mathewhe/aqua_rat huggingface dataset:
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 80 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 87
(B) 279
(C) 80
(D) 278
(E) 379
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (80 -40) = 1 hours
So, the two trains meet at 11 a.m. The two trains meet 1 * 80 = 80 km away from Mumbai.
Answer:C
Answer: (C) 80
Question: A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern ?
(A) 10 min
(B) 12 min
(C) 15 min
(D) 9 min
(E) None of these
Rationale: Work done by the waste pipe in 1 minutes
= 1⁄20 - (1⁄12 + 1⁄15) = -1⁄10 [-ve sign means emptying]
∴ Waste pipe will empty the full cistern in 10 minutes.
Answer A
Answer: (A) 10 min
Question: The present worth of Rs.1014 due in 2 years at 4% per annum compound interest is
(A) Rs.150.50
(B) Rs.937.5
(C) Rs.156.25
(D) Rs.158
(E) None
Rationale: Solution
Present Worth	= Rs.[1014/(1+4/100)²]
= Rs.(1014x25/26x25/26)
= Rs.937.5
Answer B
Answer: (B) Rs.937.5
Question: emblem is coded as 216;
crude is coded as 125
parakeets will be ?
(A) 243
(B) 866
(C) 729
(D) 456
(E) 683
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
parakeets= 9^3 =729
ANSWER:C
Answer: (C) 729
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 90
(C) 240
(D) 480
(E) 960
Rationale: Total # of outfits = 12 * 10 * 8 = 960
Answer - E
Answer: (E) 960
Question: John buys 100 shares of par value Rs. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Face value of each share = Rs.5
Total dividend received by John = 100×5×12/100 = Rs.60
Let market value of 100 shares = Rs.x
x×10/100=60
x = 600
ie, Market value of 100 shares = Rs.600
Hence, Market value of each share = Rs.6
Answer is D.
Answer: (D) 6
Question: At a summer camp with 1,500 participants, 1/2 of the campers are aged 10 to 12. Next year, the number of campers aged 10 to 12 will increase by 1/3. After this change, what percentage of the total 1,500 campers will the 10 to 12-year-olds represent?
(A) 62
(B) 64
(C) 65
(D) 66 2/3%
(E) 67
Rationale: Total - 1,500 participants
campers are aged 10 to 12 = (1/2)*1500 = 750
Next year, campers are aged 10 to 12 = (4/3)*750 = 1000
Percentage = (1000/1500)*100 = 66 2/3%
Answer: Option D
Answer: (D) 66 2/3%
Question: A cricket team plays games only against the other five teams in its league and always in the following order: A, B, C, D and E. If the team’s final game of the season is against D, which of the following could be the number of games in the team’s schedule?
(A) 18
(B) 81
(C) 56
(D) 72
(E) 24
Rationale: IMO 'E' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is E
Answer: (E) 24
Question: If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?
(A) A decrease of 4%
(B) A decrease of 14%
(C) An increase of 4%
(D) An increase of 20%
(E) An increase of 30%
Rationale: z= x*y^2
Now , since x increases by 50 % and y decreases by 20 %
z'=(3/2)x * (8/10)(8/10)y^2
= 192/200 * x*y^2
= 96/100 * x*y^2
= 96/100 * z
a decrease in 4 %
Answer A
Answer: (A) A decrease of 4%
Question: The soldiers in two armies when they met in a battle were in the ratio of 10 : 3. Their respective losses were as 20 : 3 and the survivors as 40 : 13. If the number of survivors in the larger army be 24,000, find the original number of soldiers in each army ?
(A) 28000, 8400
(B) 25000, 7500
(C) 29000, 2750
(D) 26000, 7800
(E) 27000, 7800
Rationale: Let the soldiers in the two armies be 10X, 3X and losses be 20Y, 3Y,
Then we have,
10X - 20Y = 24000 ...(i)
And 3X - 3Y = 24000 x 13/40 = 7800
Solving, we have 10X = 28000, 3X = 8400
ANSWER:A
Answer: (A) 28000, 8400
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GREEN. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
(A) 12
(B) 14
(C) 18
(D) 19
(E) 20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GREEN) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: (D) 19
Question: What percent of 11 is 11 percent of 1?
(A)  1
(B)  0.01
(C)  0.1
(D)  13
(E)  101.
Rationale: 11 % of 1 = (11/100) * 1 = 11/100
To determine what percentage of 11 this is :
[11][/100*11] *100 = 1%
Ans : A
Answer: (A)  1
Question: A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 4 letters in its codes, and all letters can be repeated in any one code?
(A) A.15600
(B) B.16226
(C) C.17576
(D) D.18278
(E) E.475254
Rationale: The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = 676
# for 3 letters : 26 * 26*26 =17576
# for 4 letters : 26 * 26*26*26 =456976
The total : By adding all of them , 26+676+17576+456976=475254
E.
Answer: (E) E.475254
Question: Mary and Mike enter into a partnership by investing $700 and $300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year?
(A) $2000
(B) $6000
(C) $4000
(D) $1333
(E) $3000
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 7 : 3.
i.e., 70% of 2x would go to Mary and 30% of 2x would go to Mike.
Hence, Mary would get (70 - 30)% of 2x more than Mike
Or 40% of 2x = $800
i.e.,(40/100)*2x = 800
or 2x = 2000.
Hence, the profit made by the company during the year $3x = $3000.
The correct choice is (E)
Answer: (E) $3000
Question: In how many ways a committee, Consisting of 5 men and 6 women can be formed from 8 men and 10 women?
(A) 266
(B) 86400
(C) 11760
(D) 5040
(E) 720
Rationale: To choose Required number of ways to form a committee:
Select 5 men out of 8 men and 6 women out of 10 women.
That is 8C5 * 10C6.
8C5=8!/3!*5!
8C5=8*7*6*5!/(3*2*1)*5!=56
10C6=10!/6!*4!
10C6=10*9*8*7*6!/6!*(4*3*2*1)=210
The Required number of ways=210*56=11760
Answer: (C) 11760
Question: If the price of 6 toys is Rs. 264.37, what will be the approximate price of 5 toys ?
(A) Rs. 140
(B) Rs. 100
(C) Rs. 200
(D) Rs. 220
(E) None of these
Rationale: Solution
Let the required price be Rs. x . Then, less toys, less cost
∴ 6 : 5 :: 264.37 : x ⇔ 6x = (5 × 264.37) ⇔ x = (5x264.37)/6 ⇔ x = 220.308.
∴ Approximate price of 5 toys = Rs. 220. Answer D
Answer: (D) Rs. 220
Question: if P represents the number of prime numbers between 1 and 102 then what is the value of P?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Rationale: Units digit of a prime number except 2 will always be odd ( 1,3 , 5 , 7 , 9 )
So start working around.
01 - 09 = 2, 3 ,5 , 7
10 - 19 = 11, 13 , 17 , 19
20 - 29 = 23 , 29
30 - 39 = 31 , 37
40 - 49 = 41 , 43 , 47
50 - 59 = 53 , 59
60 - 69 = 61 , 67
70 - 79 = 71 , 73 , 79
80 - 89 = 83 , 87 , 89
90 - 99 = 97
100 - 102 = 101
Count you will get 26 Prime numbers
ANSWER:B
Answer: (B) 26
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Six years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
(A) Can't be determined
(B) 48
(C) 27
(D) 24
(E) None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+6)/(4x+6)=11/9
⇒ 45x + 54 = 44x + 66⇒ 9(5x + 6) = 11(4x + 6)
⇒ 45x - 44x = 66 - 54
⇒ x = 12.
Anand's present age = 4x = 48 years.
Answer: B
Answer: (B) 48
Question: Pipe A can fill a tank in 6 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?
(A) 2.5 hours
(B) 3.3 hours
(C) 3.5 hours
(D) 3 hours
(E) None of these
Rationale: Explanation:
Part filled by A in 1 hour = 1/6
Part filled by B in 1 hour = 1/10
Part filled by C in 1 hour = 1/30
Part filled by (A+B+C) in 1 hour =
1/6+1/10+1/30=9/30
So all pipes will fill the tank in 3.3 hours.
Option B
Answer: (B) 3.3 hours
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 345, the cost of the article is
(A) 289
(B) 231
(C) 100
(D) 288
(E) 111
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 350 - 345 = 5
x/20 = 5 => x = 100
Answer: C
Answer: (C) 100
Question: 111 = O
222 = E
333 = T
444 = S
Reading and analyzing the above, can you find out the following ?
555 = ?
(A) J
(B) A
(C) M
(D) K
(E) O
Rationale: E
O
1 * 1 * 1 = One
2 * 2 * 2 = Eight
3 * 3 * 3 = Twenty seven
4 * 4 * 4 = Sixty Four
For all the above, you can see that the first letter of the sum is the code.
Thus 5 * 5 * 5 = One twenty five
Thus 555 = O.
Answer: (E) O
Question: How many digits 2^10 has?
(A) 3
(B) 35
(C) 50
(D) 99
(E) 101
Rationale: 2^10 = 1.024 * 10^3
therefore 3 digits would be my best guess
A
Answer: (A) 3
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are:
(A) Rs. 10,500, Rs. 13,500, Rs. 16,500
(B) Rs. 11,500, Rs. 13,000, Rs. 16,000
(C) Rs. 11,000, Rs. 14,000, Rs. 15,500
(D) Rs. 11,500, Rs. 12,500, Rs. 16,500
(E) Rs. 12,500, Rs. 12,500, Rs. 16,500
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
ANSWER:A
Answer: (A) Rs. 10,500, Rs. 13,500, Rs. 16,500
Question: A certain bus driver is paid a regular rate of $12 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
(A) 60
(B) 68
(C) 65
(D) 64
(E) 61
Rationale: For 40 hrs = 40*12=480
Excess = 976-480=496
For extra hours =.75(12)=9+12=21
Number of extra hrs =496/21=23.62
Total hrs =40+23.62=63.62=64 approx.
Answer D 64
Answer: (D) 64
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 58
(B) 60 ways
(C) 64 ways
(D) 68
(E) 90
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64 ways
Question: The last digit of 12^12+13^13–14^14×15^15=
(A) 0
(B) 1
(C) 5
(D) 8
(E) 9
Rationale: This question tests the cyclicity concept.
2 has a cyclicity of 4 i.e. 5th power of 2 has same unit digit as 1st power of 2 .
3 also has cyclicity of 4
4 has cycling of 2
5 has 0.
So this complicated calculation boils down to
2^12 +3^13 - 4^14 ×5^15
6+3-6×0=9 as unit digit is answer.
Answer E
Answer: (E) 9
Question: The H.C.F. and L.C.M. of two numbers are 14 and 5040 respectively If one of the numbers is 144, find the other number
(A) 400
(B) 256
(C) 120
(D) 490
(E) None of these
Rationale: Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 14 * 5040
x = (14*5040)/144 = 490
Option D
Answer: (D) 490
Question: Donovan took a math test and got 35 correct and 15 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
(A) 57.78%
(B) 67.78%
(C) 70.00%
(D) 47.78%
(E) 97.78%
Rationale: 35 correct our of 50 total (35+15)
35/50
correct answer C
Answer: (C) 70.00%
Question: 30 pens and 75 pencils were purchased for 690. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 10
(B) 11
(C) 18
(D) 13
(E) 14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (690 – 150) = 540
∴ Average price of a pen = 540⁄60 = 18
Answer C
Answer: (C) 18
Question: What is the normal price of an article sold at $144 after two successive discounts of 10% and 20%?
(A) $184
(B) $192
(C) $200
(D) $208
(E) $216
Rationale: 0.8*0.9*cost price = $144
cost price = $200
The answer is C.
Answer: (C) $200
Question: The sum of two numbers is 55. Five times one number is equal to 6 times the other. The bigger of the two numbers is
(A) 10
(B) 12
(C) 14
(D) 15
(E) 30
Rationale: a:b 5:6
a+b=55
5x+6x=55
x=5
then two numbers are 25,30. The bigger number is 30
ANSWER:E
Answer: (E) 30
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 246 m
(B) 240 m
(C) 257 m
(D) 577 m
(E) 567 m
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36
= 15 ==> x + 300 = 540
==> x = 240 m.
Answer: B
Answer: (B) 240 m
Question: Hannah has 5 apples and 7 bananas. If she wants to give each of her 9 friends 1 banana and 2 apples, how many more apples and bananas does she need?
(A) 2 bananas, 13 apples
(B) 5 bananas, 13 apples
(C) 8 bananas, 8 apples
(D) 13 bananas, 5 apples
(E) 13 bananas, 2 apples
Rationale: 9 friends = 9 bananas. 9 - 7 = 2 bananas needed. 9 friends = 18 apples (2 per friend). 18 - 5 = 13 apples needed. Hence, answer : A
Answer: (A) 2 bananas, 13 apples
Question: What quantity of water should be added to reduce 5 litres of 45% acidic liquid to 25% acidic liquid?
(A) 3litres
(B) 2litres
(C) 4litres
(D) 4.5litres
(E) 5litres
Rationale: Quantity of acid in 5litres =45*5/100 = 2.25litres
Let X litres of water is added to the solution, then there is 2.25litres of acid in (5+ X ) Litres of liquid.
25% of ( 5 + X ) = 2.25, 25/100* ( 5 + X ) = 2.25
X = 225-125/25 = 4
ANSWER:D
Answer: (D) 4.5litres
Question: 45 men working 8 hours per day dig 40 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: (45 * 8)/40 = (x * 6)/50 => x =75
75 – 45 =30
ANSWER:C
Answer: (C) 30
Question: If a(a + 7) = 18 and b(b + 7) = 18, where a ≠ b, then a + b =
(A)  −48
(B)  −2
(C)  −7
(D)  46
(E)  48
Rationale: a(a + 7) = 18
=> we have a = 2 or -9
also b(b + 7) = 18
=> b = 2 or -9
given a ≠ b
1) when a =2, b= -9 and a + b = -7
1) when a = -9, b= 2 and a + b = -7
Answer choice C
Answer: (C)  −7
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140
x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer is C.
Answer: (C) 26
Question: In the xy-coordinate system, if (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5, then k =
(A) 1/2
(B) 1
(C) 2
(D) 5/2
(E) 4
Rationale: The equation of the line can be re written as y = (1/2)x - 5/2.
Slope = 1/2, which means for every 1 unit increase in the y co-ordinate, x will increase by 2 units.
Hence k = 1.
ANSWER:B
Answer: (B) 1
Question: In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the number of students in the group.
(A) 100
(B) 65
(C) 75
(D) 86
(E) 98
Rationale: Let ,F Hand C represent the set of students who play foot ball, hockey and cricket respectively.
F= 65, H=45, C=42
F and H= 20
F and C=25
H and C=15
F, H and C=8
All= 65+45+42-20-25-15+8=100
ANSWER A
Answer: (A) 100
Question: Mr. Tom invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $100,000. In one year, Fund X paid 23% and Fund Y paid 17%. The interest earned in Fund Y was exactly $200 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X?
(A)  $32,000
(B)  $36,000
(C)  $42,000
(D)  $44,000
(E)  $45,000
Rationale: X+Y=100,000
0.17Y=0.23A+200
Take away decimals first: 17Y=23X+20,000
Isolate first equation to solve for X (your goal): Y=100,000-Y
Plug in for B:
17(100,000-X)=23X+20,000
1,700,000-17X=23X+20,000
1,680,000=40X
1,680,000/40=X
X=42,000=Answer Choice C
Answer: (C)  $42,000
Question: A 90 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 220 meter
(B) 225 meter
(C) 230 meter
(D) 410 meter
(E) None of these
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+90 /9=500 /9
=>x+90=500
=>x=410
So the length of the train is 410 meters
Option D
Answer: (D) 410 meter
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, the dividend is
(A) 5336
(B) 4306
(C) 4236
(D) 4336
(E) None
Rationale: Sol.
Divisor = ( 5 × 46 ) = 230.
Also, 10 × Q = 230
⇒ Q = 23. And, R = 46.
Dividend = (230 × 23 + 46 )
= 5336.
Answer A
Answer: (A) 5336
Question: Thirty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $50 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $1000m
(B) $25.5m
(C) $106.25m
(D) $127.5m
(E) $153m
Rationale: 30/100*1/6*(total) = 50
1/20*(total) = 50
(total) = 50*20 = 1000
Answer: A
Answer: (A) $1000m
Question: What must be added to each term of the ratio 2 : 3, so that it may become equal to 4 : 5?
(A) 2
(B) 4
(C) 6
(D) 9
(E) 8
Rationale: Let the number to be added be x, then (2 + x) : (3 + x) = 4 : 5
⇒ (2 + x)/(5 + x) = 4/5
5(2 + x) = 4(3 + x)
10 + 5x = 12 + 4x
5x - 4x = 12 - 10
x = 2
Answer:2
Answer: (A) 2
Question: A car after covering ½ of a journey of 100 km develops engine trouble and later travels at ½ of its original speed. As a result, it arrives 2 hours late than its normal time. What is the normal speed of the car is?
(A) 12
(B) 77
(C) 15
(D) 25
(E) 10
Rationale: [50/x + 50/(x/2)] – 100/x
= 2
x = 25
Answer: D
Answer: (D) 25
Question: The mean proportional between 4 and 9 is?
(A) 21
(B) 35
(C) 44
(D) 12
(E) 11
Rationale: 7/20 * 100
= 35
Answer: B
Answer: (B) 35
Question: Three partners A,B and C invest Rs.18000, Rs.22500 and Rs.27000 respectively in a business. If total profit is Rs.18750 then C's share is (in Rs.)
(A) 10000
(B) 6500
(C) 5000
(D) 7500
(E) 8500
Rationale: 18000:22500:27000
4:5:6
c share=18750*6/15=7500
ANSWER:D
Answer: (D) 7500
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
(A) 18 years
(B) 20 years
(C) 24 years
(D) 32 years
(E) 35 years
Rationale: Explanation:
Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
ANSWER IS A
Answer: (A) 18 years
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 6
(B) 8
(C) 7
(D) 4
(E) 2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: (B) 8
Question: The product of a and b is equal to 12 more than twice the sum of a and b. If b = 10, what is the value of b - a?
(A) 2
(B) 5
(C) 7
(D) 6
(E) 35
Rationale: ab= 12 + 2(a+b)
10a= 12+2a +20
8a= 32
a=4
b-a= 10-4=6
D is the answer
Answer: (D) 6
Question: If x^2=x+3, then x^3=?
(A) 3x+2
(B) 3x-2
(C) 4x+3
(D) 2x-3
(E) 3x+4
Rationale: Given X^2 = X+3
X^3 = X*X^2 = x*(X+3)-- Substituted from above.
= X^2 + 3X = X+3+3X = 4X+3.
Hence C.
Answer: (C) 4x+3
Question: A certain galaxy is known to comprise approximately 3 x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 6,000
(C) 8,000
(D) 12,000
(E) 80,000
Rationale: Total no. of stars on galaxy = 3 * 10^11
Of every 50 million stars, 1 is larger than sun.
1 million = 10^6 therofore, 50 million = 50 * 10^6
total no. of stars larger than sun = 3 * 10^11 / 50 * 10^6
=30 * 10^3 /5
= 6000
therefore answer is B
Answer: (B) 6,000
Question: Four persons enter the lift of a nine storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
(A) 720
(B) 1296
(C) 1540
(D) 4096
(E) 5125
Rationale: Each person out of 4 has 8 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 8*8*8*8=8^4=4096.
Answer: D.
Answer: (D) 4096
Question: In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 6 people play both cricket and football. How many people play only cricket?
(A) 11
(B) 1
(C) 5
(D) 3
(E) 9
Rationale: people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-6 = 1
Answer is B
Answer: (B) 1
Question: If x is 11 percent greater than 90, then x =
(A) 99.9
(B) 91.0
(C) 88.0
(D) 70.9
(E) 71.2
Rationale: 11% of 90 = (90*0.11) = 9.9
11% greater than 90 = 90 + 9.9 = 99.9
Answer is clearly A.
Answer: (A) 99.9
Question: In what time will a train 130 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 3.25 sec
(C) 5 sec
(D) 12.5 sec
(E) 6 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 130/40 = 3.25 sec.
ANSWER:B
Answer: (B) 3.25 sec
Question: Dawson earns $100 a week from his job. His income increased and now makes $110 a week. What is the percent increase?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: Increase = (10/100)*100 = (1/10)*100 = 10%.
B
Answer: (B) 10%
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 48%
(B) 70%
(C) 40%
(D) 45%
(E) 20%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP
= Rs. 31150
Profit(%)
= (31150 - 22250)/22250 * 100
= 40%
Answer: C
Answer: (C) 40%