mathewhe/aqua_rat huggingface dataset:
Question: How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?
(A) 26
(B) 72
(C) 28
(D) 82
(E) 27
Rationale: Explanation:
D = 100 + 180 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec
Answer: Option C
Answer: (C) 28
Question: Calculate how many men are needed to finish a specific task in 5 days if it will take 15 men to complete the same task in 10 days. ?
(A) 13
(B) 16
(C) 35
(D) 25
(E) 15
Rationale: men required to finish the work in 5 days = 5*15/5 = 15
Answer is E
Answer: (E) 15
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 9 years ago was 20 years. The present age of the husband is:
(A) 20 years
(B) 30 years
(C) 60 years
(D) 32 years
(E) 35 years
Rationale: D
32 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 9 x 2) years = 58 years.
Husband's present age = (90 - 58) years = 32 years.
Answer: (D) 32 years
Question: Find the average of x and y if the average (arithmetic mean) of x, y, and 30 is 10 greater than the average of x, y, 20, and 30.
(A) 50
(B) 75
(C) 100
(D) 125
(E) 150
Rationale: consider 30 is 10 greater than 20: 30 = 20+10
similarly
(x+y+30)/3 = (x+y+20+30)/4 + 10
get a like denominator on the right side
(x+y+30)/3 = (x+y+50)/4 + 40/4
(x+y+30)/3 = (x+y+50+40)/4
(x+y+30)/3 = (x+y+90)/4
cross multiply
4(x+y+30) = 3(x+y+90)
4x+4y+120 = 3x+3y+270
collect like terms
4x-3x + 4y-3y = 270 - 120
x + y = 150
thus (x+y)/2 = 150/2
(x+y)/2 = 75
the average of x and y is 75
B
Answer: (B) 75
Question: Insert the missing number
6, 7, 9, 13, 21, ...
(A) 25
(B) 29
(C) 37
(D) 32
(E) 30
Rationale: Difference between two numbers in the series is multiplied by 2 to get the next number
6,7 ...Difference is 1
7,9 Difference is 2
9,13 difference is 4
13,21 Difference is 8
21, 37 Difference is 16
ANSWER:C
Answer: (C) 37
Question: M = {9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5}
The mean and standard deviation of the 8 numbers in M are 10.0 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
(A) 70%
(B) 75%
(C) 80%
(D) 85%
(E) 90%
Rationale: If mean of the 8 numbers in M is 10.0 & standard deviation 0.3,
the number that lie within the 1st standard deviation (M - SD to M + SD)
range from 9.7 to 10.3 (both inclusive)
The numbers in this set in that range are 6/8 or 75%
Ans : (Option B)
Answer: (B) 75%
Question: The total circumference of two circles is 88. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
(A) 5.7
(B) 6.0
(C) 6.7
(D) 9.7
(E) 14.0
Rationale: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 88
where 2r = R
Thus:
2πr + 4πr = 88
6πr = 88
r = approx 4.7
πR + 2Rπ = 88
3πR = 88
R = approx 9.3
r + R = approx 14.0
Answer : E
Answer: (E) 14.0
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) Rs.8000, Rs.17000
(B) Rs.9000, Rs.16000
(C) Rs.18000, Rs.7000
(D) Rs.10000, Rs.15000
(E) Rs.20000, Rs.15000
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000
ANSWER:D
Answer: (D) Rs.10000, Rs.15000
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 2000. The difference between the profit shares of A and C is?
(A) 621
(B) 276
(C) 236
(D) 800
(E) 211
Rationale: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 2000
=> 5 parts out of 15 parts is Rs. 2000
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (2000) = Rs. 800
Answer: D
Answer: (D) 800
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
(A) 65
(B) 77
(C) 32
(D) 32
(E) 60
Rationale: The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = 5P3 = 60.
Answer:E
Answer: (E) 60
Question: What is the length of the longest pole which can be kept in a room 9 m long, 4 m broad and 3 m high?
(A) 10.29
(B) 9
(C) 11
(D) 13
(E) None
Rationale: Explanation:
d2 = 92 + 42 + 32 = 10.29
A)
Answer: (A) 10.29
Question: A retailer sells 7 shirts. The first 2 he sells for $38 and $42. If the retailer wishes to sell the 7 shirts for an overall average price of over $50, what must be the minimum average price of the remaining 5 shirts?
(A) $54.00
(B) $57.00
(C) $58.00
(D) $60.50
(E) $63.00
Rationale: First 2 shirts are sold for $38 and $42=$80.
To get average price of $50,total sale should be 7*$50=$350
So remaining 5 shirts to be sold for $350-$80=$270
Answer should be 270/5=$54.00 that is A
Answer: (A) $54.00
Question: What is the product of all the prime factors of 15?
(A) 12
(B) 3
(C) 4
(D) 15
(E) 20
Rationale: factors : 3,5
3*5 =15
Answer : D
Answer: (D) 15
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 1 and the 2 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
(A)  72
(B)  66
(C)  76
(D)  78
(E)  90
Rationale: Number of arrangements using 5 distinct digits = 5!
Number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 1 and 2 can be arranged as 12 or 21.
Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72
Answer : A
Answer: (A)  72
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $400, what were her original savings?
(A) $1500
(B) $1600
(C) $1700
(D) $1800
(E) $1900
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $400. So 1 / 4 of her savings is $400. So her original savings are 4 times $400 = $1600
correct answer B
Answer: (B) $1600
Question: At what time between 3 and 4 o'clock the hands are in opposite direction?
(A) 49 1/11 min past 3
(B) 16 min past 3
(C) 2 min past 4
(D) 3 2/11 min past 3
(E) 4 2/11 min past 3
Rationale: at 3'0 clock the minutes hand will be 15 min away from hours hand
both hands are opposite when they are 30 minutes away from each other
so,min hand has to gain 45 mins
to gain 1 min minute hand 12/11minutes=45*12/11=49 1/11
ans:49 1/11
ANSWER:A
Answer: (A) 49 1/11 min past 3
Question: If the average of ten numbers is 40, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 40
(A) I
(B) II
(C) all three options
(D) III
(E) I&II
Rationale: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.
IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.
C
Answer: (C) all three options
Question: If all the sides of a right triangle increase in length by 30%, then by what percentage does the area of the triangle increase?
(A) 69%
(B) 81%
(C) 85%
(D) 96%
(E) 120%
Rationale: Let B be the base and H be the height of the original triangle.
The original area is (1/2)BH.
The area of the expanded triangle is (1/2)(1.3B)(1.3H) = (1.3)(1.3)(1/2)BH = 1.69(1/2)BH
The answer is A.
Answer: (A) 69%
Question: In a contest, a bowl contains 12 keys, only one of which will open a treasure chest. If a contestant selects the key that opens the treasure chest, she wins the contents of that chest. If Anna is allowed to draw two keys, simultaneously and at random, from the bowl as the first contestant, what is the probability that she wins the prize?
(A) 1/11
(B) 1/12
(C) 1/6
(D) 11/120
(E) 2/11
Rationale: P(not winning) = 11/12*10/11 = 5/6
P(winning) = 1 - 5/6 = 1/6
The answer is C.
Answer: (C) 1/6
Question: One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader?
(A) 120 %
(B) 140 %
(C) 162/3 %
(D) 20 %
(E) None
Rationale: Sol.
CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain.
Answer D
Answer: (D) 20 %
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 10 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
(A) 1 : 2 : 400
(B) 1 : 4 : 100
(C) 20 : 4 : 1
(D) 100 : 4 : 1
(E) 400 : 4 : 1
Rationale: B.........M........Y
20.....0,10......Y
B.........4........1
What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:
B.........M........Y
200.....1.........Y
B........20......10
Then I multiplied every row by 20 (the LCM of 1 and 40), which led me to this:
B.........M........Y
4000...20.......10
Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:2:40
ANS A
Answer: (A) 1 : 2 : 400
Question: P and Q started a business with respective investments of Rs. 4 lakhs and Rs. 10 lakhs. As P runs the business, his salary is Rs. 5000 per month. If they earned a profit of Rs. 2 lakhs at the end of the year, then find the ratio of their earnings?
(A) 2:1
(B) 1:8
(C) 8:1
(D) 1:1
(E) 1:5
Rationale: Ratio of investments of P and Q is 2 : 5
Total salary claimed by P = 12 * 5000 = Rs. 60000
Total profit = Rs. 2 lakhs.
Profit is to be shared = Rs. 140000
Share of P = (2/7) * 140000 = Rs. 400000
Share of Q = Rs. 100000
Total earnings of P = (60000 + 40000) = Rs. 100000
Ratio of their earnings = 1 : 1
Answer: D
Answer: (D) 1:1
Question: A group of tourists wants to visit only an even number of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: The number of ways to choose two cities is 4C2=6.
The number of itineraries for each pair of 2 cities is 2!.
So the number of itineraries to two cities is 6*2!=12.
The number of ways to choose four cities is 4C4=1.
The number of itineraries for the group of 4 cities is 4!.
So the number of itineraries to four cities is 4!=24.
The total number of itineraries is 12+24=36.
The answer is E.
Answer: (E) 36
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 190 sec
(B) 120 sec
(C) 130 sec
(D) 210 sec
(E) 220 sec
Rationale: A
190 sec
Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10 = 190 sec.
Answer: (A) 190 sec
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 28%
(B) 20%
(C) 29%
(D) 27%
(E) 10%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer:B
Answer: (B) 20%
Question: A certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 81
(B) 82
(C) 84
(D) 86
(E) 88
Rationale: 1C4*2C7 = 4*21 = 84
the answer is (C)
Answer: (C) 84
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
(A) 9
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.
Answer:A
Answer: (A) 9
Question: If e is an even integer and q is an odd integer, which of the following must be an odd integer?
(A) e/q
(B) eq
(C) 2e+q
(D) 2(e+q)
(E) 3e/q
Rationale: this is a must question:
A. e/q
can be a non-integer
B. eq
always even
C. 2e+q
e = even -> even+odd = odd
D. 2(e+q)
always even - e+q = odd *2 -> even
E. e/q
might be a non integer.
C
Answer: (C) 2e+q
Question: Of the 90 people in a room, 2/5 are women. If 2/3 of the people are married, what is the maximum number of women in the room who could be unmarried?
(A) 26
(B) 30
(C) 32
(D) 34
(E) 36
Rationale: women = 2/5 * 90 = 36
married = 2/3 * 90 = 60
unmarried = 30
max(un-married women) = 30
B
Answer: (B) 30
Question: Matt buys a roses for his wife for rs.64.99 and then they get into a fight, so he decides to sell them for rs.74.99. Find his gain %.
(A) 17.92%
(B) 12.46%
(C) 2%
(D) 15.39%
(E) 16.88%
Rationale: sol. cp=rs64.99, sp=rs 74.99
gain=rs(74.99 –64.99)=rs10.00
so gain%={(10.00/64.99)*100}=15.39%
Answer is D.
Answer: (D) 15.39%
Question: How many five-digit numbers are there, if the two leftmost digits are even, the other digits are odd and the digit 8 cannot appear more than once in the number.
(A) 2200
(B) 2290
(C) 2280
(D) 2300
(E) 2375
Rationale: N=(4*5-1)*5*5*5=2375
where
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
1 case of 88 for two leftmost digit
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}
E
Answer: (E) 2375
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number I and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number I of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: (D) 88
Question: Dhoni is 25 years older than his daughter Mary. In 10 years Ross will be twice as old as Mary. What is Mary current age.
(A) 14
(B) 16
(C) 17
(D) 18
(E) 15
Rationale: Now: Mary = x, Dhoni =x+25
In 10 years Mary = x+10, Dhoni= x+25+10 or 2(x+10)
x+25+10 = 2(x+10)
x+35=2x+20
35-20=2x-x
15=x
Mary is 15 years old
Answer : E
Answer: (E) 15
Question: The mean of 50 observations was 36. It was found later that an observation 90 was wrongly taken as 23. The corrected new mean is?
(A) 37.3
(B) 36.1
(C) 36.5
(D) 36.9
(E) 36.3
Rationale: Correct sum
= (36 * 50 + 90 - 23)
= 1867.
Correct mean = 1825/50
= 37.3
Answer:A
Answer: (A) 37.3
Question: 80 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?
(A) 75
(B) 80
(C) 85
(D) 90
(E) 60
Rationale: Answer = E
Please refer diagram below
70 - 10 = 60
Answer: (E) 60
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 140. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
(A) 62
(B) 68
(C) 76
(D) 84
(E) 96
Rationale: We see that h will be a maximum h=140 when t-3=0, that is when t=3.
At t=5, h = -14(5-3)^2 + 140 = -14(4) + 140 = 84
The answer is D.
Answer: (D) 84
Question: A policeman noticed a criminal from a distance of 180 km. The criminal starts running and the policeman chases him. The criminal and the policeman run at the rate of 8 km and 10 km per hour respectively. What is the distance between them after 3 minutes ?
(A) 100 m
(B) 80 m
(C) 130 m
(D) 150 m
(E) None of these
Rationale: Explanation :
Solution: Relative speed = (10 - 8) = 2 km/hr.
Distance covered in 3 minutes = (2 * 3/60) km = 1/10 km = 100 m.
.'. Distance between the criminal and policeman = (180 - 100) m = 80 m.
Answer : B
Answer: (B) 80 m
Question: A transport company’s 120 buses running 20 hrs a day consume 360 of fuel in a day. In the next 3 days, the company will invest in 30 more green buses that use 30% less fuel. How many lts of fuel will be consumed in a five day week after the new buses are added to the fleet?
(A) 3,060
(B) 1, 512
(C) 1,800
(D) 1,260
(E) 3,312
Rationale: old buses use 360* 5 days = 1,800 lts
New buses use (0.70* 360)/120* 5 days * 30 buses = 1,512 lts
Total fuel is 3,312 lts
Answer is E
Answer: (E) 3,312
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
(A) 22
(B) 28
(C) 27
(D) 80
(E) 21
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer:D
Answer: (D) 80
Question: Evaluate 28% of 450 + 45% of 280
(A) 232
(B) 242
(C) 252
(D) 262
(E) 272
Rationale: Explanation:
= (28/100) * 450 + (45/100) * 280
= 126 + 126 = 252
Option C
Answer: (C) 252
Question: If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2, b2, c2 is:
(A) M2
(B) 3M2
(C) 6M2
(D) 9M2
(E) None of these
Rationale: Explanation :
We have : (a + b + c)/3 = M or (a + b + c) = 3M.
Now, (a + b + c)*(a + b + c) = (3M)^2 = 9M^2
a2 + b2 + c2 + 2 (ab + bc + ca) = 9M^2
a2 + b2 + c2 = 9M^2
Required mean = (a2 + b2 + c2)/3 = 9M^2/3 = 3M2
Answer : B
Answer: (B) 3M2
Question: Two boats are heading towards each other at constant speeds of 5 miles/hr and 25 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
(A) 1/12
(B) 5/12
(C) 1/6
(D) 1/2
(E) 1/5
Rationale: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 5+25=30 mph then 1/60 hours before they collide they'll be rate*time=distance --> 30*1/60=1/2 miles apart.
Answer: D.
Answer: (D) 1/2
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 35 kg. What is the weight of the new person?
(A) 75
(B) 65
(C) 55
(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−35
=> 20 = x - 35
=> x = 20 + 35= 55
Answer is C.
Answer: (C) 55
Question: The number of arrangements that can be made with the letters of the word MAETHS so that the word starts with M and ends with S
(A) A)2!
(B) B)3!
(C) C)4!
(D) D)6!
(E) E)7!
Rationale: M _ _ _ _ S
the remaining 4 places can be filled by 4!
C
Answer: (C) C)4!
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 210
(B) 1050
(C) 25200
(D) 21400
(E) None
Rationale: Solution
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
7C3x 4C2 = ( 7x 6x5/3x2x1x 4x 3/2x1 ) = 210
Number of group,each having 3 consonants and 2 vowels = 201 .
Each group contains 5 letter.
Number of ways of arranging 5 letters among themselves
= 5 ! = (5 × 4 × 3 × 2 × 1) = 120 .
So, Required number of words = (210 × 120) = 25200 .
Answer C
Answer: (C) 25200
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
(A) 1523
(B) 1365
(C) 1234
(D) 4512
(E) 1234
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: B
Answer: (B) 1365
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 62.9
(C) 62.6
(D) 62.1
(E) 22.4
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Answer: (A) 62.5
Question: The greatest number of four digits which is divisible by 18,27,54 and 72 is:
(A) 9300
(B) 9480
(C) 9600
(D) 9860
(E) 9936
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 18, 27, 54 and 72 is 216.
On dividing 9999 by 216, the remainder is 63.
Required number (9999 - 63) = 9936.
Answer: Option E
Answer: (E) 9936
Question: Jill is dividing her six-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?
(A) 10
(B) 25
(C) 126
(D) 252
(E) 630
Rationale: With 6 players, the process of figuring out how many groups of 3 can be formed is pretty straight-forward....
6C3 = 6!/(3!3!) = 20 possible groups of 3
Once forming that first group of 3, the remaining 3 players would all be placed on the second team by default.
The 'twist' is that the two teams of 3 canshow upin either order:
A
Answer: (A) 10
Question: The compound interest on a sum of money for 2 years is rs.832 and the simple interest on the same sum for the same period is rs.800 .the difference between the compound interest and simple interest for 3 years
(A) 98.5
(B) 08.56
(C) 98.56
(D) 98.86
(E) 98.46
Rationale: Explanation:
difference in C.I and S.I in 2years =Rs.32
S.I for 1year =Rs.400
S.I for Rs.400 for one year =Rs.32
rate=[100*32)/(400*1)%=8%
difference between in C.I and S.I for 3rd year
=S.I on Rs.832= Rs.(832*8*1)/100=Rs.66.56
Answer: C) Rs.98.56
Answer: (C) 98.56
Question: If 5% more is gained by selling an article for Rs. 220 than by selling it for Rs. 160, the cost of the article is?
(A) 127
(B) 1200
(C) 1600
(D) 1400
(E) 1202
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 220 - 160= 60
x/20 = 60 => x = 1200
Answer: B
Answer: (B) 1200
Question: A train running at the speed of 72 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 288
(B) 279
(C) 277
(D) 272
(E) 180
Rationale: Speed = 72 * 5/18 = 20 m/sec
Length of the train = speed * time = 20 * 9
= 180 m
Answer: E
Answer: (E) 180
Question: Ram paid a sum of money for purchasing 25 pens, which he recovered in full when he sold 10 of them. What was his percentage of profit or loss per pen?
(A) 80%
(B) 125%
(C) 100%
(D) 70%
(E) 90%
Rationale: B
125%
If the sum he paid whilst purchasing 25 pens = A,
Then the Cost Price of each pen = A/25.
Since the amount he got whilst selling 10 pens is also = A
Then the Selling Price of each pen = A/10.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/10 - A/25 = 3A/50.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (3A/60) / (A/25) x 100 = 125%. Answer :B
Answer: (B) 125%
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 46 hats in this group, how many of these hats are not blue?
(A) 28
(B) 42
(C) 48
(D) 32
(E) 76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=46 or 23x=46...here 7x,4x and 12x represent hats of each type
23x=46 so x=2...Blue hats =7*2=14...Not blue will be 46-14=32.
Ans D
Answer: (D) 32