mathewhe/aqua_rat huggingface dataset:
Question: In the Bargaining Bazar everyone purchase with a fair bargaining, so the traders markup the prices too much. A trader marked up an article at Rs. M expected huge profit if it is sold on marked price. But a customer purchased it at M/2 with his fine bargaining skills, so the expected profit of the trader diminished by 66.66%. What is the percentage discount fetched by the customer through bargaining?
(A) 33.33%
(B) 50%
(C) 60%
(D) 66.66%
(E) None of these
Rationale: Solution: MP = M
SP = M/2
% Discount = [(M/2) /M] *100 = 50%.
Answer: Option B
Answer: (B) 50%
Question: If 4x + 3y = 8 and y − 3x = 2, then what is the value of x + 4y?
(A) 10
(B) 3
(C) 15
(D) 52/7
(E) 60/7
Rationale: 4x + 3y = 8
−3x + y = 2
Adding both the equations --> x + 4y = 10
Answer: A
Answer: (A) 10
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B's age = 2x = 10 years.
ANSWER C
Answer: (C) 10
Question: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 39, what is the remainder when k is divided by 7?
(A) 4
(B) 5
(C) 6
(D) 3
(E) 7
Rationale: Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 39)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 39)
17 is the only common number in both the sets. Hence k = 17
Answer : D
Answer: (D) 3
Question: The sum of three consecutive multiples of 3 is 72. What is the larget number?
(A) 26
(B) 27
(C) 46
(D) 57
(E) None
Rationale: Sol.
Let the numbers be 3x, 3x + 3 and 3x + 6.
Then, 3x + (3x + 3) + (3x + 6) = 72 ⇔ 9x = 63 ⇔ x = 7.
∴ Largest number = 3x +6 = 27.
Answer B
Answer: (B) 27
Question: For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/12
(A) 12
(B) 6
(C) 29
(D) 16
(E) 32
Rationale: Now let’s look at this question from the perspective of number theory.
1/x + 1/y = 1/12
12x + 12y = xy
12x + 12y – xy =0
We need to factorize it and for that we subtract 144 from left and right parts.
12x – xy +12y – 144 = -144
(x-12)(12-y) = -144
(x-12)(y-12) = 144
Now we need to represent 144 as a product of 2 factors and find out our pairs of x and y.
(1*144) (2*72) (3*48) (4*36) (6*24) (8*18) (9*19) and 12*12.
All factor pairs (except 12*12) can be written in reverse order, so we have total 15 positive solutions.
Because we have product, x and y can also take negative values. Using same logic we got 15 negative solutions, but in this case we need to discard (-12)*(-12), because it will give us x=0, y=0. In this point the original equation is undetermined (we can’t divide by zero).
Hence we have total number of integer pairs 15 + 14 = 29
ANSWER:C
Answer: (C) 29
Question: The function f is defined for all positive integers s by the following rule. f(s) is the number of positive integers each of which is less than s and has no positive factor in common with s other than 1. If t is any prime, number then f(t)=
(A) (t-1)/2
(B) t-2
(C) (t+1)/2
(D) t-1
(E) 2
Rationale: If not the wording the question wouldn't be as tough as it is now. The GMAT often hides some simple concept in complicated way of delivering it.
This question for instance basically asks: how many positive integers are less than given prime number t which have no common factor with t except 1.
Well as t is a prime, all positive numbers less than t have no common factors with t (except common factor 1). So there would be t-1 such numbers (as we are looking number of integers less than t).
For example: if t=5 how many numbers are less than t having no common factors with 5: 1, 2, 3, 4, 5,--> 5-1=4.
Answer: D.
Answer: (D) t-1
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 2300
(B) 4500
(C) 1200
(D) 5200
(E) 1800
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: E
Answer: (E) 1800
Question: If the LCM of 8, 11, 15, and x is 25080, which of the following
could be x?
(A) 12
(B) 16
(C) 13
(D) 18
(E) 19
Rationale: Using elimination method, eliminate the option to arrive at 19
if x is replaced by 19 and the LCM is calculated you arrive at 25080
E
Answer: (E) 19
Question: In a class, the average age of 28 boys is 12 years and the average of 20 girls is 8 years. what is the average age of the whole class?
(A) 10.3 Years
(B) 12.3 Years
(C) 12.6 Years
(D) 13 Years
(E) 15 Years
Rationale: Total age of 48 students
(28X 12+20 X 8) = 496
Average = 496/48 = 10.3 Years
A
Answer: (A) 10.3 Years
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 2/22
(B) 2/20
(C) 2/21
(D) 2/23
(E) 2/29
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: (C) 2/21
Question: if the selling price of an object is rs.2300 and the profit percent is 15,what is the cost price?
(A) 1995
(B) 1945
(C) 2000
(D) 2645
(E) 2745
Rationale: cp=Sp/1.15=2300/1.15
=2000
ANSWER:C
Answer: (C) 2000
Question: A’s speed is 20/15 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/17
(B) 3/17
(C) 1/10
(D) 5/20
(E) 3/10
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 20 meters, B covers 15 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 5 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 5 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 15 meters) to reach the finish line.
So B should get a head start of 5/20th of the race.
Answer (D)
Answer: (D) 5/20
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350
(B) $10,395
(C) $10,500
(D) $11,500
(E) $12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.9 = 10,395
Answer B is correct.
Answer: (B) $10,395
Question: The age of Somu is one-third his father's. 9 years back he was one-fifth of his father's age. What is his persent age ?
(A) 11
(B) 18
(C) 14
(D) 12
(E) 10
Rationale: Explanation :
Let Somu's age be x and that of his father be 3x.
So, x - 9 = 3x - 9/5 = x = 18
Answer : Option B
Answer: (B) 18
Question: In an examination it is necessary for a candidate to get 45 % of the maximum marks to pass. A candidate who gets 180 marks, fails by 45 marks. Find the maximum marks.
(A) 450
(B) 600
(C) 500
(D) 550
(E) 650
Rationale: Let max . mark = x
pass mark =45x/100
180 = 45x/100-45
x = 180*100-4500/45 =500
ANSWER:C
Answer: (C) 500
Question: In a kickball competition of 5 teams, how many possible matches can each team play with each other?
(A)  10
(B)  16
(C)  24
(D)  36
(E)  54
Rationale: 5C2 = 10
Option A
Answer: (A)  10
Question: Find the missing in the series: 70, 54, 45, 41,___
(A) 22
(B) 287
(C) 2679
(D) 2767
(E) 2771
Rationale: Answer:B
Answer: (B) 287
Question: Tough and Tricky questions: Word Problems.
In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 2. Based on this information, how many gold coins would there be in this collection after the proposed trade?
(A) 50
(B) 60
(C) 180
(D) 200
(E) 300
Rationale: The correct answer is E.
Answer: (E) 300
Question: If x and y are even integers, which of the following is an odd integer?
(A) x+y+1
(B) x+y
(C) x-y
(D) xy
(E) x * y^2
Rationale: even + odd = odd
even + even = even
even - even = even
even * even = even
Answer : A
Answer: (A) x+y+1
Question: In a simultaneous throw of pair of dice .find the probability of getting the total more than 7?
(A) 12/5
(B) 5/12
(C) 6/4
(D) 2/3
(E) 4/7
Rationale: Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12
Option B
Answer: (B) 5/12
Question: A shopkeeper sells 400 metres of cloth for $18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) $20
(B) $43
(C) $50
(D) $70
(E) $40
Rationale: C
$50
SP per metre = 18000/400 = $45 Loss per metre = $5 CP per metre = 45 + 5 = $50
Answer: (C) $50
Question: Calculate the different number of ways 2 boys and 1 girls can sit on a bench?
(A) 6
(B) 4
(C) 5
(D) 3
(E) 2
Rationale: npn = n!
3p3 = 3 × 2 × 1 = 6
A
Answer: (A) 6
Question: Mr Sridharan invested money in two schemes A and B,offering compound interest @ 8 p.c.p.a. and 9 p.c.p.a.respectively. If the total amount of interest accured through the two schemes together in two years was 4818.30 and the total amount invested was 27,000, what was the amount invested in Scheme A?
(A) 15,000
(B) 13,500
(C) 12,000
(D) Cannot be determined
(E) None of these
Rationale: Let, in scheme A, Sridharan invest x.
Then, his investment in scheme B = (27000 – x).
Now,
x(1+8100)2+(2700−x)(1+9100)2
– 27000 = 4818.30
or, x(1.08)2 + (27000 – x)(1.09)2 = 31818.30
or, 1.1664x + 32078.7 – 1.1881x = 31818.30
or, 0.0217x = 260.4
or, x = 260.4⁄0.0217 = 12000
Answer C
Answer: (C) 12,000
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 800 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 4860.
(C) 5780.
(D) 5760.
(E) 6380.
Rationale: 1 windmill:
Normal Day = 800 kw/h
Stormy Day = 800*1.2=960 kw/h
3 windmills for 2 hours on stormy day
960*3*2=5760
Answer: D
Answer: (D) 5760.
Question: For positive integers n, the integer part of the nth term of sequence C equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, C_1 = 1.2345678…, while C_2 = 2.4681012… The sum of the first seven terms of sequence C is between:
(A) 28 and 29
(B) 29 and 30
(C) 30 and 31
(D) 31 and 32
(E) 32 and 33
Rationale: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
C_1 = 1.23…
C_2 = 2.46…
C_3 = 3.69…
C_4 = 4.812…
C_5 = 5.10…
C_6 = 6.12…
C_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
Answer: (C) 30 and 31
Question: Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 30 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
Sam rides 1 km every 5 minutes.
In the next 30 minutes, Sam rides 6 km so Sam will be 4 km ahead.
It will take Annie 80 minutes to catch Sam.
The answer is D.
Answer: (D) 80
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-fourth of all fruit exports from Country Y are orange exports. If country Y generates $40 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $800m
(C) $106.25m
(D) $127.5m
(E) $153m
Rationale: 20/100*1/4*(total) = 40
1/20*(total) = 40
(total) = 40*20 = 800
Answer: B
Answer: (B) $800m
Question: P alone can complete a job in 4 days. The work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
(A) 1.5
(B) 2.0
(C) 2.5
(D) 3.0
(E) 3.5
Rationale: P's rate is 1/4
Q's rate is 1/12
The combined rate is 1/4 + 1/12 = 1/3
If they work together, the job will take 3 days.
The answer is D.
Answer: (D) 3.0
Question: A man can do a piece of work in 5days, but with the help of his son, he can finish it in 2days. In what time can the son do it alone?
(A) 3 1/3
(B) 5 1/2
(C) 7 1/2
(D) 6
(E) 9 1/2
Rationale: Son's 1day work = 1/2 - 1/5 = 3/10
Son alone can do the work in 10/3days = 3 1/3 days
Answer is A
Answer: (A) 3 1/3
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $3 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) $193
(B) $82
(C) $110
(D) $138
(E) $192
Rationale: This question can be solved easily using a equation model.
150*p = 16500(fixed cost) + 150*80+150*3.
= 16500+ 12000+ 450
P = 193
A
Answer: (A) $193
Question: If a 3-member subcommittee is to be formed from a certain 8-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 56
(D) 108
(E) 216
Rationale: 1st member can be selected in 8 ways
2nd can be selected in 7 ways
3rd can be selected in 6 ways
So total ways : 336
But to avoid the similar scenarios 336/3!=56
ANS:C
Answer: (C) 56
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 7 days?
(A) 2/5
(B) 7/18
(C) 1/4
(D) 1/9
(E) 2/6
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 7 days = 7 (1/18) = 7/18.
ANSWER B
Answer: (B) 7/18
Question: The sum of digits of a two digit number is 11,The difference between the digits is 5. Find the number
(A) 85
(B) 94
(C) 83
(D) 72
(E) None
Rationale: Description :
=> x+y=11, x-y=5
Adding these 2x =16
=> x=8, y=3.
Thus the number is 83
Answer C
Answer: (C) 83
Question: A farmer is planting a row consisting of 5 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
(A) 512
(B) 5760
(C) 1,024
(D) 1,152
(E) 10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *5! * 4! = 5760
correct answer option B
Answer: (B) 5760
Question: If -3x+4y=28 and 3x-2y=8, what is the product of x and y?
(A) 264.
(B) 428
(C) 464.
(D) 622
(E) 642
Rationale: Given -3x+4y=28 ---Eq 1
3x -2y =8 -- Eq 2
Sum both eqns we get 2Y = 36 => Y = 18
Sub 2Y in eq 2 => 3X - 36 = 8.
=> X = 44/3
Now XY = 44/3 * 18 = 264.
Option A is correct answer.
Answer: (A) 264.
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 56 revolutions, what will be the number of revolutions made by the larger wheel?
(A) 15
(B) 24
(C) 21
(D) 9
(E) 22
Rationale: Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 56
â‡’6Ã—56=14 Ã— x
â‡’x = 24
Answer: Option B
Answer: (B) 24
Question: A man can row upstream at 7 kmph and downstream at 10kmph.find manâ€™s rate in still water and the rate of current.
(A) 1.5 km/hr
(B) 2.5 km/hr
(C) 3.5 km/hr
(D) 4.5 km/hr
(E) 5.5 km/hr
Rationale: Rate in still water=1/2(10+7)km/hr=8.5 km/hr.
Rate of current=1/2(10-7)km/hr=1.5 km/hr.
ANSWER A
Answer: (A) 1.5 km/hr
Question: A ball is bought for Rs.400 and sold at a gain of 45% find its selling price?
(A) A)Rs.480/-
(B) B)Rs.580/-
(C) C)Rs.500/-
(D) D)Rs.520/-
(E) E)Rs.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
145 % ------> 580 (120 * 4 = 580)
Selling price = Rs.580/-
B
Answer: (B) B)Rs.580/-
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 300,000 cells two hours ago, approximately how many cells will be populating the colony six hours from now?
(A) 77,500
(B) 1,860,000
(C) 2,480,000
(D) 3,720,000
(E) 4,800,000
Rationale: 300,000 × 2 × 2×2×2 = 300,000 × 16 = E
Answer: (E) 4,800,000
Question: The greatest ratio out of 2:3, 5:8, 3:2, 8:9 and 8:5 is?
(A) 2:3
(B) 3:2
(C) 5:8
(D) 8:5
(E) 8:9
Rationale: 2/3=0.666
5/8=0.625
3/2=1.5
8/9=0.888
8/5=1.6
ANSWER:D
Answer: (D) 8:5
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
(A) 6 p.m
(B) 9 p.m
(C) 5 p.m
(D) 2 p.m
(E) 1 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 5 p.m.'
Answer: C
Answer: (C) 5 p.m
Question: What is the sum of the different positive prime factors of 1092?
(A) 5
(B) 12
(C) 20
(D) 25
(E) 27
Rationale: First, we make a prime factorization by dividing 1096 by 2 then 3, etc.
1096=2^2*3*7*13
2*2+3+7+13=27
Answer (E)
Answer: (E) 27
Question: If 0 < x < 1 and x ≠ 0, which of the following inequalities must be true?
I. x^3 < x
II. x^2 < |x|
III. x^4 – x^5 > x^3 – x^2
(A)  I only
(B)  II only
(C)  III only
(D)  II and III only
(E)  I, II, and III
Rationale: Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and you can think in terms of positive fractions because the inequality is in regards to |x|). Lets set x = 1/2, then x^2 = 1/4 and 1/4<1/2
So Stmt II is always true
Stmt III. x^4 – x^5 > x^3 – x^2
This one may seem tricky but lets break it down. x^4 – x^5 > x^3 – x^2 = x^4(1-x)>x^2(x-1).
Because lets concentrate on (1-x) and (x-1). We are given that -1<x<1 which means that (1-x)>0 and (x-1)<0. x^4 will always be positive and x^2 will always be positive so without doing any math we are looking at positive > negative... which is always true.
So Stmt III is always true
B
Answer: (B)  II only
Question: In how many M ways can the letters of the word JUPITER be arranged in a row so that the vowels appear in alphabetic order?
(A)  736
(B)  768
(C)  792
(D)  840
(E)  876
Rationale: three letters can be arranged in 3! ways.
only one combination EIU is required.
7 letters can be arranged in 7! ways.
thus M=7!/ 3! * 1 = 840.
D
Answer: (D)  840
Question: Find the mean proportional between 49 & 81?
(A) 59
(B) 61
(C) 63
(D) 65
(E) 67
Rationale: Formula = √a×b
A = 49 and B = 81
√49×81 = 7 × 9 = 63
C
Answer: (C) 63
Question: X and Y started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of a total profit of Rs. 16,000, Y’s share is :
(A) 8500
(B) 9000
(C) 9500
(D) 10000
(E) 10500
Rationale: Ratio of their shares = 24000 : 40000 = 3 : 5.
B’s share = Rs. 16000 * 5/8
= Rs. 10000
ANSWER:D
Answer: (D) 10000
Question: Express a speed of 90 kmph in meters per second?
(A) 25mps
(B) 20 mps
(C) 35 mps
(D) 19 mps
(E) 21 mps
Rationale: 90 * 5/18 = 25 mps
Answer: A
Answer: (A) 25mps
Question: In the given series find the number which is wrong.
4,8,11,22,18,36,24,50
(A) 8
(B) 11
(C) 18
(D) 50
(E) 36
Rationale: Format : x and 2(x)
4 and 8
11 and 22
18 and 36
So,
24 and 48
ANSWER:D
Answer: (D) 50
Question: The speed at which a man can row a boat in still water is 20 kmph. If he rows downstream, where the speed of current is 4 kmph, what time will he take to cover 80 metres?
(A) 10.51
(B) 11.51
(C) 9.51
(D) 13.51
(E) 15.51
Rationale: Speed of the boat downstream = 20+ 4 = 24 kmph= 24 * 5/18 = 6.66 m/sHence time taken to cover 70 m = 70/6.66= 10.51 seconds.Answer:A
Answer: (A) 10.51
Question: Two airplanes take off from one airfield at noon. One flies due east at 202 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
(A) 166
(B) 332
(C) 400
(D) 483
(E) 404
Rationale: E
In two hours:
the plane flying East will be 404 miles away from airport.
the other plane will be 566 miles away from airport.
566/404 = ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 404 miles apart. E
Answer: (E) 404
Question: A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 40 percent.
(A) 120
(B) 150
(C) 175
(D) 160
(E) 130
Rationale: 1 hr =20 percent.Thus 15 min=5 percent .Now to charge 40 percent 120 min.Answer:A
Answer: (A) 120
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1:00 pm and some time later the drain that empties the pool was also opened. If the pool was filled by 7:00 pm and not earlier, when was the drain opened?
(A) at 2:00 pm
(B) at 2:30 pm
(C) at 3:00 pm
(D) at 3:45 pm
(E) at 4:30 pm
Rationale: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (6-x)/20 = 1
5x + 6 - x = 20
4x = 14
x = 3.5
The answer is 4:30 pm.
The answer is E.
Answer: (E) at 4:30 pm
Question: If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ?
(A) 32
(B) 12
(C) 82
(D) 27
(E) 17
Rationale: The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.
The first 24 of these words will start with A.
Then the 25th word will start will CA _ _ _.
The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.
The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.
Therefore, the rank of CHASM will be 24+6+2= 32
Answer: A
Answer: (A) 32