mathewhe/aqua_rat huggingface dataset:
Question: A plane flies 720 km with the wind and 630 km against the wind in the same length of time. If the speed of the wind is 15 km/h, what is the speed of the plane in still air?
(A) 205 km/h
(B) 215 km/h
(C) 225 km/h
(D) 235 km/h
(E) 245 km/h
Rationale: The speed of the plane in still air = x km/h
The speed of the wind is 15 km/h
Speed with the wind = (x + 15) km/h
Speed against the wind = (x â€“ 15) km/h
Time = Distance/ Speed
720 / (x+15) = 630 / (x-15)
720(x-15) = 630(x+15)
72x - 1080 = 63x + 945
9x = 2025
x = 225
Therefore, the speed of the plane in still air is 225 km/h.
The answer is C.
Answer: (C) 225 km/h
Question: Amar takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Amar during the time the car covers 1.6 km?
(A) 328
(B) 288
(C) 2800
(D) 600
(E) 713
Rationale: Distance covered by Amar = 18/4.8 (1.6km)
= 3/8(1600)
= 600 m
Answer:D
Answer: (D) 600
Question: The sum of the digits of a two digit number is 7. When the digits are reversed then the number is decreased by 9. Then find the number
(A) 43
(B) 34
(C) 44
(D) 35
(E) 33
Rationale: Let the original no be 10x+y
Sum of the digits x+y=7
When the digits are reversed then it is 10y+x
Since it is decreased by 9 it is written as (10y+x)-(10x+y)=9 solving this we get y=4
Substitute in x+y=7 we get x=3
so the number is 34 correct ans is B
Answer: (B) 34
Question: Craig had 200 apples. He lost 20 apples and sold 43 apples. A customer returned one apple. How many apples did he have left?
(A) 137
(B) 138
(C) 135
(D) 140
(E) 139
Rationale: For lost, use negative. For gain, use positive.
200+-20+-43+1
correct answer is B)138
Answer: (B) 138
Question: The value of x is to be randomly selected from the integers from 1 to 8, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
(A) 1/4
(B) 1/8
(C) 1/2
(D) 3/8
(E) 5/8
Rationale: y will only be negative for x=2.
(We can check the values from 1 to 8 to be certain.)
P(y is negative) = 1/8
The answer is B.
Answer: (B) 1/8
Question: A man buy a book in Rs50 & sale it Rs70. What is the rate of profit ???
(A) 10%
(B) 40%
(C) 30%
(D) 25%
(E) 28%
Rationale: cp=50
sp=70
profit=70-50=20
%=20/50*100=40%
ANSWER:B
Answer: (B) 40%
Question: John starts his journey from A to B and Tom starts his journey from B to A at the same time.After passing each other they complete their journeys in 3 1/3 and 4 4/5 hours respectively.Find the speed of Tom if John traveled at 12 miles/hr.
(A) a) 8.33 m/hr
(B) b) 9 m/hr
(C) c) 10 m/hr
(D) d) 20 m/hr
(E) e)16.66 m/hr
Rationale: Your calculations look perfect, but I think they answer a different question from the one the question designer intended. I don't find the wording of this question to be good at all, but I'm pretty sure what they mean is this: from the point in time at which John and Tom meet, it takes a *further* 3 1/3 hours for John to complete his journey, and a *further* 4 4/5 hours for Tom to complete his journey. So if it takes them t hours to meet, John will end up traveling for a total of t + 10/3 hours, and Tom a total of t + 24/5 hours. That's a more difficult problem than the one you solved. I don't have time to write up a solution at the moment, but I can later if that would be helpful.
C)
Answer: (C) c) 10 m/hr
Question: find the number, difference between number and its 3/5 is 50.
(A) 120
(B) 123
(C) 124
(D) 125
(E) 126
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 50,
=> (2/5)x = 50 => 2x = 50*5,
=> x = 125
Answer: Option D
Answer: (D) 125
Question: A four digit number is such that the product of all of its digits is 126. The sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit (Thousand digit in tens place & ten digit in units place) which in turn is equal to 19. Then difference of units and thousand place of the number is, given that this difference is positive.
(A) 1692
(B) 1792
(C) 1795
(D) 1892
(E) 1992
Rationale: the number is 1792.
Let the number be represented as 1000x+100y+10z+t
acc to ques,
xyzt=126
x + y + z + t = 10x + z = 19
so, number in thousands and tens place are 1 and 9 respectively.
the remaining factor is 14 which is 7*2
So the number is 1792.
ANSWER:B
Answer: (B) 1792
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 115 hats in this group, how many of these hats are not blue?
(A) 28
(B) 42
(C) 48
(D) 80
(E) 76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=115 or 23x=115...here 7x,4x and 12x represent hats of each type
23x=115 so x=5...Blue hats =7*5=35...Not blue will be 115-35=80.
Ans D
Answer: (D) 80
Question: In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 15% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?
(A) 39%
(B) 45%
(C) 55%
(D) 65%
(E) 75%
Rationale: Setting up a matrix is how I solve this one.
Diploma No Diploma Totals
Job of Choice w/Diploma
Job of Choice w/o Diploma = 10%
Job of Choice Total = 40%
Not Job of Choice with Diploma =.15X
Not Job of Choice w/o Diploma= .85X
Total Not Job of Choice = X
Total with Diploma
Total without Diploma
Total citizen = 100
If 40% of people have their job of choice, then 60% of people do NOT have their job of choice. 15% of 60% = 9%. We can also see that 30% of the people have their job of choice and a diploma (40%-10%=30%). 30% + 9% = 39%. Therefore 39% of the people in Country Z have a diploma.
Ans A
Answer: (A) 39%
Question: if a person has to divide equally $13011 among all his 12 people then how much minimum should he keep with himself so that he divides equally among all 12 people in whole numbers?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $9
Rationale: He would need to keep $ 3 to himself so he can give $ 1084 to all 12 people so option C is correct one
Answer: (C) $3
Question: if 50% of (x-y) = 40% of (x+y) then what percent of x is y?
(A) 2.5%
(B) 11%
(C) 5%
(D) 15%
(E) 25%
Rationale: 50% of (x-y)=40% of(x+y)
(50/100)(x-y)=(40/100)(x+y)
5(x-y)=4(x+y)
x=9y
x=9y
therefore required percentage
=((y/x) X 100)% = ((y/9y) X 100) =11%
Answer is B.
Answer: (B) 11%
Question: After replacing an old member by a new member, it was found that the average age of eight members of a club is the same as it was two years ago.What is the difference between the ages of the replaced and the new member?
(A) 2 years
(B) 4 years
(C) 8 years
(D) 16 years
(E) None of these
Rationale: Explanation :
Age decreased = (8 x 2) years
16 years
So, required difference =16 years.
Answer : D
Answer: (D) 16 years
Question: Nine coins are tossed simultaneously. In how many of the outcomes will the first coin turn up a head?
(A) 2^8
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
Rationale: Fix the first coin as H. The remaining8 coins have 2^8 outcomes.
Ans:A
Answer: (A) 2^8
Question: In how many W 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 W=7!/ 3! * 1 = 840.
D
Answer: (D)  840
Question: A 600 meter long train crosses a signal post in 30 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
(A) 4 min
(B) 2 min
(C) 8 min
(D) 3 min
(E) 5 min
Rationale: S = 600/30 = 20 mps
S = 3600/20 = 180 sec = 4 min
Answer: D
Answer: (D) 3 min
Question: A student writes a computer program that generates a sequence of numbers a1, a2, a3, ... such that a1=a2=1 and ak=a(k-1)*4+1 for 2<k<n. If n=15, find a5.
(A) 85
(B) 87
(C) 89
(D) 93
(E) 95
Rationale: a1=1
a2=1
a3=1*4+1=5
a4=5*4+1=21
a5=21*4+1=84+1=85
85
Answer: (A) 85
Question: The original price of a car was $30,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 10%. After a week, the car had not sold, so the owner discounted the new price by 10%, and the car was finally sold. What price was the car sold for?
(A) $29,660
(B) $29,680
(C) $29,700
(D) $29,720
(E) $29,740
Rationale: The car was sold for (0.9)(1.1)($30,000)=$29,700.
The answer is C.
Answer: (C) $29,700
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
(A) 12
(B) 25
(C) 28
(D) 245
(E) 21
Rationale: 39x = 5 + 12 + 15 + 19 + (x – 4)44
x = 25
Answer: B
Answer: (B) 25
Question: Six children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 1440
(D) 4320
(E) 4800
Rationale: A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 600.
A is the right answer.
Answer: (A) 600
Question: A, B, C, D and E are 5 consecutive points on a straight line. If BC = 3CD, DE = 7, AB = 5 and AC = 11, what is the length of AE?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: AC = 11 and AB = 5, so BC = 6.
BC = 3CD so CD = 2.
The length of AE is AB+BC+CD+DE = 5+6+2+7 = 20
The answer is C.
Answer: (C) 20
Question: You hold some gold in a vault as an investment. Over the past year the price of gold increases by 52%. In order to keep your gold in the vault, you must pay 6% of the total value of the gold per year. What percentage has the value of your holdings changed by over the past year.
(A) 42.88$
(B) 43%
(C) 45%
(D) 45.5%
(E) 46.3%
Rationale: (100%+52%)*(100%-6%) = 152*0.94 = 142.88% an increase of 42.88%
Your gold holdings have increased in value by 42.88%.
The Answer is A
Answer: (A) 42.88$
Question: In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 720
(B) 1720
(C) 2880
(D) 6
(E) 10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6.
Answer: D.
Answer: (D) 6
Question: 5/8 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
(A) 28%
(B) 41%
(C) 45%
(D) 72%
(E) 68%
Rationale: Total population = 80 (assume).
5/8*80=50 people from Montague.
3/8*80=30 people from Capulet.
0.2*50=10 people from Montague support Juliet.
0.7*30=21 people from Capulet support Juliet.
The probability that a Juliet supporter chosen at random resides in Capulet is 21/(10+21)=~68.
Answer: E
Answer: (E) 68%
Question: A sum of Rs. 395 was divided among A, B, and C in such a way that B gets 25% more than A and 20% more than C. What is the share of A?
(A) Rs.195
(B) Rs.180
(C) Rs. 98
(D) Rs. 120
(E) Rs. 130
Rationale: Let each one’s share is A,B and C respectively, then
B =125A/100 = 120C/100
A =100B/125 =4/5B, C = 100B/120 = 5/6B
4/5B +B +5/6B =395, 79B/30 =395, B =395*30/79 =150
A = 4*150/5 = 120
ANSWER:D
Answer: (D) Rs. 120
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 50 players took part in that tournament.
How many matches were played?
(A) 99 matches.
(B) 88 matches.
(C) 49 matches.
(D) 66 matches.
(E) 55 matches.
Rationale: Solution:
49 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 49 matches were played.
Answer C
Answer: (C) 49 matches.
Question: Two cars start at the same time from A and B which are 120 km apart. If the two cars travel in opposite direction they meet after one hour and if they travel in same direction ( from A towards B) then A meets B after 6 hours. What is the speed of the car starting from A?
(A) 70 kmph
(B) 120 kmph
(C) 60 kmph
(D) Data Inadequate
(E) None of these
Rationale: Let, speed of car from A towards B = x km/hr
Let, speed of car from B towards A = y km/hr
Two cars start at same time which 120km apart = x + y = 120-----(i)
Travel in same direction, A meets B after 6hr = 6x-6y = 120-----(ii)
By Solving equation (i) and (ii), we get
12x = 840
x = 840/12
x = 70km/hr
Substituting x value in eqn (i) or (ii), we get
y = 50km/hr
So, speed of car starting from 70kmph.
ANSWER:A
Answer: (A) 70 kmph
Question: The profit obtained by selling an article for Rs. 57 is the same as the loss obtained by selling it for Rs. 43. What is the cost price of the article?
(A) Rs. 40
(B) Rs. 50
(C) Rs. 49
(D) Rs. 59
(E) None of these
Rationale: S.P 1- C.P = C.P – S.P 2
57 - C.P = C.P - 43
2 C.P = 57 + 43;
C.P = 100/2 = 50
ANSWER:B
Answer: (B) Rs. 50
Question: Ram professes to sell his goods at the cost price but he made use of 925 grms instead of a kg, what is the gain percent?
(A) 2 9/13%
(B) 7 9/13%
(C) 3 9/13%
(D) 4 9/13%
(E) 5 9/13%
Rationale: 925 --- 75
75 --- ? =>
=75/925 *100= 7 9/13%
Answer: B
Answer: (B) 7 9/13%
Question: Two men Amar and Bhuvan have the ratio of their monthly incomes as 6 : 5. The ratio of their monthly expenditures is 3 : 2. If Bhuvan saves one-fourth of his income, find the ratio of their monthly savings?
A. 3 : 5
(A) 3:9
(B) 3:10
(C) 3:21
(D) 3:12
(E) 3:14
Rationale: Let the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.
Let the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.
Savings of Bhuvan every month = 1/4(5x)
= (His income) - (His expenditure) = 5x - 2y.
=> 5x = 20x - 8y => y = 15x/8.
Ratio of savings of Amar and Bhuvan
= 6x - 3y : 1/4(5x) = 6x - 3(15x/8) : 5x/4 = 3x/8 : 5x/4
= 3 : 10.
Answer: Option B
Answer: (B) 3:10
Question: The total of a company's assets in 1994 was 200% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
(A) 5N
(B) 7N
(C) 10N
(D) 15N
(E) 20
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 4N = 5N.
In 1994, the company's assets were 5N + 10N = 15N.
The answer is D.
Answer: (D) 15N
Question: Three men rent a pasture for Rs. 660. The first used it for 50 sheep for 4 months, the 2nd for 40 sheep for 3 months and the 3rd for 46 sheep for 5 months. How much should the first pay ?
(A) Rs. 220
(B) Rs. 235
(C) Rs. 240
(D) Rs. 276
(E) Rs. 286
Rationale: The payment should be in ratio of 200:120:230 or 20:12:23
First person should pay 20*660/55 = 240 Rs.
ANSWER:D
Answer: (D) Rs. 276
Question: In how many ways can 5 boys and 2 girls be seated on 8 chairs so that no two girls are together?
(A) 5760
(B) 14400
(C) 480
(D) 5670
(E) 40320
Rationale: Let us take opposite of the constraint.
2 girls sitting together:	:
1 case is GGBGBBBB.
Total number of ways=3!*5!*5 with just shifting the rightmost girl.
Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.
So total number of ways = 3!*5!(5+4+3+2+1)=120*90=10800
Similarly another case is:
GBGGBBBB.
Using the above reasoning, the total number of cases is: 3!*5!*(15) =10800
Let us take 3 girls sitting together
GGGBBBBB
There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways
So total is 2*10800 + 4320=25920
The total number of possibilities = 8! Ways =40,320
Answer is 40320-25920=5670
Hence D.
Answer: (D) 5670
Question: Find the average of the series : 312, 162, 132, 142 and 122?
(A) 178
(B) 172
(C) 128
(D) 107
(E) 174
Rationale: Average
= (312 + 162 + 132 + 142 + 122)/5
= 870/5 = 174
Answer: E
Answer: (E) 174
Question: In how many ways can the letters of the word 'LEADER' be arranged?
(A) 739
(B) 73
(C) 360
(D) 840
(E) 849
Rationale: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =6!/(1!)(2!)(1!)(1!)(1!)= 360.
Answer:C
Answer: (C) 360
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 100 m
(B) 150 m
(C) 190 m
(D) 200 m
(E) None of these
Rationale: Explanation:
Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr
Distance covered in 6 minutes = (1/60 × 6) km = 1/10 km = 100 m
∴ Distance between the thief and policeman = (200 – 100) m = 100 m.
Answer: A
Answer: (A) 100 m
Question: If 21520 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
(A) 9 books
(B) 8 books
(C) 1 book
(D) 4 books
(E) 5 books
Rationale: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 21520.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 21520 = 10 and 9 is divisible by 9.
Hence, we need to remove 1 to this number for it to be divisible by 9
Correct Option: C
Answer: (C) 1 book
Question: How many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 27 sec
(B) 23 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec
Rationale: D = 120 + 150 = 270
S = 36 * 5/18 = 10 mps
T = 270/10 = 27 sec
A
Answer: (A) 27 sec
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 167
(B) 240
(C) 881
(D) 278
(E) 123
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: (B) 240
Question: 287 x 287 + 269 x 269 - 2 x 287 x 269 = ?
(A) 466
(B) 646
(C) 666
(D) 324
(E) 333
Rationale: Given Exp.	= a2 + b2 - 2ab, where a = 287 and b = 269
= (a - b)2 = (287 - 269)2
= (182)
= 324
Correct Option is D
Answer: (D) 324
Question: If Re.100 amounts to Rs.300 over a period of 10 years. What is the rate of simple interest?
(A) 20%
(B) 30%
(C) 15%
(D) 10%
(E) 12%
Rationale: 200 = (100*10*R)/100
R = 20%
Answer:A
Answer: (A) 20%
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder G when N is divided by 30?
(A) (a) 4
(B) (b) 7
(C) (c) 11
(D) (d) 13
(E) (e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder G when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: (C) (c) 11
Question: A recycling facility is staffed by 12 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/11 of all wages paid at the facility, what is the value of n?
(A) 1.1
(B) 2.1
(C) 2.2
(D) 2.3
(E) 2.4
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 12x+xn and we are told that it equals to 11xn:
11x+xn=11xn --> reduce by x: 11+n=11n -->10n=11
n = 11/10 = 1.1
Answer: A
Answer: (A) 1.1
Question: 8th Dec 2007 was Saturday, what day of the week was it on 8th Dec, 2006?
(A) Sunday
(B) Tuesday
(C) Friday
(D) Tuesday
(E) Monday
Rationale: Given that 8th Dec 2007 was Saturday
Number of days from 8th Dec, 2006 to 7th Dec 2007 = 365 days
365 days = 1 odd day
Hence 8th Dec 2006 was = (Saturday - 1 odd day) = Friday
Correct answer is Friday
Answer: (C) Friday
Question: Rahul went to a shop and bought things worth Rs. 27, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19.7
(B) 20
(C) 22
(D) 20.4
(E) 21.7
Rationale: Total cost of the items he purchased = Rs.27
Given that out of this Rs.27, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (27−30/100−x)6/100 = 30/100
⇒ 6(27 −0.3 −x) = 30
⇒ (27 − 0.3 − x) = 5
⇒ x = 27 − 0.3 − 5 = 21.7
E
Answer: (E) 21.7
Question: In a school with 5 classes, each class has 2 students less than the previous class. How many students are there in the largest class if the total number of students at school is 115?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Rationale: Let x be the number of students in the largest class.
Then x + (x-2) + (x-4) + (x-6) + (x-8) = 115
5x - 20 = 115
5x = 135
x = 27
The answer is C.
Answer: (C) 27
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 44
(B) 58
(C) 74
(D) 12
(E) 23
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer:A
Answer: (A) 44
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 1:2
(B) 1:3
(C) 3:1
(D) 1:5
(E) 1:4
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/2 + 7/2 = 6 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 6 : 2 = 3:1.
Answer:C
Answer: (C) 3:1
Question: If the digits 35 in the decimal 0.00035 repeat indefinitely, what is the value of (10^5-10^3)(0.00035)?
(A) 37
(B) 41
(C) 3.5e-05
(D) 35
(E) 3.5e-07
Rationale: 99*0.35=34.65 approx. 35
Answer : B
Answer: (B) 41
Question: Coins are to be put into 10 pockets so that each pocket contains at least one coin. At most 6 of the pockets are to contain the same number of coins, and no two of the remaining pockets are to contain an equal number of coins. What is the least possible number of coins needed for the pockets?
(A) 7
(B) 13
(C) 20
(D) 22
(E) 28
Rationale: Since at most 6 of the pockets are to contain the same number of coins then minimize # of coins in each, so let each contain just 1 coin;
Next, we are told that no two of the remaining 4 pockets should contain an equal number of coins, so they should contain 2, 3, 4, and 5 coins each (also minimum possible);
Total: 1+1+1+1+1+1+2+3+4+5=20
Answer: C.
Answer: (C) 20
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1
(B) 2
(C) 3
(D) 7
(E) 5
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph Answer:A
Answer: (A) 1
Question: If a = 2, what is the value of –(a^2 + a^3 + a^4 + a^5)?
(A) -14
(B) -60
(C) 0
(D) 4
(E) 14
Rationale: if a = -1, then putting values in equation
= -[ (2)^2 + (2)^3 + (2^4) + (2^5) ]
= -[ 4 + 8 + 16 + 32 ]
= -60
Answer = B = -60
Answer: (B) -60