) 143547
Question: A person can row at 10 kmph in still water. If the velocity of the current is 2 kmph and it takes him 15 hour to row to a place and come back, how far is the place?
(A) 24km
(B) 30km
(C) 48km
(D) 72km
(E) 15km
Rationale: Speed of down stream = 10+2 = 12kmph
speed of upstream = 10-2 = 8kmph
Let the required distance be xkm
x/12 + x/8 = 15
2x+3x = 360
x = 72 km
Answer is D
Answer: (D) 72km
Question: Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs, travelling at a speed of 80 kmph. How far away from Delhi will the two trains meet?
(A) 120 km
(B) 360 km
(C) 480 km
(D) 500 km
(E) None
Rationale: Sol.
Suppose they meet x hours after 14.30 hrs.
Then, 60x = 80 (x - 2) or x = 8.
∴ Required distance = (60x8)km = 480 km.
Answer C
Answer: (C) 480 km
Question: If x/y = 3/z, then 9z^2 =
(A) y²/ x²
(B) x²y²
(C) 81y²/ x².
(D) 9y/x
(E) x²/y²
Rationale: This question is most easily solved by isolating y in the equation and substituting into the expression 9z²:
x/y = 3/z
x = 3y/z
3y = xz
z = 3y/x.
If we substitute 3y/xinto the expression for z, we get:
9(3y/x)² = 9(9y²/ x²) = 81y²/ x².
The correct answer is choice (C)
Answer: (C) 81y²/ x².
Question: A train running at the speed of 100 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 298 m
(B) 250 m
(C) 208 m
(D) 988 m
(E) 299 m
Rationale: Speed = 100 * 5/18 = 250/9 m/sec
Length of the train = speed * time = 250/9 * 9
= 250 m
Answer:B
Answer: (B) 250 m
Question: 30% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 70
(B) 97
(C) 87
(D) 100
(E) 76
Rationale: Given, 30% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 30% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/30 = 80
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (80 + 120)/2 = 100.
Answer:D
Answer: (D) 100
Question: Each of the following numbers has a remainder of 3 when divided by 8 except:
(A) 11
(B) 19
(C) 3
(D) 83
(E) 26
Rationale: It's E
26 = 8*3+2
Answer: (E) 26
Question: Sharmeeka is putting all of her pens in order by number. One has the number 4 on it, the next has number 8, the next has number 12, and the next has number 16.
What number will the next pen have on it?
(A) 20
(B) 25
(C) 32
(D) 22
(E) 24
Rationale: A) 20, because the pens are ordered by multiples of 4.
4 +4 = 8
8 + 4=12
12+4=16
16+4=20
Answer: (A) 20
Question: A standard Veggiematik machine can chop 20 carrots in 2 minutes. How many carrots can 3 standard Veggiematik machines chop in 3 minutes?
(A) 81
(B) 90
(C) 121
(D) 130
(E) 144
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 20 Carrots - 2 minutes,
1 standard Veggiematik machine - 10 Carrots - 1 minute,
Now
3 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 10X3X3 =90 Carrots
Answer B
Answer: (B) 90
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 40% profit on the cost of the item?
(A) 18
(B) 30
(C) 22
(D) 22.5
(E) 27
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 40% of the final price --> (final price)*0.6 = $18 --> (final price) = $30.
Answer: B.
Answer: (B) 30
Question: The sector of a circle has radius of 14 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 61 cm
(C) 28.9 cm
(D) 29.2 cm
(E) 98.2 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 14) + 2(14)
= 33 + 28 = 61 cm
Answer:B
Answer: (B) 61 cm
Question: If sales tax is reduced from 5% to 4%, then what difference it will make if you purchase an item of Rs. 1000
(A) 10
(B) 20
(C) 30
(D) 40
(E) 60
Rationale: Explanation:
Clue: Answer will be 5% of 1000 - 4% of 1000
Option A
Answer: (A) 10
Question: The simple interest on a sum of money is 5/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 5 4/9%
(B) 17 4/9%
(C) 7 4/9%
(D) 8 4/9%
(E) 9 4/9%
Rationale: 5/9 P = (P*R*R)/100
R = 22.36/3 = 7 4/9%
ANSWER:C
Answer: (C) 7 4/9%
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
(A) 3500
(B) 3900
(C) 3750
(D) 3840
(E) 3950
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y =	(5/2)x.
15x + 2y = 4000
15x + 2 x	(5/2)	x = 4000
20x = 4000
x = 200.
So, y =(5/2)x 200= 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer is B.
Answer: (B) 3900
Question: The greatest number by which the product of three consecutive multiples of 4 is always divisible is
(A) 54
(B) 76
(C) 152
(D) 384
(E) None of these
Rationale: Solution
Required number	= Product of first three multiplies of 3
= (4 Ã— 8 Ã— 12)= 384.
Answer D
Answer: (D) 384
Question: A man whose speed is 7.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 10
(B) 8
(C) 9
(D) 7.2
(E) 6
Rationale: M = 7.5
S = 1.5
DS = 9
US = 6
AS = (2 * 9 * 6) /15 = 7.2
Answer: D
Answer: (D) 7.2
Question: What is the smallest integer n that satisfies both of the following equations, in which p and q
are positive integers?
n = p2 + p
n = q2 + q + 2014
(A) 2024
(B) 2034
(C) 2056
(D) 2070
(E) 2196
Rationale: The term 2014 in the second equation suggests trying small numbers for q, and a
little experimentation with p close to the square root of 2014 and n = p(p + 1) leads fairly
quickly to q = 7, giving n = 2070, which is (45)(46)
correct answer D
Answer: (D) 2070
Question: What is the two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I. The number is multiple of 51.
II. The sum of the digits a and b is 6.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: From statement I:
A two digit number, greater than 9 and multiple of 51 should be 51 itself.
Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer.
From statement II:
A two digit number, greater than 9 and sum of the digit is 6.
It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone.
Thus, I alone give the answer while II alone not sufficient to answer.
ANSWER A I alone sufficient while II alone not sufficient to answer
Answer: (A) I alone sufficient while II alone not sufficient to answer
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm?
(A) 187 cm2
(B) 178 cm2
(C) 285 cm2
(D) 178 cm22
(E) 287 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
285 cm2
Answer: C
Answer: (C) 285 cm2
Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
(A) 14 min 19 sec
(B) 14 min 42 sec
(C) 14 min 20 sec
(D) 14 min 40 sec
(E) 14 min 10 sec
Rationale: :
Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec) = 14 min 40 sec.Answer: D
Answer: (D) 14 min 40 sec
Question: Jerry and Jim are opposing participants in an online auction. Each has a constant bidding strategy: Jerry always bids up by raising $40 over any previous bid. Jim always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: Jerry bids up first, and Jim follows. Jerry bids up again, and Jim follows and raises the bid to a final $600. What was the dollar value of the initial price?
(A) 90
(B) 465
(C) 656
(D) 345
(E) 35
Rationale: Initial bid = p$
Jerry = p+40
Jim = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus A is the correct answer.
Answer: (A) 90
Question: In a triangle ABC,point D is on side AB and point E is on side AC,such that BCED is a trapezium.DE:BC =3:5.Calculate the ratio of the area of triangle ADE and the trapezium BCED.
(A) 9/16
(B) 8/16
(C) 7/16
(D) 6/16
(E) 5/16
Rationale: area of tri(ADE)/area of tri(ABC) = DE^2 / BC^2 since tri(ADE) -tri(ABC)
area of tri(ADE)/area of tri(ABC) = 9/25
area of tri(ABC)/area of tri(ADE) = 25/9
area of tri(ABC) = area of tri(ADE) + area of trap(BCDE)
(area of tri(ADE) + area of trap(BCDE))/area of tri(ADE) = 25/9
1 + area of trap(BCDE)/area of tri(ADE) = 25/9
take1on both sides
area of trap(BCDE)/area of tri(ADE) = (25/9) - 1 = 16/9
since question is asking for area of tri(ADE)/area of trap(BCDE) = 9/16
ANSWER:A
Answer: (A) 9/16
Question: Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?
(A) 12
(B) 14
(C) 57
(D) 53
(E) 47
Rationale: In this series, each number is repeated, then 13 is subtracted to arrive at the next number.
27-13=14
Option B
Answer: (B) 14
Question: A train running at a speed of 36 km/h passes an electric pole in 15 seconds. In how many seconds will the whole train pass a 380-meter long platform?
(A) 47
(B) 49
(C) 51
(D) 53
(E) 55
Rationale: Let the length of the train be x meters.
When a train crosses an electric pole, the distance covered is its own length x.
speed = 36 km/h = 36000 m / 3600 s = 10 m/s
x = 15 * 10 = 150 m.
The time taken to pass the platform = (150 +380)/ 10 = 53 seconds
The answer is D.
Answer: (D) 53
Question: The difference between the place value and the face value of 5 in the numeral 856973 is
(A) 973
(B) 6973
(C) 5994
(D) 49995
(E) None of these
Rationale: (Place value of 5) - (Face value of 5) = (50000 - 5) = 49995
Answer: Option D
Answer: (D) 49995
Question: Express a speed of 66 kmph in meters per second?
(A) 10.33 mps
(B) 17 mps
(C) 97 mps
(D) 17.33 mps
(E) 18.33 mps
Rationale: 66 * 5/18
= 18.33 mps
Answer: E
Answer: (E) 18.33 mps
Question: A group of 8 cups need to be arranged. There are 2 blue cups and 2 red cups and the two of the pair of cups must be kept togather. in how many arrangements can the cups be arranged?
(A) A.1296
(B) B.1850
(C) C.2880
(D) D.3546
(E) E.4200
Rationale: Glue cupstogether: {AB}, {CD}.
6 units {AB}, {CD}, {E}, {F}, {G}, {H} can be arranged in 6! ways. Each cups within their unit can be arranged in 2! ways.
Therefore the final answer is 6!*2!*2!=2,880.
Answer: C.
Answer: (C) C.2880
Question: Given a number, there is an algorithm described here to find it's sum and number of factors. For example, let us take the number 1225?
(A) 1767
(B) 1800
(C) 1812
(D) 1890
(E) None
Rationale: Solving for 1225=52×72
Sum of divisors = (ap+1–1)/(a–1)×(bq+1–1)/(b–1)
Here a=5, b=7 prime factors
p=2 and q=2
Sum of divisors = (53–1)/(5–1)×(73–1)/(7–1)
= (124/4)×(342/6)
= (31×57)
= 1767
Option A
Answer: (A) 1767
Question: Last year, Company X made q dollars in profit. One thrid of the profit went to the company’s founder. The rest was split evenly among his four other partners. In terms of q, how much did each of the other partners receive?
(A) q/4
(B) q/5
(C) q/8
(D) q/6
(E) q/7
Rationale: Profit = q
Profit to company founder = q/3
Profit to other partners = 2q/3
Number of other partners = 4
Profit to each partner = (2q/3)/4 = q/6
Answer: D
Answer: (D) q/6
Question: A and B together can do a piece of work in 5 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
(A) 0.35 days
(B) 0.45 days
(C) 0.55 days
(D) 0.25 days
(E) 0.15 days
Rationale: B = 1/5 – 1/20 =0.15 days
ANSWER:E
Answer: (E) 0.15 days
Question: For some integer n, n^2 - 5 is divisible by all of the following EXCEPT
(A) 41
(B) 38
(C) 29
(D) 30
(E) 31
Rationale: Hint: n^2-5 (n is an integer) is never multiple of 3 (try to prove this), hence 30 is out.
Answer: D
Answer: (D) 30
Question: Riya and Priya set on a journey. Riya moves eastward at a speed of 30 kmph and Priya moves westward at a speed of 50 kmph.How far will be priya from Riya after 45 minutes
(A) 25kms
(B) 60kms
(C) 50kms
(D) 30kms
(E) 40kms
Rationale: total eastward distance= 30kmph*3/4hr=22.50 km
total westward distance= 50kmph*3/4hr=37.5 km
total distn betn them= 22.5+37.5=60km
ans 60km
ANSWER:B
Answer: (B) 60kms
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 10 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
(A) 0.1
(B) 0.6
(C) 1
(D) 1.2
(E) 2
Rationale: Option C
10+40t=50t
t=1
Answer: (C) 1
Question: There are 3 kids in a family-Anna, Peter and Maria. Anna can clean the house
for 1 hour, Peter can do the same job for 3 hours and Maria needs 6 hours.
How much time do they need to work to finish the same cleaning if they do it
together?
(A) 20min
(B) 40min
(C) 30min
(D) 50min
(E) 60min
Rationale: In 6 hours, Anna will do 6 times the work, Peter will do
2 times the work and Maria will just finish the work. So if they
work together they would do 9 times the work required in 6 hours.
Answer:40 minutes
correct answer B
Answer: (B) 40min
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $9. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 90/(xy)
(B) 90xy
(C) xy/90
(D) xy/10
(E) 81/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 9 / (xy/9) = 81/(xy).
The answer is E.
Answer: (E) 81/(xy)
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 19 cm2
(B) 30 cm2
(C) 17 cm2
(D) 18 cm2
(E) 12 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B
Answer: (B) 30 cm2
Question: In the class of 100 students, 70 speak Tamil and 70 speak Telugu. What is the lowest possible number of students who
speak both the languages?
(A) A)8
(B) B)10
(C) C)20
(D) D)30
(E) E)40
Rationale: let the student who speaks Tamil-x
let the student who speaks Telugu-y
as (xuy)-(xny)=total
70+70-(xny)=100
=40
E)
Answer: (E) E)40