mathewhe/aqua_rat huggingface dataset:
Question: If 48 men can do a piece of work in 25 hours, in how many hours will 15 men
do it ?
(A) 80 hours
(B) 75 hours
(C) 70 hours
(D) 65 hours
(E) 60 hours
Rationale: Let the required number of hours be x. Then,
Less men, More hours	(Indirect Proportion)
15 : 48 : : 25 : x<=>(15 x x) =(48 x 25)<=>(48 x 25)/15 = 80
Hence, 15 men can do it in 60 hours
Answer is A.
Answer: (A) 80 hours
Question: Two boats are heading towards each other at constant speeds of 3 miles/hr and 21 miles/hr respectively. They begin at a distance 20 miles from each other. How far are they (in miles) one minute before they collide ?
(A) 1/12
(B) 5/12
(C) 1/6
(D) 1/3
(E) 3/15
Rationale: The question asks: how far apart will they be 1 minute=1/60 hours before they collide?
Since the combined rate of the boats is 3+21=24 mph then 1/60 hours before they collide they'll be rate*time=distance --> 24*1/60=3/15 miles apart.
Answer: E.
Answer: (E) 3/15
Question: There are 250men and 150 women in a committee, if all will work they will complete 12 units per day, if all men work they will complete 15 units per day, how many units will women complete per day?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: I think there is a mistake in this question. If all men and women together complete 12 units, how only men can do 15 Units of work a day?
Forgetting about the reality, Women can do -3 units a day.
Answer:	B
Answer: (B) 3
Question: If A is thrice as fast as B and together can do a work in 18 days. In how many days A alone can do the work?
(A) 36
(B) 42
(C) 24
(D) 54
(E) 45
Rationale: A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/18
= 3+1/3x = 4/3x = 1/18
x = 18*4/3 = 24
ANSWER:C
Answer: (C) 24
Question: In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?
(A) 4236
(B) 4306
(C) 4336
(D) 5336
(E) None of these
Rationale: Divisor = (5 x 46) = 230
10 x Quotient = 230 =	230/10= 23
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
Answer :D
Answer: (D) 5336
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 2 ½ hours if they are walking in the same direction?
(A) 7 km
(B) 6 km
(C) 3 1/8 km
(D) 9 km
(E) 5 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 2 ½ h.
D = 5/4 * 5/2 = 25/8
= 3 1/8 km
Answer:C
Answer: (C) 3 1/8 km
Question: Kelly and Jody packed boxes with books. If Jody packed 40% of the total number of boxes, what was the ratio of the number of boxes Kelly packed to the number that Jody packed?
(A) 1 to 6
(B) 1 to 4
(C) 2 to 5
(D) 3 to 5
(E) 3 to 2
Rationale: Explanation:
If Jody packed 40% of the boxes then Kelly packed 60%. The ratio of the number of boxes Kelly packed to the number Jody packed is thus 60%/40%=3/2
Answer: Option E
Answer: (E) 3 to 2
Question: How many 1/8's are there in 371/2 ?
(A) 1384
(B) 1484
(C) 1584
(D) 1684
(E) 1784
Rationale: no of 1/8 's in 371/2 = (371/2)/(1/8)= 8*371/2= 371*4= 1484
ANSWER:B
Answer: (B) 1484
Question: Three candidates contested an election and received 1136, 7636 and 14628 votes respectively. What percentage of the total votes did the winning candidate got?
(A) 55%
(B) 56%
(C) 62.5%
(D) 58%
(E) 59%
Rationale: Total number of votes polled = (1136 + 7636 + 14628) = 23400
So, Required percentage = 14628/23400 * 100 = 62.5%
ANSWER : C
Answer: (C) 62.5%
Question: what is the least number by which 2,100 must be divided to get a number perfect square
(A) 21
(B) 42
(C) 24
(D) 40
(E) 45
Rationale: 2,100/21=100
100=(10)^2
Ans-21
ANSWER:A
Answer: (A) 21
Question: Rick deposited $750 to his bank account using $5 and $15 dollar bills only. If Rick came to the bank with 70 bills and left with 10 bills only, how many $15 dollar billsმ did he deposit?
(A) 5.
(B) 45.
(C) 50.
(D) 55.
(E) 65.
Rationale: 5x+15y=750 --1
x+y=60 ---2
multiply eq 2 with 5 and subtract from eq 1
5x+15y=750
5x+5y=300
10y= 450
y=45 and x = 15
therefore $15 bills = 45
Answer B
Answer: (B) 45.
Question: Find large number from below question The difference of two numbers is 1390. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1245
(B) 1345
(C) 1455
(D) 1577
(E) 1665
Rationale: Let the smaller number be x. Then larger number = (x + 1390).
x + 1390 = 6x + 15
5x = 1375
x = 275
Large number = 275+1390 = 1665
E
Answer: (E) 1665
Question: 10 litres of water are poured into an aquarium of dimensions 50cm length, 20cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm³)
(A) 6
(B) 8
(C) 10
(D) 20
(E) 40
Rationale: lXbXh= 10000
h= 10000/50*20= 10 cm
'C' is the answer.
Answer: (C) 10
Question: The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination
(A) 12 years 8 month
(B) 13 years
(C) 14 years 8 month
(D) 15 years 7 month
(E) 16 years 9 month
Rationale: (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy = 18 years – 3 years 4 month
= 14 years 8 month
C
Answer: (C) 14 years 8 month
Question: What is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477
(A) 85
(B) 84
(C) 86
(D) 87
(E) 99
Rationale: Explanation :
W = (1.5)11
Take log both sides:
=> logW = 11 x log(1.5) =11 x log(3/2)
=> logW = 11 x (log3 - log2) = 11 x 0.176 = 1.936
=> W = 101.936
=> W = 86 (approx)
Answer : C
Answer: (C) 86
Question: Jane had an average of 87 on his first 7 tests. She had an average score of 90 on her first 6 tests. What did he score on the 7th test?
(A) 69
(B) 75
(C) 90
(D) 86
(E) 50
Rationale: The sum of Jane's first 7 scores is 7 Â· 87 and the sum of her first 6 scores is 6 Â· 90, so she received
7 Â· 87 âˆ’ 6 Â· 90 on her 7th quiz. You can do the arithmetic or notice that the answer ends in a 9. The correct answer is A.
Answer: (A) 69
Question: Find the remainder when 6^23 is divided by 5 ?
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
Rationale: 6^23 = 6^(4*5+3) = 6^(20) * 6^3 last 3 digits = 216
216/5 remainder = 1
ANSWER:C
Answer: (C) 1
Question: 60 percent of movie theatres in Town X have 3 screens or less. 20% of those theatres sell an average of more than $300 worth of popcorn per showing. 50 percent of all the movie theatres in Town X sell $300 or less of popcorn per showing. What percent of all the stores on the street have 4 or more screens and sell an average of more than $300 worth of popcorn per day?
(A) 12
(B) 18
(C) 32
(D) 40
(E) 44
Rationale: Lets take numbers here.
Assume that the total number of movie theaters in the town = 100
Then number of movie theaters with 3 screens or less = 60
=> Number of movie theaters with 4 screens or more = 40
Movie theaters with 3 screens or less selling popcorn at more than $300 = 20% of 60 = 12
Number of movie theaters selling popcorn at $300 or less = 56
=> Number of movie theaters selling popcorn at more than $300 = 100-56 = 44
Of these 44 theaters, 12 are those with 3 screens or less
Therefore 44 (44-12) must be those with four screens or more
E is the answer
Answer: (E) 44
Question: Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 16 is 6?
(A) 168
(B) 172
(C) 170
(D) 174
(E) 176
Rationale: First we need to figure out what numbers are exactly divisible by 7,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(7,12,16) = 48*7 = 336
The numbers which will leave remainder 6 will be {336+6, 336x2 +6, 336x3 +6,...}
The largest such number less than or equal to 1856 is 336x5+6 or 1686
To obtain this you need to subtract 170.
C
Answer: (C) 170
Question: There are 40 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
(A) 780
(B) 667
(C) 661
(D) 297
(E) 261
Rationale: Explanation:
Total number of persons = n = 40
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 40C2
40C2 = (40 * 39) /(2 * 1) = 780
ANSWER:A
Answer: (A) 780
Question: A and B invests Rs.10000 each, A investing for 9 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.21000, find their shares?
(A) 1300,1500
(B) 9000,12000
(C) 7290,8000
(D) 15000,12000
(E) 72821,75000
Rationale: The ratio of their profits A:B = 9:12 = 3:4
Share of A in the total profit = 3/7 * 21000 = Rs.9000
Share of B in the total profit = 4/7 * 21000 = Rs.12000
Answer:B
Answer: (B) 9000,12000
Question: A can do a piece of work in 3days of 8 hours each and B alone can do it in 4 days of 9 hours each.how long will they take it to do working together
7 1/5 hours a day?
(A) 3 days
(B) 2 days
(C) 5 days
(D) 7 days
(E) 4 days
Rationale: A's work per hour=1/24
B's work per hour=1/36
A & B's work per hour together=(1/24)+(1/36)=5/72
so A & B together complete the work in 72/5 hours...
if they work 7 1/5=36/5 hours a day,
it will take (72/5)/(36/5) days=2 days...
ANSWER:B
ANSWER:B
Answer: (B) 2 days
Question: If n > 0 , which of the following must be true?
I n^2 > 1
II	n - n^2 < 0
III	2n - 1 < 0
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) none
Rationale: I. True for all values of n except 1
When n = 1 ; n^2 = 1
II. True for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III	false for all values of n
Hence the correct answer will be (D)
Answer: (D) I and II only
Question: What value of K gives the equation,3k-2=2k-1?
(A) ONE
(B) TWO
(C) THREE
(D) FOUR
(E) NONE
Rationale: 3k-2=2k-1
If k=1
3(1)-2=2(1)-1
3-2=2-1
1=1
Option A is answer
Answer: (A) ONE
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
(A) 99
(B) 88
(C) 77
(D) 55
(E) 22
Rationale: Answer: Option A
Explanation:
30 * 33/2 = 5/2 * 2 * x => x = 99
Answer: A
Answer: (A) 99
Question: The average temperature for Tuesday, Wednesday and Thursday was 42°C. The average temperature for Wednesday, Thursday and Friday was 44°C. If the temperature on Friday be 43°C, what was the Temperature on Tuesday?
(A) 39°C
(B) 44°C
(C) 37°C
(D) 42°C
(E) None of these
Rationale: Explanation:
T + W + T = 42 × 3 = 126°C
W+ T+ F = 44 × 3 = 132°C
Also, temperature on Friday = 43°C
Temperature on Tuesday = 126 +43 - 132 = 37°C
Answer: Option C
Answer: (C) 37°C
Question: A trader has 40 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
(A) 4 and 36 kg
(B) 10 and 40 kg
(C) 15 and 35 kg
(D) 20 and 30 kg
(E) 40 and 30 kg
Rationale: Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 40/1+9 *1 = 4 kg
Quantity sold at 6% loss = 40/1+9 *9 = 36kg
ANSWER:A
Answer: (A) 4 and 36 kg
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 9 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.4538
(B) s.8154
(C) s.4518
(D) s.4530
(E) s.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 9 = Rs.8154
Answer: B
Answer: (B) s.8154
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
(A) 10
(B) 15
(C) 30
(D) 34
(E) 36
Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
C
Answer: (C) 30
Question: Divide $672 among A,B in the ratio 5:3. How many $ that A get?
(A) $120
(B) $500
(C) $420
(D) $610
(E) $315
Rationale: Sum of ratio terms = 5+3 = 8
A = 672*5/8 = $420
Answer is C
Answer: (C) $420
Question: P alone can complete a job in 5 days. The work done by Q alone in one day is equal to one-fourth 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) 2.5
(B) 3.0
(C) 3.5
(D) 4.0
(E) 4.5
Rationale: P's rate is 1/5
Q's rate is 1/20
The combined rate is 1/5 + 1/20 = 1/4
If they work together, the job will take 4 days.
The answer is D.
Answer: (D) 4.0
Question: Find the compound ratio of (2:3), (5:11) and (11:2) is
(A) 3:2
(B) 2:1
(C) 1:2
(D) 4:5
(E) 5:3
Rationale: Required ratio = 2/3 * 5/11 * 11/2 = 2/1 = 5:3
Answer is E
Answer: (E) 5:3
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) 28999
(B) 27888
(C) 27838
(D) 59000
(E) 28992
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer: D
Answer: (D) 59000
Question: How many seven-digit numbers that do not contain the digits 2 or 9 are there?
(A) 178546
(B) 44786544
(C) 435786
(D) 1599678
(E) 1835008
Rationale: We can have 7 digits ( 1,3,4,5,6,7,8) for the first place ( million's place).
and similarly 8 digits for hundred thousands, ten thousands, thousands, hundred's, tenth's and unit digit. ( 0,1,3,4,5,6,7,8)
So in total 7*8*8*8*8*8*8= 1835008
Hence E
Answer: (E) 1835008
Question: A salesman's income consists of a commission and a base salary of $370 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
(A) $150
(B) $345
(C) $365
(D) $715
(E) $730
Rationale: Total weekly income over 5 weeks=$406+$413+$420+$436+$395=$2070
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2070=$1430
From this, we subtract base salary for 2 weeks i.e $370*2=$740
Therefore, commission=$1430-$740=$690 for 2 weeks
Avg weekly commission=$345
Answer B
Answer: (B) $345
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 60 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
(A)  80%
(B)  32%
(C)  48%
(D)  84%
(E)  92%
Rationale: This is easiest to solve with a bell-curve histogram. m here is equal to µ in the Gaussian normal distribution and thus m = 50% of the total population.
So, if 60% is one st.Dev, then on either side of m we have 60/2 = 30%. So, 30% are to the right and left of m (= 50%). In other words, our value m + d = 50 + 30 = 80% goingfrom the mean m, to the right of the distributionin the bell shaped histogram.. This means that 80% of the values are below m + d.
Like I said, doing it on a bell-curve histogram is much easier to fullygethow this works, or you could apply GMAT percentile jargon/theory to it
A
Answer: (A)  80%
Question: If the average ages of three groups of 30, 40, 50 people respectively is 30,40,50 what is the average ages of all the people?
(A) 23.78
(B) 41.66
(C) 34.67
(D) 23.9
(E) 43.98
Rationale: Average ages of group 1 =30
people in group 1 = 30
Total ages of group 1 = 30*30
Average ages of group 2 = 40
people in group 2 = 40
Total ages of group 2 = 40*40
Average ages of group 3 = 50
people in group 3 = 50
Total ages of group 3 = 50*50
Total people = 40 + 30 + 50 = 120
Average ages of all the people
=((40*40)+(50×50)+(30×30))/120
=125/3
=41.66
Answer is B.
Answer: (B) 41.66
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
(A) 17/22
(B) 17/25
(C) 17/21
(D) 17/91
(E) 17/12
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer:B
Answer: (B) 17/25
Question: If a large pizza has a radius that is 50% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
(A) 25%
(B) 50%
(C) 75%
(D) 125%
(E) 150%
Rationale: Let the radius of medium pizza be r. Then the radius of large pizza is 1.5r.
The area of the medium pizza is pi*r^2
The area of the large pizza is pi*(1.5*r)^2 = 2.25*pi*r^2, an increase of 125%.
The answer is D.
Answer: (D) 125%
Question: Raju age before 5 years will be 2 times his age 5 years back, What is the present age of Raju
(A) 9 years
(B) 8 years
(C) 5 years
(D) 6 years
(E) 7 years
Rationale: Explanation:
Clearly,
x-5 = 2(x-5)
=> x = 5
Option C
Answer: (C) 5 years
Question: If integers c and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. cb + b^2
II. (c + b)^2
III. c + b
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. cb + b^2 --> if c=1 and b=2 then cb + b^2=6, which is a factor of 30. OK;
II. c + b)^2 --> (c + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. c + b --> if c=1 and b=2 then c + b=3, which is a factor of 30. OK.
Answer: B.
Answer: (B) II only
Question: A train 165 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
(A) 9 sec
(B) 6 sec
(C) 7 sec
(D) 10 sec
(E) None
Rationale: Solution
Speed of train relative to man =(60+6) km/hr= 66km/hr
=(66x5/18) m/sec =(55/3) m/sec
∴ Time taken to pass the man = (165x3/55)sec = 9 sec
Answer A
Answer: (A) 9 sec
Question: A letter lock consists of five rings each marked with four different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
(A) 3177
(B) 3124
(C) 3215
(D) 168
(E) 167
Rationale: Since each ring consists of four different letters, the total number of attempts possible with the five rings is
= 5 * 5 * 5 * 5 *5 = 3125. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 3125- 1
= 3124.
Answer: C
Answer: (C) 3215
Question: A soft drink company had 6000 small and 15000 big bottles in storage. If 12% of small 14% of big bottles have been sold, then the total bottles remaining in storage is
(A) 15360
(B) 16010
(C) 18180
(D) 14930
(E) 16075
Rationale: 6000 + 15000 - (0.12*6000 + 0.14*15000) = 18180.
Answer: C.
Answer: (C) 18180
Question: A dog has 15 bones, then he finds 8 more bones. Now how many bones does he have.
(A) A) 7
(B) B) 27
(C) C) 23
(D) D) 19
(E) E) 21
Rationale: 15 + 8 = 23. Answer is C.
Answer: (C) C) 23
Question: Car Dealership X, the total profit from sales increased by 30 percent over the previous years, while the number of cars sold decreased by 30 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
(A) 18%
(B) 30%
(C) 52%
(D) 63%
(E) 85.71%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.3x / 0.7 y = 13/7 (x/y)
Increase in profit per car = ((6/7) (x/y)) / (x/y) * 100 = 85.71%
Answer = E
Answer: (E) 85.71%
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 46 years, was replaced by a new person. Find the age of the new person?
(A) 18
(B) 56
(C) 16
(D) 17
(E) 14
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average
= (P-3) 10(P-3)
= 10P - 46 + Q
=> Q = 16
Answer:C
Answer: (C) 16
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score
did he make by running between the wickets
(A) 40%
(B) 50%
(C) 60%
(D) 70%
(E) None of these
Rationale: Explanation:
Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
Answer: Option B
Answer: (B) 50%
Question: In a race of 150 m, A gives B a start of 20 m. What distance will be covered by B ?
(A) 100 m
(B) 130 m
(C) 170 m
(D) 160 m
(E) 180 m
Rationale: Required distance = (150 - 20) m = 130 m
Answer :B
Answer: (B) 130 m
Question: A train 285 m long, running with a speed of 54 km / hr will pass a tree in
(A) 19 sec
(B) 15 sec
(C) 16 sec
(D) 20 sec
(E) None
Rationale: Sol.
Speed = (54 x 5/18) m/sec.
= 15 m / sec.
Time taken = (285 x 1/15) sec = 19 sec
Answer A
Answer: (A) 19 sec
Question: A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 6 years ago?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Let's say
Age of Richard is "R"
Age of David is "D"
Age of Scott is "S"
Now
Richard is 6 years older than David,
i.e. R = D +6
David is 8 years older than Scott
i.e. D = S +8
If in 8 years, Richard will be twice as old as Scott
i.e. R+8 = 2x(S+8)
i.e. R+8 = 2S + 16
i.e. R = 2S+8
But R = D+6 = (S+8)+6 = S+14
therefore, 2S + 8 = S +14
i.e. S = 6
i.e. R = 20
i.e. D = 14
Now,
how old was David 6 years ago?
i.e. D-6 = 14-6 = 8 years
ANSWER:A
Answer: (A) 8
Question: A cricketer scored 132 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
(A) 46.2%
(B) 54.54 %
(C) 63%
(D) 70%
(E) None of these
Rationale: Explanation :
Number of runs made by running = 132 - (12 x 4 + 2 x 6)
= 132 - (60)
= 72
Now, we need to calculate 72 is what percent of 132.
=> 72/132 * 100 = 54.54 %
Answer : B
Answer: (B) 54.54 %
Question: the ratio of type of pen and type of notebook is 5:4.and in 80 ways one can start writing.tell me the no. of pen and no. of notebook.
(A) 6,12
(B) 10,6
(C) 10,8
(D) 8,4
(E) 6,8
Rationale: let the ratio constant be x.
no. of pen=5x,no. of notebook =4x.
total no. of ways of start writing=5x*4x=20(square of x)=80
x=âˆš4=2
pen=10,notebook=8
answer C
Answer: (C) 10,8
Question: A train 150 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 5 sec
(B) 9 sec
(C) 12 sec
(D) 18 sec
(E) 15 sec
Rationale: Answer : B.
Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 150 m at 50/3 m / sec = 150 *3/ 50 sec = 9sec
Answer: (B) 9 sec
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 13 years and that of the other 9 students is 16 years, The age of the 15th student is
(A) 11
(B) 16
(C) 13
(D) 14
(E) 15
Rationale: Explanation:
Age of the 15th student = [15 * 15 - (13 * 5 + 16 * 9)] = 16 years. Answer: B
Answer: (B) 16
Question: What is the average of the first 10 multiples of 11?
(A) 55.5
(B) 61.5
(C) 53.5
(D) 78.5
(E) 60.5
Rationale: (11 + 22 + ... + 110)/10
=11(1 + 2 + ... + 10)/10
=11(10)(11)/(10*2)
=121/2
=60.5
Option E
Answer: (E) 60.5
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 110 miles per hour, while the slower train travels at 100 miles per hour. At 1 o’clock the faster train is 40 miles behind the slower one. How far apart are the two trains at 7 o'clock?
(A) 20 miles
(B) 80 miles
(C) 90 miles
(D) 120 miles
(E) 400 miles
Rationale: Answer = A. 20 miles
Relational speed = 110 - 100 = 10 miles per hour
In 6 hours, difference = 10 * 6 = 60 miles
Fast train trailing 40 miles, so effective difference = 60 - 40 = 20 miles
Answer: (A) 20 miles