mathewhe/aqua_rat huggingface dataset:
Question: If the ratio of x to y is 2 to 6, then (y-x)/(x+y)?
(A) -7/3
(B) -3/7
(C) 1/2
(D) 1/4
(E) 7/3
Rationale: I believe this problem can be solved using algebra.
The ratio of x to y is 2 to 6 means
(x/y)=(2/6)
Cross-multiply
2x = 6y or 1x=3y
x = (1/3)*y
Then, substitute x in the original equation in the problem with the value we just found.
(y - (1/3)*y) / ((1/3)*y + y)
= ((2/3)*y) / ((4/3)*y)
Simplify by canceling the y in the numerator with the y in the denominator.
(2/3) / (4/3)
= (2/3) * (4/3)
The 3s cancel each other out, and you are left with 2/4 to 1/2.
Answer: (C) 1/2
Question: Find the ones digit of 73^350
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: 3,9,7,1 repeats after every four times
therefore 350/4 = 87 + 2 remainder
9 is the ones digit
so E is correct
Answer: (E) 9
Question: Today is Thursday. The day after 59 days will be
(A) Monday
(B) Tuesday
(C) Saturday
(D) Sunday
(E) None of these
Rationale: Explanation :
59 days = 8 weeks 3 days = 3 odd days
Hence if today is Thursday, After 59 days, it will be = (Thursday + 3 odd days)
= Sunday. Answer : Option D
Answer: (D) Sunday
Question: In how many ways letters of the word PRESS be arranged?
(A) 10
(B) 20
(C) 60
(D) 80
(E) 40
Rationale: PRESS has 5 letters, out of which S repeated 2 time. Hence total ways = 5! / (2!) = 60 ways
C
Answer: (C) 60
Question: The average age of 16 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
(A) 9
(B) 11
(C) 15
(D) 12
(E) 26
Rationale: Age of the 15th student = 16*15 - (14*5+16*9) = 240-214 = 26 years
Answer is E
Answer: (E) 26
Question: At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
(A) (54 + 6/11) past 00
(B) (54 + 6/11) past 29
(C) (54 + 6/11) past 19
(D) (54 + 6/11) past 4
(E) (54 + 6/11) past 12
Rationale: 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min
50 min. spaces are gained in min. or
Required time = min. past 4
Answer: D)
Answer: (D) (54 + 6/11) past 4
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 66900. What is his profit percent?
(A) 22
(B) 77
(C) 18
(D) 21.6
(E) 88
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 66900
Profit(%) = (66900 - 55000)/55000 * 100 = 21.6%
Answer: D
Answer: (D) 21.6
Question: Determine the equation for the line parallel to r ≡ 3x + 2y − 4 = 0 that passes through the point A = (2, 3).
(A) 2x + 3y +12= 0
(B) 2x + 3y -12= 0
(C) 3x + 2y − 12= 0
(D) 3x + 2y +12= 0
(E) x + y − 6= 0
Rationale: the equation for the line parallel to r ≡ 3x + 2y − 4 = 0 is
3x + 2y + K= 0
3 • 2 + 2• 3 + k = 0
k = −12
3x + 2y − 12= 0
ANSWER C 3x + 2y − 12= 0
Answer: (C) 3x + 2y − 12= 0
Question: Graph G has a line of symmetry of x = –3. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
(A)  –9
(B)  –7
(C)  –5
(D)  –4
(E)  2
Rationale: Line of symmetry is X=-3; one point is (3,3)
Right side distance =3+3(distance from origin) = 6; therefore Left side distance should be same from line of symmetry =6;
therefore left side co-ordinate=6+ 3(distance from origin) = 9; as the X coordinate is in 2nd quadrant hence -9
Therefore answer is A
Answer: (A)  –9
Question: 170kg of an alloy A is mixed with 250 kg of alloy B. If alloy A has lead and tin in the ratio 1:3 and alloy B has tin and copper in the ratio 3:5, then the amount of tin in the new alloy is?
(A) 210.6kg
(B) 221.3kg
(C) 229.5kg
(D) 110.8kg
(E) 114kg
Rationale: Quantity of tin in 170kg of A = 170*3/4 = 127.5kg
Quantity of tin in 250kg of B = 250*3/8 = 93.75kg
Quantity of tin in the new alloy = 127.5+93.75 = 221.25kg
Answer is B
Answer: (B) 221.3kg
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 12 1/2
(B) 12 1/6
(C) 12 1/9
(D) 12 1/5
(E) 12 1/1
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years
Answer: A
Answer: (A) 12 1/2
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 3000
(B) 4000
(C) 5000
(D) 4000
(E) 2000
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
ANSWER E
Answer: (E) 2000
Question: If 4/p=8 & 6/q=18 then p-q=?
(A) 5/24
(B) 6/24
(C) 7/24
(D) 1/6
(E) 9/24
Rationale: p=4/8 , q=6/18=>q=1/3
therefore
p-q=(1/2)-(1/3)=1/6
ANSWER:D
Answer: (D) 1/6
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
(A) 25
(B) 29
(C) 48
(D) 26
(E) 54
Rationale: A
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer: (A) 25
Question: If x is a number such that x^2 + 5x - 6 = 0 and x^2 - 5x + 4 = 0, then x =
(A) -1
(B) 1
(C) 4
(D) -6
(E) 6
Rationale: x^2 + 5x - 6 = (x+6)(x-1) = 0
Then x=-6 or x=1.
x^2 - 5x + 4 = (x-4)(x-1) = 0
Then x=4 or x=1.
Thus x=1.
The answer is B.
Answer: (B) 1
Question: An association of mathematics teachers has 1,500 members. Only 525 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 40 percent of the votes cast?
(A) 75%
(B) 58%
(C) 42%
(D) 34%
(E) 14%
Rationale: Total umber of members = 1500
Number of members that cast votes = 525
Since , winning candidate received 40 percent of the votes cast
Number of votes for winning candidate = (40/100)*525 = 210
Percent of total membership that voted for winning candidate = (210/1500)*100 = 14%
Answer E
Answer: (E) 14%
Question: A starts business with Rs.3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital?
(A) 6000
(B) 9000
(C) 9500
(D) 12000
(E) None
Rationale: Sol.
Let B’s capital be Rs. x. Then, 3500 * 12 / 7x = 2/3 ⇔ 14x = 126000 ⇔ x = 9000.
Answer B
Answer: (B) 9000
Question: What is the sum Y of all 3 digit numbers that leave a remainder of '2' when divided by 3?
(A) 897
(B) 164,850
(C) 164,749
(D) 149,700
(E) 156,720
Rationale: The series is => 101+...998
Number of terms => 300
sum => 300/2 * [101+998]
hence sum Y=> 164850 i.e. option B
Answer: (B) 164,850
Question: 210 reputed university students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?
(A) 25
(B) 40
(C) 50
(D) 60
(E) 75
Rationale: We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20.
So, if we use your formula it should be: 210={Mac}+{Windows}-{Both}+{Neither}=(60+20)+x-20+90 --> x=60 (# of student who prefer Windows) --> # of the students who preferred Windows to Mac is x-20=40.
Answer: (B) 40
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 21/9 sec
(B) 32/3 sec
(C) 20/7 sec
(D) 32/3 sec
(E) 53/2 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer:C
Answer: (C) 20/7 sec
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 3 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,000 nuts and 1,000 bolts?
(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,500 seconds
(E) 3,000 seconds
Rationale: To minimize the amount of time, we should make both machines work all the time while producing 1,000 nuts and 1,000 bolts.
Two machines to produce 1,000 bolts will need (1,000*3)/2 = 1500 seconds.
Two machines to produce 1,000 nuts will need (1,000*2)/2 = 1,000 seconds.
Total = 1500 + 1,000 = 2,500.
Answer:D.
Answer: (D) 2,500 seconds
Question: The average of four numbers is 27. If one number is excluded, the average becomes 25. The excluded number is
(A) 25
(B) 27
(C) 30
(D) 33
(E) 40
Rationale: Sol.
Therefore excluded number
= (27 × 4) - ( 25 × 3)
= 108– 75
= 33.
Answer D
Answer: (D) 33
Question: Which of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?
(A) f(x) = x2
(B) f(x) = x + (x−1)^2
(C) f(x) = x-1
(D) f(x) = 5/x
(E) f(x) = x/5
Rationale: E. f(x) = x/5
Now for LHS x=y-z
so F(x) = F(y-z)
put x as Y-Z in X/5
f(y-z)=y-z/5= y/5-z/5---------1
similarly RHS
F(Y) = y/5---
F(Z)=Z/5 ---
F(Y)-F(Z)=Y/5 - Z/5------------2
we can see LHS =RHS ..so E remains.
ANSWER:E
Answer: (E) f(x) = x/5
Question: In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the even positions?
(A) None of these
(B) 64
(C) 120
(D) 36
(E) 360
Rationale: OEOEOE
3 vowels EAI can be arranged on even places in 3!=6 ways. Similarly 3 consonants can be arranged on odd places in 3!=6 ways.
Total = 6*6 = 36.
Answer: D.
Answer: (D) 36
Question: A boy rides his bicycle 10 km at an average sped of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately.
(A) 10.2 kmph
(B) 10.4 kmph
(C) 10.8 kmph
(D) 11.8 kmph
(E) None
Rationale: Sol.
Total distance travelled = (10+12) km/hr = 22 km/hr.
total time taken = [10/12 + 12/10] hrs = 61/30 hrs
∴ Average speed = [22*30/61] km/hr = 10.8 km/hr.
Answer C
Answer: (C) 10.8 kmph
Question: If 0 < y < 1, what is the median of the values y, y^-1, y^2, y^1/2 and y^3?
(A) y
(B) y^-1
(C) y^2
(D) y^1/2
(E) y^3
Rationale: A. To make the problem less confusing, I picked a number between 0 and 1 such as y = 1/4 and calculate:
y = 1/4
y^-1 = 4
y^2 = 1/16
y^(1/2) = 1/2
y^3 = 1/8.
From this, rearrange the number and the median is 1/4, which is y. Answer A
Answer: (A) y
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18
(B) 30/19
(C) 30/15
(D) 30/13
(E) 30/11
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer: D
Answer: (D) 30/13
Question: In a certain city, 60% of the registered voters are congress supporters and the rest are BJP supporters. In an assembly election, if 75% of the registered congress supporters and 20% of the registered BJP supporters are expected to vote for candidate A, what percent of the registered voters are expected to vote for candidate A?
(A) 53
(B) 66
(C) 77
(D) 89
(E) 11
Rationale: let the people in the city be 100
Congress supporters = 60% of 100 = 60
40% are BJP=40% of 100 = 40
out of 60,75% voted for congress=75%(60)=45
out of 40%,20% voted for congress=20%(40)=8
Total=45 + 8 = 53
Total percent= 53%
Answer:A
Answer: (A) 53
Question: In a certain match all the teams were to play with each other. If there are 8 teams, how many matches will have to be played?
(A) 40
(B) 28
(C) 60
(D) 90
(E) None of the above
Rationale: 8c2
=28
ANSWER:B
Answer: (B) 28
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2772?
(A) 2277
(B) 2669
(C) 2200
(D) 2800
(E) 2998
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2772.
=> (90%) of (110%) of x = Rs. 2772.
=> (90/100)(110/100)x = 2772
=> x = (2772 * 100)/(9 * 11)
=> x = Rs. 2800
Answer: D
Answer: (D) 2800
Question: The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 3 in the prime factorization of F(3)/G(3) is
(A) 	1
(B) 	2
(C) 	3
(D) 	4
(E) 	5
Rationale: F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 1
Answer: A
Answer: (A) 	1
Question: In the quiet town ofNothintodothere are 500 inhabitants, 300 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
(A) 50.
(B) 100.
(C) 150.
(D) 200.
(E) 300.
Rationale: Total = 500
unemployed=300
employed=500-300=200
som=300
unemployed som = 300/2=150
employed som = 150
employed that are not som = 200-150=50
Answer:A
Answer: (A) 50.
Question: At what price must an Book costing $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) 72.5
(B) 55.5
(C) 62.5
(D) 82.5
(E) 60.5
Rationale: C
$62.50
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: (C) 62.5
Question: In how many ways can 5 boysand 2 girls be arranged at a table if 2 girls are never together?
(A) 400
(B) 420
(C) 430
(D) 450
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
(A) 16 2/3% loss
(B) 16 2/8% loss
(C) 16 8/3% loss
(D) 18 2/3% loss
(E) 26 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer:A
Answer: (A) 16 2/3% loss
Question: On decreasing the price of a Computer by 10%, its sale is increased by 40%. The effect on the revenue is?
(A) 4% decrease
(B) 28% increase
(C) 16% decrease
(D) 26% increase
(E) none of these
Rationale: Net% change in revenue
= ( x + y + xy/100) %
= [-10 + 40 + ( -10 x 40)/100]% or 26%
ANSWER:D
Answer: (D) 26% increase
Question: How many keystrokes are needed to type numbers from 56 to 200?
(A) 310
(B) 391
(C) 270
(D) 289
(E) None of these
Rationale: Explanatory Answer
While typing numbers from 56 to 200, there are 44 two-digit numbers: from 56 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 88 keystrokes to type the 2-digit numbers.
There are 101 three-digit numbers: from 100 to 200.
Each of these numbers requires 3 keystrokes.
Therefore, 303 keystrokes to type the 3-digit numbers.
Totally, therefore, one requires 88 + 303 = 391 keystrokes.
Choice B is the correct answer.
Answer: (B) 391
Question: A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group?
(A) 33
(B) 38
(C) 23
(D) 10
(E) 27
Rationale: Explanation:
It can be solved easily through option.
\inline \left ( 10+9+8+....+1 \right )=10\left ( 10\times \frac{55}{100} \right )
55 = 55 Hence correct
Alternatively:
\inline \frac{n(n+1)}{2}=n\times \frac{55n}{100}
=> n= 10
In Both cases total work is 55man-days.
Answer: D) 10
Answer: (D) 10
Question: What approximate value should come in place of question mark (?) in the following equations ?
(0.0078 ÷ 0.00012) x 77.88 = ?
(A) 5010
(B) 5040
(C) 5070
(D) 5100
(E) 5400
Rationale: Explanation :
? = 65 x 78 = 5070
Answer : Option C
Answer: (C) 5070
Question: In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated ?
(A) 14400
(B) 36000
(C) 18000
(D) 24000
(E) 22200
Rationale: We have 3 vowels: AIO and 5 consonants: MNFLD.
Consider the following case: *M*N*F*L*D* If we place vowels in any 3 empty slots (*) then all vowels will be separated by at least one consonant:
The # of ways to choose 3 empty slots out of 6 for 3 vowels = C36=20C63=20;
The # of ways to arrange the vowels: 3! (or instead of these two steps we could use P36)P63);
The # of ways to arrange MNFLD = 5!.
Total = 20*3!*5! = 14,400.
Answer: A
Answer: (A) 14400
Question: There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 28 possible combinations in which Michael is not selected, what is the value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: The combinations of two people, in which Michael was not selected = 28
The number of ways two people can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael.
Then m*(m-1) = 56 = 8*7
Thus, n = m + 1(Michael) = 9
The answer is C.
Answer: (C) 9
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
(A) 6/7
(B) 15/7
(C) 8/9
(D) 7/15
(E) 4/3
Rationale: .let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Ans: D
Answer: (D) 7/15
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 179
(B) 367
(C) 269
(D) 177
(E) 191
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 – 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 208
2x = 358
x = 179 runs
ANSWER: A
Answer: (A) 179
Question: In a coconut grove, (x + 1) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 1) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
(A) 2
(B) 4
(C) 5
(D) 6
(E) None of the above
Rationale: (x+1)×60+x×120+(x−1)×180/(x+1)+x+(x−1)=100
⇒ 360x−120/3x = 100
⇒ 60x = 120 ⇒ x = 2
Answer A
Answer: (A) 2
Question: The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
(A) 75
(B) 66
(C) 55
(D) 44
(E) 12
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 150 + P
C + M = 150
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2 = 75.
Answer:A
Answer: (A) 75
Question: a box contain 4 small bos, each small box again contain 3 box,again these box contain 2 box . total how many boxes
(A) 38
(B) 39
(C) 40
(D) 42
(E) 41
Rationale: a box contain 4 small box means 1+4 = 5 Boxes
each small box again contain 3 box means 4*3 = 12 boxes
Again these 12 boxes contain 2 boxes each... means 12*2 = 24
Total Boxes till now are 5 + 12 + 24 = 41
ANSWER:E
Answer: (E) 41
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?
(A) 50
(B) 100
(C) 200
(D) 1,000
(E) 2,000
Rationale: y = 50% of 50% 0f x
= x/4
and
y/100 of x = 100
y /100 *4y =100
y = 50
and x= 200
Answer - C
Answer: (C) 200
Question: Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:
(A) 53
(B) 108
(C) 77
(D) 107
(E) 109
Rationale: Explanation:
Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.
Answer: Option D
Answer: (D) 107
Question: An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets liquid in at the rate of 8 litres/min then outlet pipe would take 6 hours longer. Find the capacity of the tank.
(A) 8600 litres
(B) 12800 litres
(C) 12100 litres
(D) 11200 litres
(E) 13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 8*60 = 480 liters/hour;
Net outflow rate when both pipes operate would be x-480 liters/hour.
Capacity of the tank = x*10 hours = (x-480)*(10+6) hours
10x=(x-480)*16 --> x=1280 --> capacity = 10x = 12800 liters.
Answer: B
Answer: (B) 12800 litres
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
(A) Rs. 4000
(B) Rs. 4500
(C) Rs. 5500
(D) Rs. 6000
(E) Rs. 7000
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12	x x +	15	x (12000 - x) = 1360.
120	125
x	+	3	(12000 - x) = 1360.
10	25
5x + 72000 - 6x = 1360 x 50
x = 4000.
ANSWER:A
Answer: (A) Rs. 4000
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a + b + c > a^3
II. a × b × c < a^3
III. 5b < bc
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
Rationale: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid.
Answer: (A) I only
Question: If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,5], what is the probability that x < y?
(A) 23/30
(B) 7/12
(C) 11/15
(D) 7/10
(E) 3/4
Rationale: Since x is in [0,3] and y is in [0,5] we can draw a rectangle in the coordinate plane with vertices (0, 0), (3, 0), (0, 5), and (3, 5).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 4.5.
The whole rectangle has an area of 15.
P(x < y) = (15-4.5)/15 = 21/30 = 7/10
The answer is D.
Answer: (D) 7/10
Question: There are 3 sections with 4 questions each. If three questions are selected from each section, the chance of getting different questions is________
(A) 10
(B) 78
(C) 89
(D) 64
(E) 56
Rationale: we have to select three questions from each section so the chances are 4C3.4C3.4C3=64
ANSWER:D
Answer: (D) 64