mathewhe/aqua_rat huggingface dataset:
Question: 7 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
(A) 30
(B) 21
(C) 18
(D) 15
(E) 10
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 7(7-1)/2 = 7*6/2 = 42/2 = 21
=> the answer is B(21)
Answer: (B) 21
Question: A, B and C enter into a partnership by investing $15000, $21000 and $27000 respectively. At the end of 8 months, B receives $1540 as his share. Find the share of A.
(A) $800
(B) $900
(C) $1000
(D) $1100
(E) $1200
Rationale: The ratio of capital of A, B and C = 15000 : 21000 : 27000 = 5 : 7 : 9
A's share = (5/7)*1540 = $1100
The answer is D.
Answer: (D) $1100
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/23
(C) 5/29
(D) 5/12
(E) 5/92
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability
= (5C2 * 6C1)/10C5
= (10 * 6)/252 = 5/21
Answer: A
Answer: (A) 5/21
Question: Create 2 equivalent fractions with the numbers 4, 9, 2, and 18
(A) 2/9 and 5/18
(B) 2/9 and 4/18
(C) 3/9 and 4/18
(D) 2/9 and 6/18
(E) None
Rationale: Solution:
We're searching for pairs of numbers which, when multiplied, have the same product. We observe that 4 x 9 = 18 x 2 = 36, so the fractions will be 2/9and4/18
Answer B
Answer: (B) 2/9 and 4/18
Question: The average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years. Find the average age of the women?
(A) 42
(B) 40
(C) 30
(D) 18
(E) 11
Rationale: Explanation:
26 + 30 + 7 * 4 = 84/2 = 42
Answer: A
Answer: (A) 42
Question: One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 17 percent sugar by weight. The second solution was what percent sugar by weight?
(A) 34%
(B) 24%
(C) 22%
(D) 38%
(E) 8.5%
Rationale: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.
3 parts of 10% + 1 part of x (unknown) % = 4 parts of 17%
=> x% = 68%-30% = 38%
ans D it is.
Answer: (D) 38%
Question: xy=1 then what is (3^(x+y)^2) / (3^(x-y)^2)
(A) 81
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
3^4 = 81
Answer A
Answer: (A) 81
Question: There are 10 slate rocks, 15 pumice rocks, and 6 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
(A) 2/19
(B) 3/31
(C) 4/37
(D) 5/41
(E) 6/53
Rationale: 10/31*9/30 = 3/31
The answer is B.
Answer: (B) 3/31
Question: Which of the following fractions is greater than 1/7?
(A) 1. 12/50
(B) 2. 3/11
(C) 3. 2/9
(D) 4. 4/17
(E) 5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
A
Answer: (A) 1. 12/50
Question: 3 men or 6 women can do a piece of work in 23 days. In how many days will 12 men and 8 women do the same work?
(A) 15/9 days
(B) 15/4 days
(C) 18/4 days
(D) 69/16 days
(E) 35/4 days
Rationale: 3M = 6W ---- 23 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 23 32 -----?
6 * 23 = 32 * x => x = 69/16 days
Answer:D
Answer: (D) 69/16 days
Question: A train running at the speed of 72 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 286
(B) 278
(C) 255
(D) 180
(E) 287
Rationale: Speed=(72 * 5/18) m/sec = (20) m/sec Length of the train
= (Speed x Time) = (20 * 9) m
= 180 m.
Answer:D
Answer: (D) 180
Question: Joshua and Jose work at an auto repair center with 3 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
(A) 1/15
(B) 1/10
(C) 1/9
(D) 1/6
(E) 1/3
Rationale: Two Methods
1) Probability of chosing Josh first = 1/5
Probability of chosing Jose second = 1/4
total = 1/20
Probability of chosing Jose first = 1/5
Probability of chosing Josh second = 1/4
Total = 1/20
Final = 1/20 + 1/20 = 1/10
B
Answer: (B) 1/10
Question: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
(A) 1 day
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
A
Answer: (A) 1 day
Question: All of the stocks on the over-the-counter market are designated by either a 8-letter or a 9-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) a. 27(26^8)
(B) b. 26(26^4)
(C) c. 27(26^4)
(D) d. 26(26^5)
(E) e. 27(26^5)
Rationale: no of different stocks for 8-letter code = 26^8
no of different stocks for 9-letter code = 26^9
total = 26^8 + 26^9 = 26^8(26+1) = 27(26^8)
[Reveal]Spoiler:
Option A
Answer: (A) a. 27(26^8)
Question: The average (arithmetic mean) of 4 positive integers is 45. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?
(A) 55
(B) 65
(C) 100
(D) 89
(E) 115
Rationale: a + b + c + d = 180
a + b = 90
c + d = 90
Greatest possible = 89 (Just less than 1)
Answer = D
Answer: (D) 89
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent W of the distribution is less than m +d ?
(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
Rationale: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, W=(68+16)% or (100-16)% of the population is less than m+d.
Answer: (D) 84%
Question: Twelve men and six women together can complete a piece of work in four days. The work done by a women in one day is half the work done by a man in one day. If 12 men and six women started working and after two days, six men left and six women joined, then in hoe many more days will the work be completed?
(A) 2 (1/9)
(B) 2 (4/2)
(C) 5 (1/2)
(D) 2 (1/2)
(E) 2 (1/6)
Rationale: Work done by a women in one day = 1/2 (work done by a man/day)
One women's capacity = 1/2(one man's capacity)
One man = 2 women.
12 men = 24 women.
12 men + 6 women = 30 women
30 women can complete the work in four days. In the first 2 days they can complete 1/2 of the work. Remaining part of the work = 1/2. If 6 men leave and 6 new women join, then new work force = 30 women - 12 women + 6 women = 24 women.
Time taken by them to complete the remaining work = 1/2 (Time taken by 24 women to complete the work) = 1/2 * (30 * 4)/24 = 2 (1/2) days.
Answer: D
Answer: (D) 2 (1/2)
Question: If KING is coded as 17 and MASS is coded as 29 Then DOC is coded as
(A) 21
(B) 20
(C) 19
(D) 5
(E) None
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DOC = 4+14+3=21 i.e(2*2)+(1*1)=5
ANSWER:D
Answer: (D) 5
Question: The number 130 can be written as the sum of the squares of 2 different positive integers. What is the sum of these 2 integers?
(A)  17
(B)  16
(C)  15
(D)  14
(E)  13
Rationale: 11^2 + 3^2 = 130 --> 11 + 3 = 14.
D
Answer: (D)  14
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 28
(B) 50
(C) 88
(D) 22
(E) 12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.Answer:B
Answer: (B) 50
Question: Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 208.
(A) 15
(B) 37
(C) 55
(D) 26
(E) 73
Rationale: Using the elimination method the option that fits this description is 26
6-2 = 4 (unit's digit that exceeds its ten's digit by 3)
26*8 = 208 (the product of the given number and the sum of its digits is equal to 175)
answer :D
Answer: (D) 26
Question: Which of the following equations has a root in common with x^2−4x+4=0 ?
(A) x^2-1=0
(B) x^2-2=0
(C) x^2-3=0
(D) x^2-4=0
(E) x^2-5=0
Rationale: If we carefully look at the given equation we can arrange it in the following manner:
(x-2)^2= 0
so the two root is 2.
Now put 2 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 2: we get 3. Reject this option.
(B) putting 2: we get 2. Reject this option.
(C) putting 2: we get 1. Reject this option.
(D) putting 2: we get 0. This is the equation, no need to check other option.
D is the answer.
Answer: (D) x^2-4=0
Question: A hungry child reaches into a candy jar filled with 5 different candies; red, green, yellow, black, and white colored candies. If the child randomly picks three candies, what is the probability the child will pick the red and green colored candies as two of the three candies?
(A) 3/10
(B) 1/10
(C) 1/15
(D) 3/15
(E) 2/5
Rationale: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.
Total number possible = 5C3 = 5!/(3!(5 - 3)!) = 10
Number red possible = 1C1 = 1
Number green possible = 1C1 = 1
Number other possible = 3C1 = 3
Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)
P(RG) = (1C1)(1C1)(3C1)/5C3 = 3/10
Answer: A
Answer: (A) 3/10
Question: If x and y are positive integers, and 4x^3=3y, then which of the following must be a multiple of 9?
I. x^2
II. y^2
III. xy
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: 4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is D
Answer: (D) I and II only
Question: How many different positive integers are factors of 196 ?
(A)  1
(B)  2
(C)  3
(D)  49
(E)  36
Rationale: 15, 14×15, 14=7^2 × 2^2
So total factors = (6+1)(6+1) = 49
Answer: D
Answer: (D)  49
Question: It takes 10 days for digging a trench of 100 m long, 50 m broad and 10 m deep. What length of trench,25 m broad and 15 m deep can be dug in 30 days ?
(A) 400 m
(B) 200 m
(C) 100 m
(D) 89 m
(E) 79 m
Rationale: More days, more length (Direct)
Less breadth, more length (Indirect)
More depth, less length (Indirect
Days 10 : 30;
Breadth 25 : 50; : : 100 : x
Depth 15 : 10;
:. 10 * 25* 15 * x = 30 *50 * 10 *100
x= (30*50*10*100)/10*25*15 = 400
So the required length = 400m
ANSWER:A
Answer: (A) 400 m
Question: If a/b=3/4 and 8a+5b=22,then find the value of a.
(A) 3/2
(B) 5/2
(C) 1/2
(D) 4/2
(E) None of them
Rationale: (a/b)=3/4 =>b=(4/3) a.
Therefore, 8a+5b=22 => 8a+5*(4/3) a=22 => 8a+(20/3) a=22
=>44a = 66 => a=(66/44)=3/2
Answer is A
Answer: (A) 3/2
Question: Sid and Bonnie are opposing participants in an online auction. Each has a constant bidding strategy: Sid always bids up by raising $40 over any previous bid. Bonnie always bids up by doubling any previous bid. The auction begins with an initial bid by a third player, and progresses as follows: Sid bids up first, and Bonnie follows. Sid bids up again, and Bonnie follows and raises the bid to a final $600. What was the dollar value of the initial price?
(A) 46
(B) 90
(C) 68
(D) 568
(E) 464
Rationale: Initial bid = p$
Sid = p+40
Bonnie = 2p
The sequence is R---> B ---> R -----> B ---> 600
Thus per the sequence we have: p+40, 2(p+40), 2p+80+40 , 2(2p+120)
Now given, 2(2p+120) = 600----> p =90$. Thus B is the correct answer.
Answer: (B) 90
Question: A cyclist covers a distance of 750 meter in 2 minutes 10 seconds. What is the speed in km/hr of cyclist
(A) 20.88 km/hr
(B) 17 km/hr
(C) 18 km/hr
(D) 19 km/hr
(E) 20 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=750meter
Time=2 min 10sec=130sec
Speed=750/130=5.8m/sec
=>5.8âˆ—18/5km/hr=20.88km/hr
Option A
Answer: (A) 20.88 km/hr
Question: A company has two models of computers, model M and model N. Operating at a constant rate, a model M computer can complete a certain task in 24 minutes and a model N computer can complete the same task in 12 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model M computers were used?
(A) 3
(B) 4
(C) 5
(D) 8
(E) 6
Rationale: Let's say 1 work is processing 24 gb of data.
Model M : 1 gb per min
Model N : 2 gb per min
Working together, 1 M and 1 N = 3 gb per min
So, 8 times as many computers would work at 18 gb per min.
So no. of M = 8
Answer is D
Answer: (D) 8
Question: six family members: 5 grandchildren (3 brothers and 2 sisters) and their 1 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
(A) 120
(B) 48
(C) 1440
(D) 2880
(E) 8640
Rationale: Answer: B.
Answer: (B) 48
Question: If there are 50 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3, what is the probability that, drawing twice, you will select two red marbles if you return the marbles after each draw?
(A) 1/25
(B) 2/25
(C) 3/25
(D) 4/25
(E) 21/25
Rationale: 50 red and blue marbles in a jar, and the ratio of red to blue marbles is 2:3
So, 5x=50 ---> x=10
Red marbles = 2*x = 2*10 = 20
Blue marbles = 3*x = 3*10 = 30
Prob to select a red marble = 20/50 = 2/5
Prob to select 2 red marbles with replacement = 2/5*2*5 = 4/25
Hence, answer will be D.
Answer: (D) 4/25
Question: 2y - 2x = 2xy and x ≠ 0. If x and y are integers, which of the following could equal y?
(A) 2
(B) 1
(C) 0
(D) -3
(E) - 2
Rationale: Plug in the answer choices in the equation from the question stem.
A) y = 2 >>> 4-x = 4x >>> No value of x will satisfy this, not even 0. POE
B) y = 1 >>> 2 - x = 2x >>> Same, POE
C) y = 0 >>> -x = 0 >>> x can not equal 0
D) y = -1 >>> -2 - 2x = -4x >>> Holds true for x = 1, no need to check E. This is the answer.
Answer D
Answer: (D) -3
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 36 percent of the total votes?
(A) 10%
(B) 12.5%
(C) 15%
(D) 17.5%
(E) 20%
Rationale: There were 80% of the votes remaining and he needed 16%/80% = 2/10 = 20%
The answer is E.
Answer: (E) 20%
Question: x is what percent of y percent of z, in terms of x, y and z? m be the value expressed in terms of x,y and z.
(A) xyz
(B) 1/xyz
(C) 10^2 x/yz
(D) 1000 x/yz
(E) 10,000x/yz
Rationale: Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to m% of yz/100; then we have:
x = (m/100)*(yz/100)
10,000x/yz = m
E
Answer: (E) 10,000x/yz
Question: The area of a circle is added to its diameter, and the circumference is then subtracted from this total, the result is 10. What is the radius of the circle?
(A) 2*pi
(B) pi
(C) 2
(D) 4*pi
(E) 4
Rationale: The equation is; diameter + Area - Circumference = d + A - C = d + pi * r^2 - 2 * pi * r = 2r + pi * r(r - 2).
By plugging in the answers we can test the answers quickly; then, 4 is the only possible answer.
Answer: E
Answer: (E) 4
Question: Sandy buys an old scooter for $900 and spends $300 on its repairs. If Sandy sells the scooter for $1260, what is the gain percent?
(A) 3%
(B) 5%
(C) 7%
(D) 9%
(E) 11%
Rationale: selling price / total cost = 1260/1200 = 1.05
The gain percent is 5%.
The answer is B.
Answer: (B) 5%
Question: Each of the 50 members in a high school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 17 students sign up for the poetry club, 24 students for the history club, and 22 students for the writing club. If 3 students sign up for exactly two clubs, how many students sign up for all three clubs?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: The total number in the three clubs is 17+24+22=63.
All 50 students signed up for at least one club.
3 of those students signed up for exactly one more club.
63 - 53 = 10 so 5 students must have signed up for exactly three clubs.
The answer is A.
Answer: (A) 5
Question: Working at a constant rate, P can finish a job in 3 hours. Q, also working at a constant rate, can finish the same job in 18 hours. If they work together for 2 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?
(A) 32
(B) 36
(C) 40
(D) 44
(E) 48
Rationale: Each hour they complete 1/3 + 1/18 = 7/18 of the job.
In 2 hours, they complete 2(7/18) = 7/9 of the job.
The time for P to finish is (2/9) / (1/3) = (2/3) hour = 40 minutes
The answer is C.
Answer: (C) 40
Question: The average weight of A, B and C is 44 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 17 kg
(B) 28 kg
(C) 26 kg
(D) 31 kg
(E) 35 kg
Rationale: let d sum of a, b, c is 3*44=132
and sum of a and b s 2*40=80
sum of b and c is 2 *43=86
hence 80+86-132=28
ans=28
ANSWER:B
Answer: (B) 28 kg
Question: Which of the following is closest to (120!-119!)/(120!+119!)
(A) 2
(B) 2.5
(C) 3
(D) 1
(E) 3.2
Rationale: (120!-119!)/(120!+119!)
119! (120-1)/119! (120+1)
119/121 = 1 (approximately)
D is the answer
Answer: (D) 1
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/6.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 250 balls, how many yellow balls are in the Jar?
(A) 25.
(B) 34.
(C) 53.
(D) 60.
(E) 73.
Rationale: We need to get some number which is less than 250 and exactly divisible by 8,6 and 10
Lets take LCM of three balls 8,6 and 10 = 120.
The probability of drawing a blue ball is 1/8...For every 8 balls we get 1 BLUE ball then out of 120 balls we get 15 BLUE balls.
The probability of drawing a red ball is 1/6...For every 5 balls we get 1 RED ball then out of 120 balls we get 12 REB balls.
The probability of drawing a green ball is 1/10. For every 10 balls we get 1 GREEN ball then out of 120 balls we get 20 GREEN BALLS.
Then out of 120 - ( 15 + 20 + 12 ) = 73 YELLOW balls.
IMO option E is correct.
Answer: (E) 73.
Question: There are 10 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 156
(B) 167
(C) 132
(D) 352
(E) 380
Rationale: The total number of stations = 12
From 12 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 12P₂ ways.
²⁰P₂ = 12 * 11
= 132.
Answer: C
Answer: (C) 132
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 25% to $6 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
(A) $1.25 million
(B) $800,000
(C) $750,000
(D) $27,000
(E) $160,000
Rationale: Let sales in previous month = X
1.25 X=6,000,000
5/4 X= 6,000,000 ..........> X=4,800,000
sales per day= 4,800,000/30= less than 160,000
Answer: E
Answer: (E) $160,000
Question: John bought 15 apples for Rs.10 and sold them at the rate of 12 apples for Rs.12. What is the percentage of profit made by him?
(A) 50 %
(B) 60 %
(C) 65 %
(D) 100 %
(E) None
Rationale: Profit % = 15/10 * 12/12 = 1.5 ⇒ 50%.
Answer A
Answer: (A) 50 %
Question: An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 80 cm, find the sum of the perimeters of all the triangles.
(A) 180 cm
(B) 220 cm
(C) 240 cm
(D) 270 cm
(E) 480 cm
Rationale: We have 80 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues.
So we have 80,40,20,...
We have ratio = 1/2, and it is GP type.
Sum of infinite triangle is a/1-r = 80/1-(1/2) = 160
Equilateral triangle perimeter is 3a = 3*160 = 480.
So option E.
Answer: (E) 480 cm
Question: A train passes a station platform in 30 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) 150
(B) 166
(C) 240
(D) 157
(E) 198
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 30 = 15
x + 300 = 450
x = 150 m.
Answer: A
Answer: (A) 150
Question: In an office, totally there are 2800 employees and 25% of the total employees are males. 30% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 390
(B) 490
(C) 400
(D) 460
(E) None of these
Rationale: Number of male employees = 2800* 25/100 = 700
Required number of male employees who are less than 50 years old = 700* (100 - 30)%
= 700* 70/100 = 490.
ANSWER:B
Answer: (B) 490
Question: A number is increased by 60% and then decreased by 60%, the final value of the number is ?
(A) decrease by 36%
(B) decrease by 30%
(C) decrease by 32%
(D) decrease by 34%
(E) decrease by 35%
Rationale: Here, x = 60 and y = - 60
Therefore, the net % change in value
= ( x + y + xy/100)%
= [60 - 60 + (60 * -60)/100]% or - 36%
Since the sign is negative, there is a decrease in value by 36%.
ANSWER: A
Answer: (A) decrease by 36%
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 12 sec
(B) 30 sec
(C) 86 sec
(D) 16 sec
(E) 18 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer: B
Answer: (B) 30 sec
Question: The sequence S is defined as Sn = (n + 1)! for all integers n >= 1. For example, S3 = 4! = (4)(3)(2)(1). Which of the following is equivalent to the difference between S100 and S99?
(A) 101!
(B) 100!
(C) 99^2(98!)
(D) 100^2(99!)
(E) (100!)2
Rationale: According to this Symbolism question, we're asked to figure out S100 - S99. According to the description of the symbol in the question, we're asked to figure out:
101! - 100!
Both these terms have something in common: 100! so we can factor that out of each piece...
101! - 100!
100!(101 - 1)
Simplifying the parentheses, we get...
100!(100)
Unfortunately, THAT answer isn't listed. We've done the math correctly though, so all we can do is try to convert "our" answer into the format that appears in the answer choices...
100! = (100)(99!) so our answer can be rewritten as...
(100)(99!)(100)
Or....
(100^2)(99!)
ANSWER:D
Answer: (D) 100^2(99!)
Question: If books bought at prices ranging from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs 350, what is the greatest possible profit that might be made in selling 15 books ?
(A) Rs. 2500
(B) Rs. 3000
(C) Rs. 3500
(D) Rs. 3200
(E) Rs. 3600
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 15 books = 150*15 = Rs. 2,250
Maximum selling price of 15 books = 350 *15 = Rs. 5,250
So, maximum profit = 5250 - 2250 = Rs. 3,000
ANSWER : OPTION B
Answer: (B) Rs. 3000