mathewhe/aqua_rat huggingface dataset:
Question: A man cycled 25 kilometer in 1 hour 40 minutes. what was the average speed of cylcle in kilometer per hour?
(A) 7 miles / hour
(B) 9 miles / hour
(C) 10 miles / hour
(D) 13 miles / hour
(E) 15 miles / hour
Rationale: We first convert the time of 1 hours 10 minutes in minutes
1 hours 10 minutes = 1* 60 + 40 = 100 minutes
Average speed S is given by distance / time. Hence
S = 25 miles / 100 minutes = 0.25 mile / minute
= 15 miles / hour
correct answer E
Answer: (E) 15 miles / hour
Question: Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
(A) 10
(B) 25
(C) 12
(D) 20
(E) 30
Rationale: Explanation:
Speed of train 1 = 12 m/sec
Speed of train 2 = 8 m/sec
if they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec
distance covered = 120 + 120 = 240 m
time = distance/speed = 240/20 = 12 sec
ANSWER IS C
Answer: (C) 12
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
(A) 36
(B) 56
(C) 65
(D) 75
(E) 35
Rationale: (3x-9):(5x-9) = 9:17
x = 12 => 3x = 36
Answer:A
Answer: (A) 36
Question: A man swims downstream 18 km and upstream 12 km taking 3 hours each time, what is the speed of the man in still water?
(A) 3
(B) 5
(C) 6
(D) 4
(E) 8
Rationale: 18 --- 3 DS = 6
? ---- 1
12 ---- 3 US =4
? ---- 1 M = ?
M = (6+4)/2 = 5
Answer: B
Answer: (B) 5
Question: Find the number such that when 15 is subtracted from 7 times the number,the result is 10 more than twice the number?
(A) 4
(B) 3
(C) 5
(D) 2
(E) 6
Rationale: Let the number be x.
7x-15=2x+10
7x-2x=15+10
5x=25
x=5
answer is option C
Answer: (C) 5
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 1/13
(B) 2/21
(C) 5/26
(D) 3/25
(E) 3/28
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: A train sets off at 9:00 am at the speed of 70 km/h. Another train starts at 9:30 am in the same direction at the rate of 80 km/h. At what time will the second train catch the first train?
(A) 12:30
(B) 1:00
(C) 1:30
(D) 2:00
(E) 2:30
Rationale: In thirty minutes the first train travels 35 km.
The second train catches the first train at a rate of 80 km/h - 70 km/h = 10 km/h.
The second train will catch the first train in 35/10 = 3.5 hours, so at 1:00 pm.
The answer is B.
Answer: (B) 1:00
Question: A 250 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train?
(A) 228
(B) 108
(C) 1266
(D) 75
(E) 211
Rationale: S = 250/12 * 18/5 = 75kmph
Answer: D
Answer: (D) 75
Question: While flying over the Pacific, an airplane makes a 25° turn to the right to avoid a storm. If, as a result, the airplane is traveling in a direction 15° east of north, in what direction was it originally flying?
(A) (a) 30° west of north
(B) (b) 30° east of north
(C) (c) 10° west of north
(D) (d) 10° east of north
(E) (e) 5° west of north
Rationale: If after a turn of 25° you are 15°NEast, with a 10° turn you would be perfectly pointing at north. So you were, before the turn, 10° to the other side (West).
Answer C)
Answer: (C) (c) 10° west of north
Question: A can do a piece of work in 30 days while B can do it in 40 days. In how many days will they finish it together?
(A) 120/7
(B) 95/8
(C) 123/9
(D) 150/7
(E) None
Rationale: 1/30 + 1/40 = 7/120
Both can finish the work in 120/7 days
Answer: A
Answer: (A) 120/7
Question: Robert's salary was decreased by 70% and subsequently increased by 70%. how much percentage does he lose?
(A) 10%
(B) 20%
(C) 25%
(D) 30%
(E) 49%
Rationale: let original salary be $100
Salary after decreasing 70% = 100 - 100 x 70/100 = $30
Salary after increasing 70% on $30 = 30 + 30 x 70/100 = $51
Percentage of loss = 100 - 51 = 49%
Answer : E
Answer: (E) 49%
Question: Tough and Tricky questions: Remainders.
1^1 + 2^2 + 3^3 + ... + 6^6 is divided by 5. What is the remainder?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: a number is divisible by 5, if its last digit is divisible by 5
let's look into the sum of last digits of each term of the given expression
1^1=1
2^2=4
3^3=7
4^4=6
5^5=5
6^6=6
adding all these numbers we get 29 which gives a remainder of 4 when divided by 5. so answer must be 4.
bunuel, can you please confirm the answer of this question.
Yes, the OA is C. Clicked the wrong button when posting. Edited. Thank you.
E
Answer: (E) 4
Question: A work can be finished in 30 days by 30 women. The same work can be finished in fifteen days by 15 men. The ratio between the capacity of a man and a woman is
(A) 1:3
(B) 4:3
(C) 2:3
(D) 4:1
(E) 2:4
Rationale: Work done by 30 women in 1 day = 1/30
Work done by 1 woman in 1 day = 1/(30×30)
Work done by 15 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×15)
Ratio of the capacity of a man and woman =1/(15×15) : 1/(30×30)) = 1/225 : 1/900
= 1/1 :1/4 = 4:1
Option D
Answer: (D) 4:1
Question: Simplfy
b - [b -(a+b) - {b - (b - a+b)} + a]
(A) a
(B) 2a
(C) 4a
(D) 0
(E) 1
Rationale: Explanation:
b-[b-(a+b)-{b-(b-a+b)}+a]
=b-[b-a-b-{b-(2b-a)}+a]
=b-[-a-{b-2b+a}+a]
=b-[-a-{-b+a}+a]
=b-[-a+b-a+a]
=b-[-2a+b+a]
=b-b+a
=a
Option A
Answer: (A) a
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 5 hours?
(A) 2.4.
(B) 3.6.
(C) 4.2.
(D) 8.
(E) 6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 4 carpenters in 5 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 5= 8 desks
D is the correct answer.
Answer: (D) 8.
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.99
(B) 2.88
(C) 2.91
(D) 2.77
(E) 2.11
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: (B) 2.88
Question: 9.7 , 9.7 , 9.9 , 9.9 , 10.0 , 10.1 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.25 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
(A) 90%
(B) 85%
(C) 80%
(D) 75%
(E) 70%
Rationale: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.25; 10+0.25} = {9.75; 10.25}.
From the 8 listed numbers, 5 are within this range so 5/8=75%.
Answer: D.
Answer: (D) 75%
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 6% sugar. What percentage of the gallon is dye?
(A)  6
(B)  6.5
(C)  7.5
(D)  4.8
(E)  24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/6
=> 4/5 = x/6 => x = 4*6/5 = 4.8
Answer is D.
Answer: (D)  4.8
Question: A library has an average of 630 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
(A) 250
(B) 305
(C) 280
(D) 285
(E) None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (630x5 + 240x25 /30) = 305
Answer: Option B
Answer: (B) 305
Question: Of the 200 employees in a certain company, 30 percent will be relocated to City X and the remaining 70 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?
(A)  115
(B)  120
(C)  140
(D)  152
(E)  165
Rationale: 120 prefer X (Group 1);
80 prefer Y (Group 2).
City Y needs 140 people: letall 80 who prefer Y (entire Group 2) be relocated there, the rest 60 will be those who prefer X from Group 1;
City X needs 60 people: 120-60=60 from Group 1 will be relocated to X, which they prefer.
So, the highest possible number of employees who will be relocated to the city they prefer is 80+60=140.
Answer: C.
Answer: (C)  140
Question: Water is poured into a tank so that the tank is being filled at the rate of 5 cubic feet per hour. If the empty rectangular tank is 10 feet long, 6 feet wide, and 5 feet deep, approximately how many hours does it take to fill the tank?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: The volume the tank is: length*width*depth = 10*6*5= 300 cubic feet.
300 cubic feet / 5 cubic feet per hour = 60 hours.
It will take 60 hours to fill the tank.
The answer is E.
Answer: (E) 60
Question: The length and breadth of a rectangle is increased by 3% and 6% respectively. What is the increase in the area?
(A) 9.18
(B) 9.25
(C) 9.5
(D) 8.98
(E) 8.88
Rationale: 100*100=10000
103*106=10918
-----------
918
10000-------918
100----------9.18
Ans A
Answer: (A) 9.18
Question: One machine takes 3 minutes to check fault in 100 km fiber optic cable.Another machine does the same job in 3 seconds.What time will it take to do the same job when both machines are put to work?
(A) 2.00 seconds
(B) 2.20 seconds
(C) 2.50 seconds
(D) 2.95 seconds
(E) 3.00 seconds
Rationale: By guess it is clear that the time taken will be less than 3 seconds and very near to it. Therefore, answer 2.95 seconds will be correct. Answer-D
Answer: (D) 2.95 seconds
Question: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 24 days
(B) 65 days
(C) 86 days
(D) 45 days
(E) 17 days
Rationale: 10/40 + 10/30 + 10/x = 1
x = 24 days
Answer:A
Answer: (A) 24 days
Question: A straight pipe 2 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
(A)  1/6 and 1/4 only
(B)  1/4 and 1/3 only
(C)  1/6, 1/4, and 1/3
(D)  1/12, 1/6 and 1/4
(E)  1/12, 1/6, and 1/3
Rationale: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/3, 4-3=1=1/12and 6-4=2=2/12=1/6meters long pieces.
Answer: E.
Answer: (E)  1/12, 1/6, and 1/3
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed amount A, B and C?
(A) 3 : 5 : 2
(B) 3 : 5 : 5
(C) 6 : 10 : 5
(D) None of these
(E) Cannot be determined
Rationale: Solution
Let the initial investments of A and B be 3x and 5x.
A : B : C	=(3x ×12):(5x ×12):(5x×6)
= 36 : 60 : 30
= 6 : 10 : 5.
Answer C
Answer: (C) 6 : 10 : 5
Question: How is 3% expressed as a decimal fraction?
(A) 0.3
(B) 0.03
(C) 0.003
(D) 0.0003
(E) 3
Rationale: 3/100= 0.03
ANSWER:B
Answer: (B) 0.03
Question: What should come in place of the question mark (?) in the following number series?
11 21 33 47 63 ?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: The numbers increase by 10, 12, 14, 16,...
The next number should be 63+18 = 81
The answer is B.
Answer: (B) 81
Question: If f(x)=4x−1 and g(x)=2x+4 for all integers, which of the following is a possible value of g(f(x))?
(A) -23
(B) -17
(C) 0
(D) 18
(E) 22
Rationale: g(f(x)) = 2*f(x)+4 = 2*(4x-1)+4 = 8x+2
Of these five options, only 18 has the form 8x+2.
The answer is D.
Answer: (D) 18
Question: A committee that includes 8 members is about to be divided into 2 subcommittees with 4 members each. On what percent of the possible subcommittees that Michael is a member of is Annie also a member?
(A) 43%
(B) 39%
(C) 35%
(D) 31%
(E) 27%
Rationale: Michael is a member of one of the subcommittees.
P(Annie is on the same subcommittee) = 3/7 which is about 43%.
The answer is A.
Answer: (A) 43%
Question: The sale price at which a store sells an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
(A) $28
(B) $40
(C) $56
(D) $63
(E) $72
Rationale: Sale Price = (5/4)*(Cost Price)
If the sale price is an integer, then the cost price must be divisible by 4.
The answer is D.
Answer: (D) $63
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of water ?
(A) Red
(B) BLUE
(C) PINK
(D) ORANCE
(E) BLACK
Rationale: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of water is 'Blue' but in coding language, 'Blue' is called 'Red'.
ANSWER: A
Answer: (A) Red
Question: A candidate got 35% of the votes polled and he lost to his rival by 2430 votes. How many votes were cast?
(A) 7500
(B) 3388
(C) 8100
(D) 2888
(E) 2661
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2430
100%---------? => 8100
Answer: C
Answer: (C) 8100
Question: Suppose there is a number 235 such that sum of first two digits is equal to the third digit. How many such 3 digits numbers are possible?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: As we know that total digits are
0 ,1, 2, 3,4,5,6,7,8,9
if three digit no is xyz
this means x+y=z must hold
so we have to select two no out of 10
ans is 10 c 2=45
ANSWER:D
Answer: (D) 45
Question: If all the sides of a right triangle increase in length by 20%, then by what percentage does the area of the triangle increase?
(A) 36%
(B) 44%
(C) 50%
(D) 64%
(E) 80%
Rationale: Let B be the base and H be the height of the original triangle.
The original area is (1/2)BH.
The area of the expanded triangle is (1/2)(1.2B)(1.2H) = (1.2)(1.2)(1/2)BH = 1.44(1/2)BH
The answer is B.
Answer: (B) 44%
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?
(A) 22
(B) 31
(C) 66
(D) 78
(E) 76
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (21 * 3) years and (34 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 21 * 3 - 34 * 3 = 196 - 63 - 102 = 31 years.Answer: B
Answer: (B) 31
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 16
(B) 55
(C) 72
(D) 88
(E) 12
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
Answer: (C) 72
Question: 26
a2
+2b
___
99
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
(A) 345
(B) 45
(C) 51
(D) 43
(E) 34
Rationale: 6+2+b=9
b=1
2+a+2=9
a=5
ab=51
ans=C
Answer: (C) 51
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 14%
(B) 16%
(C) 18%
(D) 22%
(E) None of these
Rationale: Total CP = Rs. 42000 + Rs. 13000 = Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100 = 18%
ANSWER:C
Answer: (C) 18%
Question: At a conference table, 6 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these six employees?
(A) 60
(B) 80
(C) 100
(D) 120
(E) 140
Rationale: Head's sit is fixed. Now 5 people is left with 5 seats.
5 people can sit on 5 seats in 5! ways or 120 ways.
Ans is D
Answer: (D) 120
Question: In a certain town, the ratio of NY Yankees fans to NY Mets fans is 2:1, and the ratio of NY Mets fans to Boston Red Sox fans is 3:7. If there are 352 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
(A) 58
(B) 66
(C) 74
(D) 82
(E) 90
Rationale: The ratio of Yankees:Mets:Red Sox = 6:3:7
The Mets fans are 3/16 of the population.
(3/16)*352 = 66
The answer is B.
Answer: (B) 66
Question: Look at this series: 15, 15, 27, 27, ?, 39 What number should fill the blank?
(A) 51
(B) 39
(C) 23
(D) 15
(E) None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option B
Answer: (B) 39
Question: Harriet, Isabella and Karen are business partners. Harriet invested Rs.13000. If her share of a profit of Rs.3000 is Rs.1100 and Karen's share is Rs.1000, what is Isabella's capital?
(A) 8676.67
(B) 8666.67
(C) 896.67
(D) 8566.67
(E) 8662.67
Rationale: 1200 + 1000 = 2200
3000 - 2200 = 800
1200 ---- 13000
800 ---- ? => 8666.67
ANSWER:B
Answer: (B) 8666.67
Question: Given the following equation 30% of 3485 + 20% of 6218 = ?, Find the approximate value should come in place of the question mark (?).
(A) 2290
(B) 2280
(C) 2260
(D) 2240
(E) 2220
Rationale: ? = 30% of 3485 + 20% of 6218
? = 30/100*3485 + 20/100* 6218
? = 2289.1
≈ 2290
Answer A
Answer: (A) 2290
Question: Meena bought a watch with 25% discount on the selling price. If the watch cost her Rs.1545. What is the original selling price of the watch?
(A) Rs.2050
(B) Rs.2040
(C) Rs.2030
(D) Rs.2060
(E) None of these
Rationale: Explanation:
CP of Meenal is 75% of the Original SP.
:. Original SP = 1545x100/75 = Rs.2060.
Answer: Option D
Answer: (D) Rs.2060
Question: Rob also compared the Empire State Building and the Petronas
Towers. What is the height difference between the two if the Empire
State Building is 435m tall and the Petronas Towers is 458m tall?
(A) 9
(B) 17
(C) 23
(D) 45
(E) 12
Rationale: 458-435=23.Answer is C.
Answer: (C) 23
Question: What approximate value should come in place of the question mark (?) in the following equation ?
3⁄7 of 1596 + 3015 = ? – 2150
(A) 7200
(B) 48000
(C) 5830
(D) 58000
(E) 6300
Rationale: ? ≈ 3 × 230 + 3000 + 2150
= 680 + 3000 + 2150 = 5830
Answer C
Answer: (C) 5830
Question: Due to reduction of 25/4% in the price of sugar , a man is able to buy 1kg more for Rs.120. Find the original and reduced rate of sugar.
(A) Rs.7.50 per kg
(B) Rs.2.50 per kg
(C) Rs.5 per kg
(D) Rs.6.25 per kg
(E) Rs.10 per kg
Rationale: Let the original rate be Rs.x per kg.
Reduced rate = Rs.[(100-(25/4))*(1/100)*x}]=Rs.15x/16per kg
120/(15x/16)-(120/x)=1
(128/x)-(120/x)=1
x=8.
So, the original rate = Rs.8 per kg
Reduce rate = Rs.[(15/16)*8]per kg = Rs.7.50 per kg
Answer is A.
Answer: (A) Rs.7.50 per kg
Question: Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
(A) 277
(B) 100
(C) 247
(D) 288
(E) 261
Rationale: Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 100 min.
Answer: B
Answer: (B) 100
Question: After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
(A) 50299
(B) 50289
(C) 5000
(D) 17728
(E) 50189
Rationale: Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000
If SP = Rs. 8000, profit = 60%
CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000
Answer: C
Answer: (C) 5000
Question: Solve x2 – 3x – 4 = 0.
(A) 1,4
(B) -1,4
(C) 2,3
(D) 2,-3
(E) 3,4
Rationale: This one factors easily:
x2 – 3x – 4 = 0
(x + 1)(x – 4) = 0
x + 1 = 0 or x – 4 = 0
x = –1 or x = 4
The solution is x = –1, 4
ANSWER B -1,4
Answer: (B) -1,4
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 36, then find the smaller number?
(A) 25
(B) 66
(C) 77
(D) 60
(E) 44
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 36
3x = 36 => x = 12
=> Smaller number = 5x = 60.
Answer: D
Answer: (D) 60
Question: The larger of two negative consecutive odd integers 5t and 5(t-1) is multiplied by 3 and then added to the smaller of the two original integers. Which of the following represents this operation?
(A) 6t-2
(B) 8t-2
(C) -2
(D) 20t-5
(E) -2-4t^2
Rationale: larger of 5t-5, 5t (when they are negative) is 5t. the smallest of 5t and 5t-5 when they are positive is 5t-5.
therefore 3* 5t + 5t-5 = 20t-5.
option D.
Answer: (D) 20t-5
Question: There are 1000 students in a school and among them 25 % of them attends chess class. 50% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
(A) 1
(B) 10
(C) 125
(D) 50
(E) 20
Rationale: 25% of 1000 gives 250. so 250 attends chess and 50% of 250 gives 125
so 125 enrolled for swimming
Answer: C
Answer: (C) 125
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/8
(B) 5/4
(C) 5/2
(D) 5/6
(E) 5/1
Rationale: P(at least one graduate) = 1 - P(no graduates)
1 = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6.Answer: D
Answer: (D) 5/6
Question: In how many different number of ways 3 boys and 4 girls can sit on a bench?
(A) 5700
(B) 5710
(C) 5040
(D) 8000
(E) 5820
Rationale: npn = n!
7p7 = 7 X 6 × 5 × 4 × 3 × 2 × 1 = 5040
C)
Answer: (C) 5040
Question: The mean of 50 observations was 40. It was found later that an observation 45 was wrongly taken as15 The corrected new mean is
(A) 40
(B) 36.5
(C) 46.5
(D) 20.5
(E) 40.6
Rationale: Explanation:
Correct Sum = (40 * 50 + 45 - 15) = 2030
Correct mean = = 2030/50 = 40.6
Answer: E
Answer: (E) 40.6
Question: A and B joined a partnership business. In which A invested rs. 10,000 for 6 months and B invested Rs. 6000 for 8 months. If they earn a profit of Rs. 3000. find A's share in the profit.
(A) rs 2500
(B) rs 1500
(C) rs 1000
(D) rs 1667
(E) rs 1567
Rationale: 10,000*6==60000
6000*8== 48000
60000:48000=15:12
a=15, b==12
sp A share= 15*3000/15+12==1667
ANSWER:D
Answer: (D) rs 1667
Question: If the reciprocals of two consecutive positive integers are added together, what is the sum in terms of the greater integer b?
(A) b^2- b
(B) 2b-1
(C) (2b-1)/(b^2- b)
(D) 2b-3
(E) 2b-5
Rationale: Let two consecutive positive integers be b and b-1 (Greater integer is b)
So,
(1/b) + [1/(b-1)]
= (2b-1)/b(b-1)
=(2b-1)/(b^2- b)
Answer : C
Answer: (C) (2b-1)/(b^2- b)
Question: (10+0.0001)/(0.04+1)
The value of the expression above is closet to which of the following?
(A) 0.0001
(B) 0.001
(C) 0.1
(D) 1
(E) 10
Rationale: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 10 and the denominator is very close to 1, hence the value of the fraction is very close to 10/1=10
Answer: E.
Answer: (E) 10
Question: The squared value of the diagonal of a rectangle is (64 + B2) sq cm, where B is less than 8 cm. What is the breadth of that rectangle?
(A) 6 cm
(B) 10 cm
(C) 8 cm
(D) Data inadequate
(E) None of these
Rationale: Diagonal2 = 64 + B2 or, 10(2) = 64 + 6(2)
Answer A
Answer: (A) 6 cm
Question: What is the least common multiple of 5,40,36,50
(A) 3698
(B) 874
(C) 3692
(D) 1800
(E) 3214
Rationale: The given numbers are 5,40,36,50
thus the l.c.m is 5*2*2*1*2*9*5=1800
the answer is D
Answer: (D) 1800
Question: The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 50 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons?
(A) 55
(B) 56
(C) 57
(D) 58
(E) 59
Rationale: 20x + 50 = 21(x – 5)
X=55
ANSWER:A
Answer: (A) 55