mathewhe/aqua_rat huggingface dataset:
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 1.5 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
(A) 1.065
(B) 1.125
(C) 1.225
(D) 1.375
(E) 1.425
Rationale: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 1.5 km/hour
x/3 = 1.5
x = 4.5 km
The average speed while climbing = distance/time = 4.5/4 = 1.125 km/h
The answer is B.
Answer: (B) 1.125
Question: Griffin has a bag of marbles that contains 7 black marbles and 4 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?
(A) 2/55
(B) 3/85
(C) 4/105
(D) 4/165
(E) 8/165
Rationale: P(3 red marbles) = 4/11*3/10*2/9 = 4/165
The answer is D.
Answer: (D) 4/165
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
(A) 26
(B) 32
(C) 87
(D) 20
(E) 23
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
Answer:B
Answer: (B) 32
Question: A 280 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train.
(A) 210m
(B) 220m
(C) 230m
(D) 240m
(E) 250m
Rationale: Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+280/9=500/9
x=220
Ans is 220m
ANSWER:B
Answer: (B) 220m
Question: There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
(A) A)5/4
(B) B)5/8
(C) C)6
(D) D)6/7
(E) E)7
Rationale: Let the two numbers be x and y.
20/100 * x + y = 5/4y
=> 1/5 x = 1/4 y => x/y = 5/4
A)
Answer: (A) A)5/4
Question: In a kilometer race, A beats B by 25 meters or 10 seconds. What time does A take to complete the race?
(A) 290 sec
(B) 390 sec
(C) 199 sec
(D) 192 sec
(E) 193 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/25 = 400 sec.
Time taken by A = 400 - 10 = 390 sec.
Answer: B
Answer: (B) 390 sec
Question: Which of the following CANNOT be a value of 9/(x–9)?
(A) -1
(B) -1/2
(C) 0
(D) 2
(E) 9
Rationale: The question doesn't ask for the value of x here, but for the possible results of the equation.
If 9/(x-9) = 0, then the numerator must be 0. But since the numerator is 9, the fraction can not be equal to 0.
The answer is C.
Answer: (C) 0
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent H of the gasoline in the tank is brand Z?
(A) 50%
(B) 40%
(C) 37.5%
(D) 331⁄3%
(E) 25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) H= 3/8 = 37.5%
Answer (C)
Answer: (C) 37.5%
Question: If f(f(n))+f(n)=2n+3 and f(0)=1, what is the value of f(2012)?
(A) 222
(B) 2787
(C) 2013
(D) 2778
(E) 10222
Rationale: Put n = 0
Then f(f(0))+f(0) = 2(0) + 3 ⇒⇒ f(1) + 1 = 3 ⇒⇒ f(1) = 2
Put n = 1
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) + 2 = 5 ⇒⇒f(2) = 3
Put n = 2
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) + 3 = 7 ⇒⇒ f(3) = 4
......
f(2012) = 2013
Answer:C
Answer: (C) 2013
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) 1:9
(B) 1:8
(C) 1:4
(D) 1:1
(E) 1:2
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 circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of v when angle D is 140 degrees?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle D = 140 degrees
Thus,
arc ABC = 280 degrees
A whole circle has 360 degrees of arc, so arc ADC should be the rest of the circle.
arc ADC = 360 - 280 = 80 degrees
The angle that intersects this arc, angle B, should have half this measure.
angle B = v = 80/2 = 40 degrees
Answer =(B)
Answer: (B) 40
Question: What is the next number: 2, 10, 82, __
(A) 630
(B) 730
(C) 830
(D) 848
(E) 900
Rationale: 3^0 + 1 = 2
3^2 + 1 = 10
3^4 + 1 = 82
3^6 + 1 = 730
The answer is B.
Answer: (B) 730
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 1218
(B) 2777
(C) 1200
(D) 2688
(E) 1991
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer: C
Answer: (C) 1200
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 65 years
(B) 88 years
(C) 18 years
(D) 55 years
(E) 11 years
Rationale: 9 * 2 = 18 years
Answer: C
Answer: (C) 18 years
Question: If 0 < a< 1 < b, which of the following must be true?
(A) 1 < 1/a< 1/b
(B) 1/a< 1 < 1/b
(C) 1/a< 1/b< 1
(D) 1/b< 1 < 1/a
(E) 1/b< 1/a< 1
Rationale: 0<a<1<b. Let a=1/2 and b=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: (D) 1/b< 1 < 1/a
Question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
(A) 2178
(B) 1087
(C) 2800
(D) 2689
(E) 2081
Rationale: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer: C
Answer: (C) 2800
Question: A man gains 20% by selling an article for a certain price. If the sells it at double the price, the percentage of profit will be?
(A) 76%.
(B) 66%.
(C) 89%.
(D) 140%.
(E) 91%.
Rationale: Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Answer: D
Answer: (D) 140%.
Question: How many times in a day, the hands of a clock are straight?
(A) 42
(B) 41
(C) 44
(D) 45
(E) 46
Rationale: Explanation:
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer is C
Answer: (C) 44
Question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many E hours will it take if Jim types the report and Mary edits it immediately after he is done?
(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8
Rationale: Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;
Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;
Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;
How many E hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4
Answer: A.
Answer: (A) 41.4
Question: A vessel of capacity 50 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 23.89
(B) 72.9
(C) 33.62
(D) 78.3
(E) 79.3
Rationale: Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 50, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(50 - 9)/50]^2 (50) = 33.62 litres.
Answer: Option C
Answer: (C) 33.62
Question: If 9a - b = 10b + 70 = -12b - 2a, what is the value of 11a + 11b?
(A) -4
(B) -2
(C) 0
(D) 2
(E) 4
Rationale: (i) 9a - 11b = 70
(ii) 2a + 22b = -70
Adding (i) and (ii):
11a + 11b = 0
The answer is C.
Answer: (C) 0
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 108.Find the number of notes of Rs.50 denomination.
(A) 15
(B) 21
(C) 17
(D) 19
(E) 97
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 108 - X
Now,
50*X + 500 * (108 - X) = 10350
50X + 54000 - 500X = 10350
- 450X = - 43650
X = 97.
No. of 50 rupees note = 97.
Answer: Option E
Answer: (E) 97
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by three when k is any of the following values EXCEPT
(A) -4
(B) -2
(C) -1
(D) 2
(E) 5
Rationale: There is probably an easier way, but I just used the picking numbers option for this.
I chose x=2
2(1)(2-k) then just plugged in the answer choices for K until one wasn't evenly divisible by 3.
B gives you 8. 8/3 is not an integer.
B is the answer
Answer: (B) -2
Question: Sunitha’s age is 1/6th of her father’s age. Her father’s age will be twice of Varun’s age after 10 years. If Varun’s eight birthday was celebrated two years ago, then what is Sunitha’s present age?
(A) 30 years
(B) 24 years
(C) 6 years
(D) 7 years
(E) None of these
Rationale: Varun’s present age = 8 + 2 = 10 yrs
F + 10 = 2 (V + 10) = 2 (10+ 10)
F = 30, S = 30/6 = 5 years.
Therefore its none of the these.
ANSWER:E
Answer: (E) None of these
Question: Walking at 4/5 of her normal speed, a worker is 10 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
(A) 30
(B) 35
(C) 40
(D) 45
(E) 50
Rationale: Let V be her normal speed and let T be her normal time.
D = (4/5)V * (T+10)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (4/5)V * (T+10)
T/5 = 8
T=40
The answer is C.
Answer: (C) 40
Question: What number comes next?
428, 693, 714, 286, 937, ?
(A) 142
(B) 231
(C) 245
(D) 148
(E) 123
Rationale: A
142
The numbers 42869371 are being repeated in the same sequence.
Answer: (A) 142
Question: A square, with perimeter 20, is inscribed in a circle. What is the area of the circle?
(A) 8π
(B) 11π
(C) 10π
(D) 12π
(E) 12.5π
Rationale: Area of circuscribed circle = pi/2*area of square
Area of square = (20/4)^2 = 5^2= 25
Area of circle = pi/2*4=12.5pi
Answer E
Answer: (E) 12.5π
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 18 2/18%
(B) 18 2/11%
(C) 18 3/11%
(D) 18 2/17%
(E) 18 3/18%
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B
Answer: (B) 18 2/11%
Question: A certain population of bacteria doubles every 10 minutes. If the number of bacteria in the population initially was 10^5, then what was the number in the population 90 minutes later?
(A) 2(10^5)
(B) 9(10^5)
(C) (2^9)(10^5)
(D) (10^9)(10^5)
(E) (10^5)^9
Rationale: Every 10 minutes, the population is double the previous population.
In 90 minutes, the population doubles 9 times.
The population then is 2^9*10^5.
The answer is C.
Answer: (C) (2^9)(10^5)
Question: If (a – b) is 17 more than (c + d) and (a + b) is 3 less than (c – d), then (a – c) is:
(A) 6
(B) 2
(C) 3
(D) 7
(E) 5
Rationale: (a – b) – (c + d) = 17 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 17 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 17 and (b + d) = (c – a) – 3
=> (a – c) – 17 = (c – a) – 3 => 2(a – c) = 14 => (a – c) = 7
ANSWER:D
Answer: (D) 7
Question: In a game of 100 points,A can give B 20 points and C 28 points.Then, B can give C :
(A) 8 points
(B) 10 points
(C) 14 points
(D) 40 points
(E) 50 points
Rationale: Solution
A : B = 100 : 80 and A : C = 100 : 72.
∴ B/C=(B/C x A/C) = (80/100 x 100/72)= 10/9 =100/90= 100 : 90.
∴ B can give C 10 points.
Answer B
Answer: (B) 10 points
Question: The price for a loaf of bread in April was $1.17, in May the price was $1.32, and in June the price was $1.08. If 2/3 as much bread was sold in April as in May, and twice as much was sold in June as in April, what was the average price for a loaf of bread sold during the three-month period?
(A) $1.16
(B) $1.17
(C) $1.18
(D) $1.19
(E) $1.20
Rationale: Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(117) + 132x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(78 + 132 + 144) / (3) = 354/3 = $1.18
The answer is C.
Answer: (C) $1.18
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price B per t-shirt that the vendor paid for these purchases?
(A) $12.20
(B) $12.50
(C) $12.55
(D) $12.70
(E) $13.00
Rationale: Correct Answer: A
Explanation: The relevant formula for this problem is Average B= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Answer: (A) $12.20
Question: The average of 13 numbers is 60. Average of the first 7 of them is 54 and that of the last 7 is 61. Find the 8th number?
(A) 25
(B) 83
(C) 45
(D) 53
(E) 64
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 54 = 378
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 378 - 780 = 25.
Answer:A
Answer: (A) 25
Question: A shop that sells phone accessories had the following sales: 10 thousand earbuds at $10 each, 5300 phone cases at $12 each and 450 power banks at $50 each. What % of the shop's revenue is from power banks?
(A) 11.1%
(B) 12.1%
(C) 10.1%
(D) 9.1%
(E) 13.1%
Rationale: Correct Answer: B
The company's total revenue from earbuds=10000*$10=$100000
The company's total revenue from phone cases=5300*$12=$63600
The company's total revenue from power banks=450*$50=$22500
The combined total of all sales=$186100
Therefore % of power banks sales=22500/186100*100= 12.1%
Answer: (B) 12.1%
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is
(A) 276
(B) 299
(C) 312
(D) 322
(E) None
Rationale: Solution
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14)	= 322.
Answer D
Answer: (D) 322
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 25 minutes?
(A) 80
(B) 100
(C) 150
(D) 240
(E) 300
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 25 minutes the population increases by 25 x 4 = 100 people.
Answer. B.
Answer: (B) 100
Question: The greatest number of 5 digits = 99999.
(A) 137
(B) 143
(C) 77
(D) 88
(E) 11
Rationale: Answer:B
Answer: (B) 143
Question: The Full House Casino is running a new promotion. Each person visiting the casino has the opportunity to play the Trip Aces game. In Trip Aces, a player is randomly dealt three cards, without replacement, from a deck of 8 cards. If a player receives 3 aces, they will receive a free trip to one of 10 vacation destinations. If the deck of 8 cards contains 3 aces, what is the probability that a player will win a trip?
(A) 1/336
(B) 1/120
(C) 1/56
(D) 1/720
(E) 1/1440
Rationale: P=P(ace in the first draw)*P(ace in the second draw)*P(ace in the third draw)=3/8*2/7*1/6=1/56.
Answer: C.
Answer: (C) 1/56
Question: A goods train runs at the speed of 72 km/hr and crosses a 150 m long platform in 26 sec. What is the length of the goods train?
(A) 299
(B) 277
(C) 276
(D) 370
(E) 281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 150)/26 = 20
x = 370 m.
Answer: D
Answer: (D) 370
Question: If a certain number of people can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of people will require to dig earth 75m deep, 20m long and 50m broad.
(A) 12
(B) 18
(C) 6
(D) 1
(E) 17
Rationale: Explanation:
More number of days means – more length, more depth and more width. Hence, it’s a direct proportion.
(100*25*30):(75*20*50)::12:x
75000:75000::12:x
x = 12
ANSWER A
Answer: (A) 12
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $700 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $2,100 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
(A) 25%
(B) 15%
(C) 20%
(D) 40%
(E) 45%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 700 : 2100 -----> 1 : 3
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 4) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/4) * 100 ---> 25%
Answer : A
Answer: (A) 25%
Question: A person purchased a TV set for Rs. 2700 and a DVD player for Rs. 200 . He sold both the items together for Rs. 3180. What percentage of profit did he make?
(A) 20%
(B) 6%
(C) 40%
(D) 5%
(E) 3%
Rationale: The total CP = Rs. 2700 + Rs. 300
= Rs. 3000 and SP = Rs. 3180
Profit(%)
= (3180- 3000)/3000 * 100
= 6%
Answer: B
Answer: (B) 6%
Question: Three cubes of edges 6 cms, 8 cms and 10 cms are meted without loss of metal into a single cube. The edge of the new cube will be:
(A) 8 cms
(B) 12 cms
(C) 14 cms
(D) 16 cms
(E) None
Rationale: Volume of new cube = Volume of cube 1 + cube 2 + cube 3 = 63 + 83 + 103, = 216 + 512 + 1000
a3 = 1728,
a = (1728)1/3 = 12
Answer: B
Answer: (B) 12 cms
Question: The ratio of the ages of Maala and Kala is 1 : 4. The total of their ages is 2.0 decades. The proportion of their ages after 0.5 decades will be
[1 Decade = 10 years]
(A) 6:5
(B) 3:4
(C) 2:5
(D) 7:9
(E) 3:6
Rationale: Let, Maala’s age = A and Kala’s age =4A
Then A + 4A = 20
A =5
Maala’s age = 5 years
and Kala’s age = 20 years
Proportion of their ages after 5 is = (5 + 5) : (20 + 5)
= 10 : 25
= 2 : 5
Answer : C
Answer: (C) 2:5
Question: If grapes are 92% water and raisins are 20% water, then how much did a quantity of raisins, which currently weighs 13 pounds, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
(A) 25 pounds
(B) 46 pounds
(C) 92 pounds
(D) 130 pounds
(E) 146 pounds
Rationale: Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*13 --> x = 130.
Answer: D.
Answer: (D) 130 pounds
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/4 of the sum. If the numbers representing rate percent and time in years be in the ratio 1:4, then the rate of interest is:
(A) 4 1/2 %.
(B) 3 1/2 %.
(C) 2 1/2 %.
(D) 2 3/4 %.
(E) 4 3/4 %.
Rationale: Explanation :
Let sum = x. Then, S.I. = x/4
Let rate = R% and time = R years.
[x * R * 4R / 100] = x / 4 ? R^2 = 25/4
R = 5/2 = 2 1/2.
Hence, R = 2 1/2 %.
Answer : C
Answer: (C) 2 1/2 %.
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) 26
(B) 88
(C) 90
(D) 42
(E) 22
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs. 90
Answer:C
Answer: (C) 90
Question: Which of the following fraction is smallest?
(A) 23/28
(B) 14/15
(C) 15/19
(D) 21/24
(E) 23/25
Rationale: 23/28 =0.821
14/15 = 0.933
15/19 = 0.7894
21/24 = 0.875
So, 15/19 = 0.7894 is smallest.
ANSWER:C
Answer: (C) 15/19
Question: A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.2 m and its walls are 5 cm thick. The thickness of the bottom is:
(A) 90 cm
(B) 2 dm
(C) 1 m
(D) 1.1 cm
(E) None of these
Rationale: Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (120 - x)] = 8000 × 1000
=> 320 × 250 × (120 - x) = 8000 × 1000
=> (120 - x) = 8000×1000/320=
100
=> x = 20 cm = 2 dm.
Answer: B
Answer: (B) 2 dm
Question: A classroom has equal number of boys and girls. Eight girls left to play kho-kho, leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?
(A) 16
(B) 24
(C) 32
(D) 48
(E) 54
Rationale: after 8 girls left remaining 8 girls
now boys 16 are twice as many as remaining girls.
initially boys=16 and girls=16.
ANSWER:C
Answer: (C) 32
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony twelve hours from now?
(A) 77,500
(B) 1,860,000
(C) 2,480,000
(D) 3,720,000
(E) 39,680,000
Rationale: 310,000 × 2 × 2×2×2x2×2×2 = 310,000 × 128 = E
Answer: (E) 39,680,000
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 30 runs. Find his average in all the 30 matches?
(A) 31
(B) 36.67
(C) 88
(D) 13
(E) 12
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 300.
Total score of the batsman in the 30 matches = 1100.
Average score of the batsman = 1100/30 = 36.67.
Answer:B
Answer: (B) 36.67
Question: An investment yields an interest payment of $240 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
(A) $28,300
(B) $30,400
(C) $31,300
(D) $32,500
(E) $32,000
Rationale: Let the principal amount = P
Simple annual interest = 9%
Simple monthly interest = (9/12) = (3/4)%
(3/4)*(P/100) = 240
=>P = (240 *4 * 10^2 )/3
= 80*4*10^2
= 320 * 10^2=32000
Answer E
Answer: (E) $32,000
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
(A) 3.1
(B) 3.4
(C) 3.6
(D) 4
(E) 4.5
Rationale: 3.6
Option 'C'
Answer: (C) 3.6