mathewhe/aqua_rat huggingface dataset:
Question: A 300 m long train crosses a platform in 33 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 286 m
(B) 250 m
(C) 277 m
(D) 278 m
(E) 267 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/33 = 50/3
=> x = 250 m.
Answer:B
Answer: (B) 250 m
Question: A train running at the speed of 72 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150 meter
(B) 299 meter
(C) 666 meter
(D) 155 meter
(E) 180 meter
Rationale: Speed = 72*(5/18) m/sec = 20 m/sec
Length of Train (Distance) = Speed * Time
(20) * 9
= 180 meter
Answer: E
Answer: (E) 180 meter
Question: A 240 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 260
(C) 267
(D) 256
(E) 298
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 240)/9 = 500/9 => x = 260.
Answer: B
Answer: (B) 260
Question: If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
(A) 2278
(B) 388
(C) 1500
(D) 2776
(E) 8811
Rationale: Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500
Answer:C
Answer: (C) 1500
Question: If 8 men do a work in 80 days, in how many days will 20 men do it?
(A) 18 days
(B) 32 days
(C) 42 days
(D) 48 days
(E) 44 days
Rationale: 8 * 80 = 20 * x
x = 32 days
ANSWER:B
Answer: (B) 32 days
Question: A train 160 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
(A) 54 kmph
(B) 60 kmph
(C) 66 kmph
(D) 72 kmph
(E) 90 kmph
Rationale: speed of train relative to man: 160/6 * 18/5 km/hr
= 96 km/hr
let speed of train= x
therefore x+6 = 96
x= 96-6
x=90 km/hr
ANSWER:E
Answer: (E) 90 kmph
Question: The angle between the minute hand and the hour hand of a clock when the time is 12.30, is
(A) 35°
(B) 65°
(C) 45°
(D) 195°
(E) 95°
Rationale: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 12, M = 30 and minute hand is behind the hour hand.
Hence the angle
=30(H−M/5)+M/2
=30(12−30/5)+30/2
=30(12−6)+15
=30×6+15 =195°
Answer is D.
Answer: (D) 195°
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 5, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
(A) 27
(B) 72
(C) 36
(D) 112
(E) 422
Rationale: {1}{2}{greater than 5}{divisible by 3}{3x}{x}:
The third digit can take 4 values:6, 7, 8, or 9.
The fourth digit can take 3 values: 3, 6, or 9.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 4*3*3 = 36.
Answer: C.
Answer: (C) 36
Question: The taxi charges in a city comprise of a fixed charge, together with the charge of the distance covered. For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204. What will a person have to pay for travelling a distance of 30 km?
(A) Rs. 236
(B) Rs. 240
(C) Rs. 248
(D) Rs. 252
(E) Rs. 352
Rationale: For a journey of 16 km, the charges paid are Rs. 156 and for a journey of 24 km, the charges paid are Rs. 204.
Additional charges for 8 kms = 204-156 = 48 Rs
additional charge/km= 48/8 = Rs 6
additional charge for 6 kms = 6*6 = Rs 36.
total charges for 30 kms = 204 +36 = Rs 240
ANSWER:B
Answer: (B) Rs. 240
Question: A boatman goes 3 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
(A) 40 minutes
(B) 1 hour 7 min
(C) 1 hour 15 min
(D) 1 hour 30 min
(E) 1 hour 10 min
Rationale: speed (upstream) =3/1 = 3 kmhr
speed (downstream)=1/(10/60)= 6 kmhr
speed in still water = 1/2 (3+6) = 4.5 kmhr
time taken in stationary = 5/4.5 = 1 hrs 7 min
ANSWER:B
Answer: (B) 1 hour 7 min
Question: In a mens hostel, there were 95 students. To accommodate 30 more students the average is decreased by rupees 5. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now ?
(A) Rs.4680
(B) Rs.4287
(C) Rs.4129
(D) Rs.4112
(E) Rs.4101
Rationale: Explanation:
Let the expenditure on the 95 students be 'x'
Then,
95x + 500 = 120(x â€“ 5)
95x + 500 = 120x - 600
120x - 95x = 1100
25x = 1100
=> x = 44
Therefore, total expenditure of the hostel becomes
95 x 44 + 500 = 4680.
Answer: A
Answer: (A) Rs.4680
Question: For the set {2, 2, 3, 3, 4, 4, 5, 5,7,7 x}, which of the following values of x will most increase the standard deviation?
(A) 1
(B) 2
(C) 3
(D) (-3.2)^2
(E) 5
Rationale: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4.2
Step 2, For each number: subtract the Mean and square the result =
(1-4.2)^2=(-3.2)^2
(2-4.2)^2=(-2.2)^2
(3-4.2)^2 =(-1.2)^2
(4-4.2)^2=(.2)^2
(5-4.2)^2=(.8)^2
Clearly (1-3.5)^2=(-3.2)^2 will give you the greatest value among all the other options.
Hence D
Answer: (D) (-3.2)^2
Question: The population of a town is 186800. If it increase at the rate of 7% per annum. What will be its population for 2years hence?
(A) 200000
(B) 215600
(C) 194582
(D) 213867
(E) 215460
Rationale: population after 2years = 186800*(1+ 7/100)^2 = 213867
Answer is D
Answer: (D) 213867
Question: 0,2,6,12,20, ____
(A) 25
(B) 28
(C) 30
(D) 26
(E) 35
Rationale: 0,2,6,12,20, .....
1*1-1=0
2*2-2=2
3*3-3=6
4*4-4=12
5*5-5=20
So 6*6-6=30
ANSWER:C
Answer: (C) 30
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 30 people owned cats, 40 owned dogs, 14 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
(A) 2
(B) 4
(C) 6
(D) 12
(E) 32
Rationale: You are considering a case when cat dogs and rabbit are not exactly equal to 12 .
The solution shall be 60=30+40+14-12-2x
and hence x shall be 6.
Answer C
Answer: (C) 6
Question: If the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
(A) 4
(B) 8
(C) 12
(D) 3
(E) 18
Rationale: Let length of rectangle = L
3^2 = L*4
=> L = 9/4 = 3
Answer D
Answer: (D) 3
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 5429
(B) 2897
(C) 5400
(D) 2689
(E) 2781
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer:C
Answer: (C) 5400
Question: The digital sum of a number is the sum of its digits. For how many of the positive integers 24-80 inclusive is the digital sum a multiple of 7?
(A) 7
(B) 9
(C) 14
(D) 16
(E) 20
Rationale: is there other way than just listing?
25
34
43
52
59
61
68
70
77
9 ways..
B
Answer: (B) 9
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 8 years
(B) 16 years
(C) 4 years
(D) 18 years
(E) 12 years
Rationale: Let the age of first child be x years.
since all the children got birth in interval of 3 years so the age of 2nd,3rd,4th and 5th child would be x-3 , (x-3)-3 ,((x-3)-3)-3 ,(((x-3)-3)-3)-3 respectively,
also the sum of ages of all children is 50,
= x+(x-3)+(x-6)+(x-9)+(x-12)=50
=5x-30=50
=5x=80
=x=16
so the age of youngest child would be 16-12 = 4 years. ANSWER : C
Answer: (C) 4 years
Question: Jamboree and GMAT Club Contest Starts
QUESTION #20:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
(A)  660
(B)  600
(C)  500
(D)  300
(E)  240
Rationale: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.
Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together
In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!
Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.
Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)
Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.
Option B is correct!
Answer: (B)  600
Question: Which of the following lines has x-intercept and y-intercept that are integers W?
(A) y=3x+1
(B) y=√x+1
(C) y=-2/x
(D) y=x^2-1
(E) xy=1
Rationale: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers W and the correct answer is D.
Answer: (D) y=x^2-1
Question: A no.when divided by 224 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
(A) 2
(B) 7
(C) 9
(D) 11
(E) 12
Rationale: 224 + 43 = 267/17 = 12 (Remainder)
E
Answer: (E) 12
Question: In X game of billiards, X can give Y 20 points in 60 and he can give Z 30 points in 60. How many points can Y give Z in X game of 80?
(A) 30
(B) 20
(C) 25
(D) 40
(E) 50
Rationale: X scores 60 while Y score 40 and Z scores 30.
The number of points that Z scores when Y scores 80 = (80 * 30)/40 = 60.
In X game of 100 points, Y gives (80 - 60) = 20 points to C.
B
Answer: (B) 20
Question: Stella buys an advertising agency for rs.16,000,000 and sells it for rs.20,000,000. Find her gain %.
(A) 9%
(B) 20%
(C) 14%
(D) 87%
(E) 25%
Rationale: sol. cp=rs16,000,000, sp=rs 20,000,000
gain=rs(20,000,000 –16,000,000)=rs4,000,000
so gain%={(4,000,000/16,000,000)*100}=25%
Answer is E.
Answer: (E) 25%
Question: Two dice are rolled. What is the probability the sum will be greater than 8?
(A) 2/9.
(B) 1/12.
(C) 5/36.
(D) 7/36.
(E) 1/5.
Rationale: Combinations possible: (6,6) , (5,6) , (6,5) , (4,6), (6,4) , (5,5) , (5,4), (4,5) = 8
Total combinations possible: 6*6=36
Answer = 8/36 = 2/9 Option A.
Answer: (A) 2/9.
Question: The length and breadth of a room are 8 m and 6 m respectively. A cat runs along all the four walls and finally along a diagonal order to catch a rat. How much total distance is covered by the cat?
(A) 22
(B) 88
(C) 38
(D) 99
(E) 11
Rationale: Answer: C) 38
Answer: (C) 38
Question: A bag of potatoes weighs 12 lbs divided by half of its weight. How much does the bag of potatoes weight?
(A) 20 lb
(B) 18 lb
(C) 12 lb
(D) 15 lb
(E) 5 lb
Rationale: Sol.
12÷1 = 12.
Answer : C
Answer: (C) 12 lb
Question: The difference between simple and compound interests annually on a particular sum of money for 2 years at 4% per annum is Rs. 1. What is the sum?
(A) 600
(B) 625
(C) 650
(D) 675
(E) 700
Rationale: sum consider as x
CI = (x(1+4/100)^2-x) = 676/625x-x
=>51/625x
SI = x*4*2/100 = 2x/25
51x/625 - 2x/25 = 1
x= 625
ANSWER B
Answer: (B) 625
Question: If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.
(A) 33
(B) 38
(C) 77
(D) 50
(E) 29
Rationale: Explanation:
Let x and y be the length and breadth of the rectangle respectively.
Then, x - 4 = y + 3 or x - y = 7 ----(i)
Area of the rectangle =xy; Area of the square = (x - 4) (y + 3)
(x - 4) (y + 3) =xy <=> 3x - 4y = 12 ----(ii)
Solving (i) and (ii), we get x = 16 and y = 9.
Perimeter of the rectangle = 2 (x + y) = [2 (16 + 9)] cm = 50 cm.
Answer: D) 50
Answer: (D) 50
Question: A man starts walking at 3 pm, He walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill, 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: if x km is level ground and y km is hill road, then
x/4 + y/3 +y/6+x/4= 6
6(x+y)=72
x+y=12 km
so one side distance is 12 kms.
ANSWER:E
Answer: (E) 12
Question: The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(A) 4.5
(B) 4.6
(C) 4.7
(D) 4.8
(E) 4.9
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.4 × 2) + (3.85 × 2)]
= 23.70 – (6.8 + 7.7)
= 23.70 – 14.5 = 9.20
∴ Required average = (9.2⁄2) = 4.6
Answer B
Answer: (B) 4.6
Question: What day of the week was 1 January 1901
(A) Monday
(B) Tuesday
(C) Saturday
(D) Friday
(E) None of these
Rationale: Explanation :
1 Jan 1901 = (1900 years + 1-Jan-1901)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601-1900
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
1-Jan-1901 = 1 odd day
Total number of odd days = (0 + 1 + 1) = 2
2 odd days = Tuesday
Hence 1 January 1901 is Tuesday.
Answer : Option B
Answer: (B) Tuesday
Question: Car A runs at the speed of 50km/hr & reaches its destination in 8hr. Car B runs at the speed of 25 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?
(A) 4 : 1
(B) 11 : 8
(C) 13 : 7
(D) 15 : 7
(E) 16 : 9
Rationale: Sol. Distance travelled by Car A = 50 × 8 = 400 km
Distance travelled by Car B = 25 × 4 =100 km
Ratio = 400/100 = 4 : 1
Answer : A
Answer: (A) 4 : 1
Question: A tradesman by means of his false balance defrauds to the extent of 18%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 44%
(B) 48%
(C) 94%
(D) 45%
(E) 39%
Rationale: g% = 18 + 18 + (18*18)/100
= 39%
Answer: E
Answer: (E) 39%
Question: If x and y are positive integers such that (3x + 7y) is a multiple of 11, then which of the following will be divisible by 11 ?
(A) 9
(B) 11
(C) 17
(D) 21
(E) 27
Rationale: By hit and trial, we put x = 5 and y = 1 so that (3x + 7y) = (3 x 5 + 7 x 1) = 22, which is divisible by 11.
(4x + 6y) = ( 4 x 5 + 6 x 1) = 26, which is not divisible by 11;
(x + y + 4 ) = (5 + 1 + 4) = 10, which is not divisible by 11;
(9x + 4y) = (9 x 5 + 4 x 1) = 49, which is not divisible by 11;
(4x - 9y) = (4 x 5 - 9 x 1) = 11, which is divisible by 11.
Option B
Answer: (B) 11
Question: A cycle is bought for Rs.900 and sold for Rs.1350, find the gain percent?
(A) 27%
(B) 20%
(C) 50%
(D) 30%
(E) 24%
Rationale: 900 ---- 450
100 ---- ? => 50%
Answer: C
Answer: (C) 50%
Question: which number need to add to 859622 to get a number exactly divisible by 456?
(A) 454365
(B) 412343
(C) 546573
(D) 567683
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: What is the maximum number of pieces that a circular pizza can be cut into with 5 linear cuts?
(A) 10
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: 1 cut makes 2 pieces
a second cut can make 4 pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
a fifth cut can make 16 pieces by cutting through 5 of the pieces
D
Answer: (D) 16
Question: A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 50% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) $40
(B) $60
(C) $80
(D) $90
(E) $150
Rationale: Purchase price = 150
Selling price = x
150 + 0.5*x = x
0.5*x = 150
x = 300
Profit = 300 - 150 = 150
ANSWER:E
Answer: (E) $150
Question: A meeting has to be conducted with 5 managers. Find the number of ways in which the managers be selected from among 8 managers, if 2 managers will not attend the meeting together?
(A) 40
(B) 36
(C) 42
(D) 45
(E) 47
Rationale: we can either choose all 5 people from 6 manager who have no problems or choose 4 from the 6 and 1 from the 2 managers who have a problem sitting together
so 6C5 + (6C4 * 2C1)
this is 6 + 30=36
Answer : B
Answer: (B) 36
Question: What is the are of an equilateral triangle of side 20 cm?
(A) 250√3
(B) 150√3
(C) 300√3
(D) 200√3
(E) 100√3
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 20, Area of triangle = √3/4 * 20 * 20
= 100√3 cm2;
Answer:E
Answer: (E) 100√3
Question: If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?
(A)  x^2 - 9x
(B)  x^2 - 9x + 20
(C)  x^2 - 2x + 3
(D)  x^2 + 2x - 3
(E)  x^2 + 5x + 4
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= -1 in the equation x^2 +5x+4 = 1-5+4 = 0
E is also the answer
Answer: (E)  x^2 + 5x + 4
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
(A) 9,343
(B) 10,982
(C) 11,881
(D) 12,988
(E) 13,547
Rationale: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is C.
Answer: (C) 11,881
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 112
(B) 50
(C) 77
(D) 14
(E) 12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr
= 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: (B) 50
Question: A teacher has 16 students, then she gets 7 more students. Now how many students does she have?
(A) A)9
(B) B)15
(C) C)15
(D) D)23
(E) E)25
Rationale: 16+7=23. Answer is D
Answer: (D) D)23
Question: Ravi can do a piece of work in 50 days while Prakash can do it in 75 days. In how many days will they finish it together?
(A) 30 days
(B) 35 days
(C) 25 days
(D) 27 days
(E) 29 days
Rationale: 1/50 + 1/75 = 5/150
30/1 = 30 days
ANSWER:A
Answer: (A) 30 days
Question: Kiran travels from A to B by car and returns from B to A by cycle in 7 hours. If he travels both ways by car he saves 3 hours. What is the time taken to cover both ways by cycle?
(A) 10 hours
(B) 16 hours
(C) 19 hours
(D) 15 hours
(E) 20 hours
Rationale: Let the time taken to cover from A to B in car and cycle be x hours and y hours respectively.
x + y = 7 --- (1) ; 2x = 4 --- (2)
solving both the equations, we get y = 5
So, time taken to cover both ways by cycle = 2y hours
=10 hours.
Answer: A
Answer: (A) 10 hours
Question: George and Mark can paint 720 boxes in 20 days. Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is
(A) 28
(B) H
(C) 27
(D) 29
(E) 271
Rationale: Answer:B
Answer: (B) H
Question: If x = a/(a – 1) and 1/(a – 1), then:
(A) x is equal to y
(B) x is equal to y only if a < 1
(C) x is greater than y
(D) x is greater than y only if a < 1
(E) y is greater than x only if a < 1
Rationale: x = a/(a – 1) = 1 + 1/(a – 1) = 1 + y.
Therefore, x > y
ANSWER:A
Answer: (A) x is equal to y
Question: In August,a cricket team that played 120 matches won 20% of the games it played.After a continuous winning streak,this team raised its average to 52%.How many matches did the team win to attain this average?
(A) 40
(B) 52
(C) 68
(D) 80
(E) 98
Rationale: let the no of matches played more=x
so,
(120+x)*52/100=24+x
by solving we get x=80
ANSWER:D
Answer: (D) 80
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?
(A) Rs. 70
(B) Rs. 71
(C) Rs. 72
(D) Rs. 90
(E) Rs. 98
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
C
Answer: (C) Rs. 72
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 63, what is the total amount?
(A) 166
(B) 105
(C) 178
(D) 177
(E) 245
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 63
35 --- ? => 245
Answer: E
Answer: (E) 245
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnut purchased if you paid $19?
(A) 24
(B) 25
(C) 35
(D) 36
(E) 37
Rationale: a is the number of dozen of doughnuts at a price of $6/dozen
1 + 6a = 19
a= 3
The total number of doughnuts purchased -->
1 + 3 * 12 = 37
ANSWER: E
Answer: (E) 37
Question: If (4.2)x = (0.42)y = 100, then (1/x) - (1/y) =
(A) 1
(B) 2
(C) 1/2
(D) 1/4
(E) 2
Rationale: (4.2)x = 100
=> (42)x = 102+x
=> 42 = 10(2/x+1) ---------- (i)
[42/100]y = 100 => 42y = 102+2y
=> 42 = 102/y+2-------- (ii)
From (i) and (ii), 2/x - 2/y = 1
=>1/x - 1/y = 1/2.
ANSWER:C
Answer: (C) 1/2
Question: In each of the following questions a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and fill in the blank spaces.
2, 7, 14, 23, 34, ?
(A) 31
(B) 47
(C) 36
(D) 31
(E) 33
Rationale: B
47
The given sequence is +5, +7, +9, ——
ie. 2+ 5 = 7, 7 + 7 = 14, 14 + 9 = 23
Answer: (B) 47
Question: Find the no.of ways of arranging 5 men and 5 ladies at a circular table so that no two ladies sit together ?
(A) 4!x4!
(B) 5!x5!
(C) 4!x5!
(D) 10!x10!
(E) 25!x25!
Rationale: The no. of ways of 5 men may be arranged in 4! ways. The ladies can arranged in themselves in 5! ways. The required no. of ways of arranging them is 4!x5! . Ans:(C)
Answer: (C) 4!x5!
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 7 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 9 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2)
= 34 kmph
Speed upstream = d/t = 45/(2 1/2)
= 18 kmph
The speed of the stream = (34 - 18)/2
= 8 kmph
Answer: D
Answer: (D) 8 kmph
Question: How many words with or without meaning, can be formed by using all the letters of the word, â€˜WORKâ€™, using each letter exactly once?
(A) 700
(B) 24
(C) 32
(D) 48
(E) 28
Rationale: The word â€˜WORKâ€™ contains 4 different letters.
Therefore, Required number of words= Number of arrangement of 4 letters, taken all at a time
=4P4
= 4!
= 4*3*2*1
= 24
ANSWER:B
Answer: (B) 24
Question: If A invested 5 times of B and at the end of the year they got a profit of Rs.36,000 in their business then share. of B in the profit was (in Rs.)
(A) 5000
(B) 4000
(C) 3000
(D) 6000
(E) 3500
Rationale: A:B=5:1
so b=1/6 *36000
=6000
ANSWER:D
Answer: (D) 6000
Question: By selling 12 toffees for a dollar, a man loses 20%. How many for a dollar should be sell to get a gain of 20%?
(A) 8
(B) 5
(C) 9
(D) 4
(E) 3
Rationale: A
8
Let S.P. of 12 toffees be $x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For $3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
Answer: (A) 8
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 50, the dividend is:
(A) 5330
(B) 6300
(C) 5343
(D) 5345
(E) 5350
Rationale: Divisor = (5 * 50) = 250
= 10 * Quotient = Divisor
=> Quotient = 250/10 = 25
Dividend = (Divisor * Quotient) + Remainder
Dividend = (250 * 25) + 50 = 6300.
B
Answer: (B) 6300