mathewhe/aqua_rat huggingface dataset:
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is 3/4 empty, it is filled with brand X 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 X gasoline. At this time, what percent of the gasoline in the tank is brand Z?
(A) 41%
(B) 42%
(C) 43%
(D) 43.75%
(E) 44%
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 (3/4)*(1/2) + 1/2 = 7/8
4th step: brand Z is (1/2)*(7/8) = 7/16 = 43.75%
Answer (D)
Answer: (D) 43.75%
Question: How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers?
(A) 1200
(B) 1092
(C) 1082
(D) 1192
(E) 1292
Rationale: 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
-----------
1092
ANSWER:B
Answer: (B) 1092
Question: A train 710 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 2898
(B) 277
(C) 500
(D) 297
(E) 590
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (710 + x)/60 = 65/3
x = 590 m.
Answer: E
Answer: (E) 590
Question: Jane makes toy bears. When she works with an assistant, she makes 53 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
(A) 20%
(B) 70%
(C) 100%
(D) 180%
(E) 200%
Rationale: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 61.2 bears per 36 hours a week or 1.7 bears/hr ([40 bears * 1.53] / [40 hrs * .90]).
[(1.7 - 1)/1] * 100% = 70%
ANSWER:B
Answer: (B) 70%
Question: A man takes 5hr 45min in walking to certain place and riding back. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
(A) 7 hr 45 min
(B) 7 hr 15 min
(C) 6 hr 45 min
(D) 6 hr 15 min
(E) 6 hr 25 min
Rationale: Let x be the speed of walked
Let y be the speed of ride
Let D be the distance
Then D/x + D/y = 23/4 hr -------------------(1)
D/y + D/y = 23/4 – 2 hr
D/y = 15/8 ----------------------------------(2)
substitute 2 in 1
D/x + 15/8 = 23/4
D/x = 23/4 -15/8 =46-15/8 =31/8
Time taken for walk one way is 31/8 hr
time taken to walk to and fro is 2*31/8 = 31/4 hr
=7 hr 45 min
Answer : A.
Answer: (A) 7 hr 45 min
Question: Two sets of 7 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
(A) 24
(B) 17
(C) 28
(D) 42
(E) it cannot be determined from the information given.
Rationale: A=(1,2,3,4,5,6,7), sum of this=28
B=(7,8,9,10,11,12,13), sum of this=70
The differenct between 70-28=42
Hence,42 is the answer i.e.D
Answer: (D) 42
Question: How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 33% iodine solution?
(A) 35
(B) 49
(C) 100
(D) 105
(E) 122
Rationale: Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.
Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.
Total iodine = 0.4x + 7
Total water = 0.6x + 28
The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 33/100
40x + 700 = 33x + 1155
7x = 855
x = 122 lts
Correct Option: E
Answer: (E) 122
Question: The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle?
(A) 432 sq m
(B) 363 sq m
(C) 452 sq m
(D) 428 sq m
(E) 528 sq m
Rationale: 2(3x + x) = 88
l = 33 b = 11
lb = 33 * 11 = 363
ANSWER:B
Answer: (B) 363 sq m
Question: A Cuban cigar would cost 2 dollar less than 1.5 times a French cigar, had the French cigar cost 0.7 dollar less than it does now. An Arabian cigar costs 50 cents more than 1.5 times the Cuban cigar. The three cigars together cost 74.7 dollars. What is the price of the French cigar?
(A) 17.7$.
(B) 15.7$.
(C) 25.5$.
(D) 35$.
(E) 37.4$.
Rationale: The three cigars together cost 74.7 dollars. If each cost the same , they would have cost a little less than 25 dollars each.
From the given data we know French cigar < Cuban cigar < Arabic cigar
and each is more expensive 1.5 times. Therefore eliminate options C,D,E straightaway . Since French cigar is at least 1.5 times cheaper we know A cannot be the answer.
Therefore B is the answer.
Answer: (B) 15.7$.
Question: If 5 and 8 are factors of 60n, what is the minimum value of n?
(A)  2
(B)  3
(C)  7
(D)  14
(E)  56
Rationale: 60n/7*8 should be integer => 2*2*3*5*n/5*2*2*2 = 3*n/2 must be an integer
for this to be true n must multiple of 2, thus min of n = 2
hence A
Answer: (A)  2
Question: Find the average of first 40 natural numbers.
(A) 20.5
(B) 18
(C) 19.5
(D) 19
(E) 20
Rationale: Sum of first n natural numbers = n( n+1)/2
So, sum of first 40 natural numbers = 40*41/2 = 820
Required average =820/40 =20.5
ANSWER:A
Answer: (A) 20.5
Question: If an item that originally sold for o dollars was marked up by m percent and then discounted by n percent, which of the following expressions represents the final price of the item?
(A) (10,000o + 100o(m – n) – mno)/10,000
(B) (10,000o + 100o(n – m) – mno)/10,000
(C) (100o(m – n) – mno)/10000
(D) (100o(n – m) – mno)/10000
(E) 10000 /(m – n)
Rationale: Assume o=100, m=10, n=10. So final price is 99. Now put these value each option. Only option A will give right answer.
Answer: (A) (10,000o + 100o(m – n) – mno)/10,000
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) Rs. 3900
(B) Rs. 4900
(C) Rs. 4980
(D) Rs. 5000
(E) Rs. 5900
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	x.
2
15x + 2y = 4000
15x + 2 x	5	x = 4000
2
20x = 4000
x = 200.
So, y = 5	x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
A)
Answer: (A) Rs. 3900
Question: A person want to give his money of $2700 to his 3 children A,B,C in the ratio 5:6:9. What is the A+C share?
(A) $1890
(B) $2002
(C) $3500
(D) $1500
(E) $5640
Rationale: A's share = 2700*5/20 = $675
C's share = 2700*9/20 = $1215
A+D = $1890
Answer is A
Answer: (A) $1890
Question: An article when sold at a gain of 5% yields Rs. 15 more than when sold at a loss of 5%. The cost price of the article is:
(A) Rs. 200
(B) Rs. 150
(C) Rs. 80
(D) Rs. 64
(E) None of these
Rationale: 10/100 × x = 15 ⇒ x=150
As the loss and profit both are earned on the cost price.
Answer: B
Answer: (B) Rs. 150
Question: In what time will a train 110 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.75 sec
(B) 4.25 sec
(C) 5 sec
(D) 12.5 sec
(E) 6 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 110/40 = 2.75 sec.
ANSWER:A
Answer: (A) 2.75 sec
Question: Simplify (212 * 212 + 312 * 312 )
(A) 132288
(B) 142088
(C) 142188
(D) 142288
(E) None of these
Rationale: Explanation:
Trick: Above equation can be solved by using following formula
(a2+b2)=1/2((a+b)2+(a−b)2)
Option D
Answer: (D) 142288
Question: (3*10^2)*(4*10^-2)=?
(A) 14
(B) 12
(C) 1200
(D) 1.2
(E) 14.11
Rationale: 3*10^2=300
4*10^-2=0.04
(3*10^2)*(4*10^-2)=300*0.04=12.00
The answer is option B
Answer: (B) 12
Question: The combined salaries of three brothers is $45,000. Mr. Big earns twice what Mr. Small earns, and Mr. Middle earns 1 1/2 times what Mr. Small earns. What is the smallest salary of the three brothers?
(A)  10,000
(B)  12,000
(C)  15,000
(D)  20,000
(E)  22,000
Rationale: Mr. Small = x;
Mr. Middle = 3/2*x;
Mr. Big = 2x.
x + 3/2*x + 2x = 45 --> x=10
Answer: A
Answer: (A)  10,000
Question: The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 1988, the price of commodity X was 4.20 and that of Y was 6.30, in which year will commodity X cost 40 paise more than commodity Y?
(A) 1997
(B) 1998
(C) 1999
(D) 2000
(E) None of these
Rationale: Suppose in ‘n’ years the price of comodity X will be more by 40 paise than that of commodity Y.
∴ 420 + 40n – 630 – 15n = 40
or, 25n – 210 = 40
or, 25n = 250
or, n = 250⁄25 = 10 years.
Answer B
Answer: (B) 1998
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 13.1 sec
(B) 12.1 second
(C) 22.1 sec
(D) 32.1 sec
(E) 13.2 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Answer: (B) 12.1 second
Question: A certain team consists of 5 professors and 4 teaching assistants. How many different teams of 3 can be formed in which at least one member of the group is a professor? (Two groups are considered different if at least one group member is different.)
(A) 74
(B) 80
(C) 86
(D) 92
(E) 98
Rationale: The total number of ways to form a group of 3 from 9 people is 9C3 = 84
The number of ways to form a group without a professor is 4C3 = 4
The total number of ways to form a valid group is 84 - 4 = 80.
The answer is B.
Answer: (B) 80
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places?
(A) 23.56
(B) 23.59
(C) 23.76
(D) 23.12
(E) 23.57
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer: E
Answer: (E) 23.57
Question: Which of the following could be the sum of the reciprocals of two different prime numbers?
(A) 7/13
(B) 10/12
(C) 11/30
(D) 23/50
(E) 19/77
Rationale: Here, the condition is that there should be two different prime nos.
A 13 = 13 x 1 ( 1 is not a prime number)
B 21 = 7 x 3 ( both 7 and 3 are prime nos)
C 30 = 10 * 3 or 5* 6 ( It can be written both ways, but 10 and 6 are not prime nos)
D 50 = 10 * 5 ( 10 is not a prime number)
E 77 = 11 * 7 ( both are prime numbers)
Options A, C, D are eliminated.
We are left with options B and E.
1/11 + 1/7 = 18/77 and not 19/77. Hence this option is eliminated.
Option B is the correct
Answer: (B) 10/12
Question: A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 200 square feet, what is the total length of the fence, in feet?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 80
Rationale: two sides EACH = x the third = 2x and the wall length is thus 2x too
x*2x = 2x^2 = 200 ie x^2 = 100 ie x = 10
L = 20 W=10
TOTAL LENGHT OF FENCE = 2*10 + 20 = 40
MY ANSWER IS D
Answer: (D) 40
Question: The price of rice is reduced by 2%. How many kilograms of rice can now be bought for the money which was sufficient to buy 49 kg of rice earlier?
(A) 48 kg
(B) 49 kg
(C) 50 kg
(D) 51 kg
(E) None
Rationale: Sol.
Let the original price be Rs. 100 per kg.
Money required to buy 49 kg of rice = Rs. (100 x 49) = Rs. 4900.
New price = Rs. 98 per kg.
∴ Quantity of rice bought = [4900 / 98] kg = 50 kg.
Answer C
Answer: (C) 50 kg
Question: Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?
(A) 9 min
(B) 8 min
(C) 4 min
(D) 6 min
(E) None of these
Rationale: Explanation:
Tank can be filled by pipe A in 12 minutes and pipe B in 24minutes.
=> Part filled by A in 1 minute= 1/12
=> Part filled by B in 1 minute= 1/24
=> Part filled by both in 1 minute= 1/12 + 1/24
= 3/24=1/8
Time taken to fill the entire tank = 8 minutes
ANSWER B
Answer: (B) 8 min
Question: H.C.F of 4 * 27 * 3125, 8 * 9 * 25 * 7 and 16 * 81 * 5 * 11 * 49 is:
(A) 240
(B) 790
(C) 840
(D) 180
(E) 120
Rationale: Explanation:
4 * 27 * 3125 = 2^2 * 3^3 * 5^5;
8 * 9 * 25 * 7 = 2^3 * 3^2 * 5^2 * 7;
16 * 81 * 5 * 11 * 49 = 2^4 * 3^4 * 5 * 7^2 * 11
H.C.F = 2^2 * 3^2 * 5 = 180.
Answer: Option D
Answer: (D) 180
Question: A train sets off at 2:00 pm at the speed of 70 km/h. Another train starts at 3:00 pm in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
(A) 10:00
(B) 10:30
(C) 11:00
(D) 11:30
(E) 12:00
Rationale: In one hour the first train travels 70 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 70/10 = 7 hours, so at 10:00 pm.
The answer is A.
Answer: (A) 10:00
Question: The H.C.F. of two numbers is 12 and their difference is 12. The numbers are
(A) 66, 78
(B) 70, 82
(C) 94, 106
(D) 84, 96
(E) None
Rationale: Solution
Out of the given numbers, the two with H.C.F. 12 and difference 12 are 84 and 96
Answer D
Answer: (D) 84, 96
Question: A positive number x is multiplied by 4, and this product is then divided by 3. If the positive square root of the result of these two operations equals x, what is the value of x ?
(A)  9/4
(B)  3/2
(C)  4/3
(D)  1/3
(E)  1/2
Rationale: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^2
3x^2 – 2x = 0
x(3x – 2) = 0
x = 0 or
3x – 2 = 0
3x = 2
x = 1/3
Because x is positive, x = 1/3. The answer is D.
Answer: (D)  1/3
Question: A(5, w^2) is the (x, y) coordinate of point located on the parabola Y = X^2 + 11. What is the value of w?
(A) 3.
(B) 4.
(C) 5.
(D) 6.
(E) 9.
Rationale: y=x^2 +11
w^2=5^2+11
w^2=36
W=6
Answer D
Answer: (D) 6.
Question: If x,2x+2,3x+3 are the first three terms of a GP,then what is its fourth term?
(A) -11.5
(B) -12.5
(C) -13.5
(D) -14.5
(E) -15.5
Rationale: (2x+2)/x= (3x+3)/(2x+2)
4x^2+8x+4 = 3x^2+3x
x^2+5x+4=0
x=-4
so series will be
-4,-6,-9,-13.5
ANSWER:C
Answer: (C) -13.5
Question: In a vessel, there are 10 litres of alcohol. An operation is defined as taking out five litres of what is present in the vessel and adding 10 litres of pure water to it. What is the ratio of alcohol to water after two operations?
(A) 1 : 0
(B) 1 : 5
(C) 1 : 1
(D) 1 : 2
(E) 1 : 9
Rationale: Final concentration = Initial concentration (1−replacement quantityfinal volume)(1−replacement quantityfinal volume)
Final concentration = =1×(1−1015)=13=1×(1−1015)=13
Final concentration = 13×(1−1020)=1613×(1−1020)=16
So ratio of alcohol : water = 1 : 5
Answer:B
Answer: (B) 1 : 5
Question: an article with cost price of 240 is sold at 20% profit. what is the selling price?
(A) 288
(B) 200
(C) 204
(D) 207
(E) 210
Rationale: sp=1.20*240=288
ANSWER:A
Answer: (A) 288
Question: If a fair coin is tossed seven times, what is the probability of getting exactly five heads in a row?
(A) 1/8
(B) 1/16
(C) 3/32
(D) 3/64
(E) 5/128
Rationale: Let X represent either H or T (it doesn't matter which).
P(HHHHHTX) = 1/64
P(THHHHHT) = 1/128
P(XTHHHHH) = 1/64
The sum of these probabilities is 5/128
The answer is E.
Answer: (E) 5/128
Question: (8^16)+(16^13)+(4^22) = ?
(A) (4)*(2^29+1)
(B) (6)*(2^48)
(C) (9)*(2^49)
(D) (28)*(2^53)
(E) 2^148
Rationale: I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ)
So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents.
Here's how my brain works with this one,
Step 1: Recognize a common base.
(8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48)
Step 2: Recognize the factor and pull out of the equation.
= (2^48)(1 + (2^4) + 1)
= (2^48)(1 + 16 + 1)
= (2^48)(18)
Step 3: Recognize this is not an answer and adapt.
(2^48)(18) = (2^48)(2)(9) = (28)*(2^53)
Answer is D.
Answer: (D) (28)*(2^53)
Question: A man sold 18 toys for Rs. 16800, gaining thereby the cost price of 3 toy find the cost price of a toy
(A) Rs. 600
(B) Rs. 800
(C) Rs.500
(D) Rs.900
(E) Rs. 990
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 16800.
Gain = SP – CP
3X = 16800 – 18X
21X = 16800
X = Rs. 800.
ANSWER : OPTION B
Answer: (B) Rs. 800
Question: If A, B and C together can finish a piece of work in 2 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 5 days
(B) 4 days
(C) 3 days
(D) 2 days
(E) 7 days
Rationale: C = 1/2 - 1/12 – 1/18 = 1/3 => 3 days
ANSWER:C
Answer: (C) 3 days
Question: Six students - 3 boys and 3 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
(A) A)12
(B) B)36
(C) C)72
(D) D)240
(E) E)720
Rationale: in order not to have two boys or two girls next to one another, we must make an alternate sitting arrangement. (B-G-B-G-B-G) or (G-B-G-B-G-B).
Total ways = 2C1*3!*3!
=2*6*6
=72
Ans - C
Answer: (C) C)72
Question: What is the probability for a family with five children to have two boys and three girls (assuming the probability of having a boy or a girl is equal)?
(A) 1/2
(B) 1/4
(C) 3/8
(D) 3/16
(E) 5/16
Rationale: One possible case is: girl - girl - girl - boy - boy
The probability of this is 1/2*1/2*1/2*1/2*1/2 = 1/32
There are 5C3 = 10 such cases so we should multiply by 10.
P(two boys and three girls) = 10/32 = 5/16
The answer is E.
Answer: (E) 5/16
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 833 1/3 grams
(B) 850 1/3 grams
(C) 825 1/3 grams
(D) 810 1/3 grams
(E) 870 1/3 grams
Rationale: A
833 1/3 grams
If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: (A) 833 1/3 grams
Question: Pick the odd man out:
154, 235, 352, 460, 324
(A) 324
(B) 323
(C) 279
(D) 266
(E) 0002
Rationale: Explanation:
Sum of the digit in each number, except 324 is 10.
ANSWER: A
Answer: (A) 324
Question: 23, 29, 31, 37, 41, 43, (...)
(A) 53
(B) 48
(C) 47
(D) 59
(E) 61
Rationale: All are prime numbers in their order, starting from 23
Hence, next number is 47
Answer is C.
Answer: (C) 47
Question: A man divides $8400 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
(A) A)$200
(B) B)$1000
(C) C)$800
(D) D)$1200
(E) E)$400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+4*4X+1*X=8400
25X+16X+X=8600
42X=8400, X=200.
Daughter receives four times of nephew so 4 * 200 = 800.
So Each Daughter receives $800. answer is option C) $800.
Answer: (C) C)$800
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,6), (10,0) and (10,6). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (5,3).
The slope of line passing through points (1,1) and (5,3) = (3-1)/(5-1) = 1/2
The answer is A.
Answer: (A) 1/2
Question: If x^6 + y^6 = 500, then the greatest possible value of x is between
(A) 0 and 3
(B) 3 and 6
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15
Rationale: for the greatest possible value of x^6, we must minimize the value of y^6 i.e. lets say y^6 = 0
then we need to find a number x such that x^6 < 500. 2^6 = 64 and 3^6 = 729 so we can say that the maximum possible value of x can be a little less than 3 hence answer = between 0 and 3
hence A
Answer: (A) 0 and 3
Question: A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
(A) 90
(B) 25
(C) 40
(D) 23
(E) 60
Rationale: 1/9 - 1/x = 1/10
=> 90 hrs
ANSWER A
Answer: (A) 90
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 8
(B) 9
(C) 4
(D) 7
(E) 1
Rationale: 7 * 8 : 9 * x = 8:9
=> x= 7
Answer: D
Answer: (D) 7
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2-12y+32=0
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=3,4 and Y= 4,8
X<= Y
D
Answer: (D) If x<=y
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.1100, what is the reduced price for kg?
(A) s.40
(B) s.46
(C) s.55
(D) s.41
(E) s.42
Rationale: 800*(25/100) = 275 ---- 5
? ---- 1
=> Rs.55
Answer: C
Answer: (C) s.55
Question: A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 810 sq. feet, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 84
(E) None
Rationale: EXPLANATION
We have: l = 30 ft and lb = 810 sq. ft.
So, b = 27 ft.
Length of fencing = (l + 2b) = (30 + 54) ft = 84 ft.
Answer D
Answer: (D) 84
Question: A train 130 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) 82 kmph
Rationale: speed of train relative to man: 130/6 * 18/5 km/hr
= 78 km/hr
let speed of train= x
therefore x+6 = 78
x= 78-6
x=72 km/hr
ANSWER:D
Answer: (D) 72 kmph
Question: The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 3 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 8
Tennis 5
Baseball 4
(A) 6
(B) 9
(C) 11
(D) 12
(E) 17
Rationale: X = 8 + 5 + 4 - (3 + 2 + 3) = 9
Answer is B
Answer: (B) 9
Question: The fuel indicator in a car shows 1/5th of the fuel tank as full. When 22 more liters of fuel are poured in to the tank, the indicator rests at the 3/4of the full mark. Find the capacity of the tank.
(A) 25 litres
(B) 35 litres
(C) 30 litres
(D) 40 litres
(E) None of these
Rationale: x/5 + 22 = 3x/4 => x = 40 litres
Answer: D
Answer: (D) 40 litres
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was?
(A) 120000
(B) 160000
(C) 187899
(D) 178968
(E) 789698
Rationale: X * (105/100) * (105/100) * (105/100) = 185220
X = 185220/1.157625
X = 160000
Answer:B
Answer: (B) 160000
Question: A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
(A) 21:23
(B) 27:25
(C) 23:27
(D) 23:24
(E) 23:26
Rationale: Solution :
Given SI1 = SI 2
P1 : P2 = 1/R1T1 : 1/R2T2
= 1/(10*5) : 1/(9:6)
27:25
B
Answer: (B) 27:25
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 360 m long platform?
(A) 37 min
(B) 55 min
(C) 48 min
(D) 67 min
(E) 45 min
Rationale: C
48 min
Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +360)/ 36 * 5/18 = 48 min.
Answer: (C) 48 min
Question: How long will it take a sum of money invested at 6 % p.a. S.I. to increase its value by 60%?
(A) 11 years
(B) 12 years
(C) 10 years
(D) 15 years
(E) 8 years
Rationale: Sol.
Let the sum be x. Then, S.I. = 60% of x = 3x/5; Rate = 6%.
âˆ´ Time = [100 * 3x/5 * 1/x*6] = 10 years
Answer C
Answer: (C) 10 years