mathewhe/aqua_rat huggingface dataset:
Question: The average (arithmetic mean) of 4 different integers is 72. If the largest integer is 90, what is the least possible value of the smallest integer?
(A) 1
(B) 19
(C) 21
(D) 30
(E) 33
Rationale: Total of Integers=72*4=288
Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.
But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89
Lowest of least possible integer = 288-(90+89+88)=288-267=21
Answer: C
Answer: (C) 21
Question: The average of 9 results is 50. The average of first four results is 52 and average of last four results is 49 . what is the fifth result?
(A) 22
(B) 27
(C) 29
(D) 46
(E) 92
Rationale: Total of results = 50 x 9 = 450
Total of first four results = 52 x 4 = 208
Total of Last four results = 49 x 4 = 196
Hence the fifth result = 450 - (208 + 196) = 46
Answer:D
Answer: (D) 46
Question: A can do a piece of work 60 days. B can do work in 90 days. In how many days they will complete the work together?
(A) 36 days
(B) 32 days
(C) 19 days
(D) 17 days
(E) 18 days
Rationale: LCM = 180, Ratio= 60:90=2:3
No of days= 180/(2 + 3) = 180/5 = 36 days
ANSWER:A
Answer: (A) 36 days
Question: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
(A) 34
(B) 677
(C) 197
(D) 177
(E) 191
Rationale: Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 34
Answer:A
Answer: (A) 34
Question: Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work?
(A) 50 days
(B) 23 days
(C) 20 days
(D) 65 days
(E) 22 days
Rationale: (5m + 9w)10 = (6m + 12w)8
=> 50m + 90w = 48w + 96 w => 2m = 6w => 1m = 3w 5m + 9w = 5m + 3m = 8m
8 men can do the work in 10 days.
3m +3w = 3m + 1w = 4m
So, 4 men can do the work in (10 * 8)/4 = 20 days.
Answer: C
Answer: (C) 20 days
Question: A computer manufacturer produces a certain electronic component at a cost of $100 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $24,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 100 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) 278
(B) 366
(C) 349
(D) 335
(E) 295
Rationale: $24500 is a fixed cost
Each component is $104 ($100 to produce, $4 to ship)
Manufacturer will be producing and selling 100 components
so therefore the equation to find price would be
100*p = 24500+(100*100)+(100*4)
p = (24500+10000+400)/100
p = 349
Answer: C
Answer: (C) 349
Question: Amit and Ananthu can do a work in 15 days and 30 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
(A) 28 days
(B) 20 days
(C) 23 days
(D) 25 days
(E) 27 days
Rationale: Amit’s one day’s work= 1/15
Amit’s 3 day’s work = 1/15 *3 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/30
Ananthu can do work in = 4/5 *30 = 24 days
So total days = 24+3 = 27 days
ANSWER:E
Answer: (E) 27 days
Question: There are 225 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
(A) 300
(B) 400
(C) 562.5
(D) 600
(E) None of these
Rationale: as per question stem 2/5M (Portion of Men employees who are managers) + 225 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+225= 2/5T, or 2/5(T-M)=225, from here we get that T-M=562.5, that would be total number of female employees and the answer (C)
Answer: (C) 562.5
Question: Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 39 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?
(A) 130
(B) 80
(C) 100
(D) 120
(E) 150
Rationale: let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =39
or 3y =39 y =13 ;x =26 , total notes they carry = 104+26 =130
A
Answer: (A) 130
Question: If two positive numbers are in the ratio 1/8 : 1/7, then by what percent is the second number more than the first?
(A) 14.3%.
(B) 70%.
(C) 60%.
(D) 68%.
(E) 80%.
Rationale: Given ratio = 1/8 : 1/7 = 7 : 8
Let first number be 7x and the second number be 8x.
The second number is more than first number by 1x.
Required percentage = 1x/7x * 100 = 14.3%.
Answer: A
Answer: (A) 14.3%.
Question: John can complete a given task in 16 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 5 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
(A) 62
(B) 64
(C) 66/7
(D) 10
(E) 68/7
Rationale: In such questions, you need to start from the end. Last 5 days John works alone and completes 5 * (1/16) = 5/16 of the work.
So 11/16 of the work should have been completed by the two of them together before Jane left.
Their combined rate of work is 1/16 + 1/12 = 7/48
Time taken to complete 11/16 of the work = (11/16)/(7/48) = 33/7 days.
So total number of days taken to complete the work =33/7 + 5 = 68/7 days.
E
Answer: (E) 68/7
Question: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(A) 25200
(B) 2543
(C) 2344
(D) 233445
(E) 52757
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) = ( 7 x 6 x 5 x 4 x 3 ) 3 x 2 x 1 2 x 1 = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200.
Answer:A
Answer: (A) 25200
Question: The average expenditure of the hotel when there are 10 guests is Rs. 60 per guests and the average expenditure is Rs.40 when there are 20 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average expenditure per guest whe there are 40 guests in the hotel.
(A) 30
(B) 88
(C) 26
(D) 18
(E) 11
Rationale: Explanation:
Let the fixed expenditure of the hotel be Rs.x and the variable expenditure ( which is dependent on the guest ) is Rs.y , then
x + 10y = 600 ---------(1)
x + 20y = 800 ----------(2)
\inline \Rightarrow 10y = 200
y = Rs. 20 and x= 400
Hence the total expenditure when there are 40 guests = 400 + 40 x 20 = 1200
\inline \therefore average expenditure = \inline \frac{1200}{40} = Rs. 30
Answer: A
Answer: (A) 30
Question: The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?
(A) 1
(B) 2
(C) 6
(D) 8
(E) 7
Rationale: Let the two-digit number be 10a + b
a = b + 2 --- (1)
10a + b = 7(a + b) => a = 2b
Substituting a = 2b in equation (1), we get
2b = b + 2 => b = 2
Hence the units digit is: 2.
Answer: B
Answer: (B) 2
Question: A bottle company produces 100 glass bottles per day. One-fifth of the bottles produced are defective and one-quarter of all bottles produced are rejected by quality control technician. If one-tenth of the nondefective bottles are rejected by mistake, and if all the bottles not rejected are sold, then what percent of the bottles sold by the company are defective?
(A) 16%
(B) 8%
(C) 4%
(D) 2%
(E) 1%
Rationale: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. Correct Answer is C
Answer: (C) 4%
Question: Three years ago the average age of a class of six members was 20 years. A boy have been added, the average age of the class is the same today. What is the age of the boy?
(A) A)1
(B) B)2
(C) C)3
(D) D)4
(E) E)5
Rationale: 6 * 23 = 138
7 * 20 = 140
`2
B
Answer: (B) B)2
Question: What is the minimum number of years upon which SI on Rs 2600 at 6.67% interest rate will be in whole number?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Explanation:
Simple Interest =Principal * Rate * Time
Principal = 2600 Rs
Interest Rate = 6.67%
=> SI = 2600 * (20/3)*Time
SI of the number will be a whole number for the first time when time is three as denominator of rate is 3.
Hence time should be set to 3 years.
ANSWER: A
Answer: (A) 3
Question: there is 16 question. when u attempted paper you get 20 marks. for correct answer u get 5 marks and wrong answer you get 0 marks . if you dot attempt question you get 2 marks. which is not attainable marks.
(A) 97
(B) 95
(C) 96
(D) ALL
(E) NONE
Rationale: there are 16 questions each of 5, so totally 80 marks+20 marks for attempting
95: it can be attained if 15 answers are answered and last one was a wrong atempt
97: it can be attained if 16 are attempted and in which one was wrong
"96" was the answer which cannot be attained in any manner
ANSWER:C
Answer: (C) 96
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 83.37%
(B) 83.23%
(C) 83.39%
(D) 82.33%
(E) 83.33%
Rationale: Percentage of milk in the mixture formed
= [80/100 (180) + 36] / (180 + 36) * 100%
= (144 + 36)/216 * 100%
= 5/6 * 100%
= 83.33%
Answer: E
Answer: (E) 83.33%
Question: √1919/√0.1919 =
(A) 0.0001
(B) 0.01
(C) 100
(D) 1,000
(E) 10,000
Rationale: Soln:
√1919−/√0.1919
= [(1,919/(1919*10^-4)]^1/2 =>
[1/10^-4]^1/2 =>
[10^4]^1/2 = 100
Hence answer is C
Answer: (C) 100
Question: If the simple interest on a certain sum of money for 8 years is one–fifth of the sum, then the rate of interest per annum is
(A) 4.1%
(B) 7%
(C) 2.5%
(D) 2.8%
(E) 3%
Rationale: Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 8 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 8) = 20/8 = 2.5%
Answer: Option C
Answer: (C) 2.5%
Question: A can do a piece of work in 4 days. B can do it in 7 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 22 days
(B) 28/3 days
(C) 67 days
(D) 17/5 days
(E) 18 days
Rationale: C = 1/2 - 1/4 - 1/7 =3/28
=> 28/3 days
Answer:B
Answer: (B) 28/3 days
Question: Jackson has $313,197 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
(A) $6
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,197 = 24 and 18 is divisible by 9.
Hence we need to subtract 6 to this number for it to be divisible by 9
Correct Option: A
Answer: (A) $6
Question: If −2≤w≤0 and n > 19, which of the following CANNOT be the value of wn?
(A) -48
(B) -38
(C) -20
(D) 0
(E) 19
Rationale: value of wn not equal to -19=E -19....Rest all are achievable
Answer: (E) 19
Question: Four machines, each working at the same constant rate, together can complete a certain job in 20 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 10 days?
(A) 5
(B) 3
(C) 4
(D) 6
(E) 1
Rationale: Rate of one machine = 1 job / (20*4) days
let X = number of machines needed to complete the job in 10 days
1/(4*20) * 10 * X = 1 job
X = 8
8-4= 4
ANSWER: C
Answer: (C) 4
Question: There are 4 more women than men on Centerville's board of education. If there are 6 members on the board, how many are women?
(A)  3
(B)  5
(C)  6
(D)  7
(E)  8
Rationale: Given: M=W-4 so, W+(W-4)=6 --> W=5.
Answer: B.
Answer: (B)  5
Question: Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 60 mph. What is his average speed of travel for the entire journey?
(A) 53.33 mph
(B) 56.67 mph
(C) 52 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Average Speed = Total distance/ Total time = (40 * 2 + 60 * 3)/(2 + 3) = 260/5 = 52
Answer: C
Answer: (C) 52 mph
Question: If David bought TV for Rs.20000 and He luckily bought with 50% due to his lottery. What was the price if David didn't select for a lottery.
(A) 30000
(B) 35000
(C) 40000
(D) 45000
(E) 50000
Rationale: CP* (50/100) = 20000
CP= 400 * 100 => CP = 40000
Answer:C
Answer: (C) 40000
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 36, what is the total amount?
(A) 115
(B) 116
(C) 117
(D) 118
(E) 156
Rationale: x:y:z = 100:45:50
20:9:10
9 --- 36
39 --- ? => 156
ANSWER:E
Answer: (E) 156
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 30% on hers. If Mindy earned 5 times as much as Mork did, what was their combined tax rate?
(A)  32.5%
(B)  34%
(C)  35%
(D)  31.67%
(E)  37.5%
Rationale: Say Morks income is - 100
So tax paid will be 40
Say Mindys income is 5*100 = 500
So tax paid is 30% * 500 = 150
Total tax paid = 40+150 = 190.
Combined tax % will be 190/100+500 = 31.67%
Answer: (D)  31.67%
Question: Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 40?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: 210=2*3*5*7, so the # of factors 210 has is (1+1)(1+1)(1+1)(1+1)=16 (see below);
42=2*3*7, so out of 16 factors only two are multiples of 42: 42 and 210, itself;
So, the probability is 2/16=1/16.
Answer: A
Answer: (A) 1/16
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 1 : 3?
(A) 76.66 kmph
(B) 69.66 kmph
(C) 48 kmph
(D) 66.66 kmph
(E) 56.66 kmph
Rationale: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (x)/40 + (3x)/60 = (3x + 6x)/120 = 9x/120 = 3x/40 Average speed = (2x + 3x)/(3x/40)
= 200/3 kmph.
=66.66 kmph
ANSWER:D
Answer: (D) 66.66 kmph
Question: I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?
(A) 10 min
(B) 12 min
(C) 20 min
(D) 19 min
(E) 24 min
Rationale: Let the distance be x km. Then,
( Time taken to walk x km) + (time taken to ride x km) =37 min.
( Time taken to walk 2x km ) + ( time taken to ride 2x km )= 74 min.
But, the time taken to walk 2x km = 55 min.
Time taken to ride 2x km = (74-55)min =19 min.
ANSWER D
Answer: (D) 19 min
Question: The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144,
find the other number
(A) 400
(B) 256
(C) 120
(D) 420
(E) 560
Rationale: Explanation:
Solve this question by using below formula.
Product of 2 numbers = product of their HCF and LCM
144 * x = 12 * 5040
x = (12*5040)/144 = 420
Answer: Option D
Answer: (D) 420
Question: 2^(10) + 2^(11) + 2^(12) + ... + 2^(39) + 2^(40) =
(A) 2^8(2^(29)-1)
(B) 2^9(2^(30)-1)
(C) 2^10(2^(31)-1)
(D) 2^11(2^(32)-1)
(E) 2^12(2^(33)-1)
Rationale: 2^(10) + 2^(11) + 2^(12) + ... + 2^(39) + 2^(40) =
2^(10)*(1+2+4+...+2^(30)) =
2^(10)*(2^(31) - 1)
The answer is C.
Answer: (C) 2^10(2^(31)-1)
Question: Two trains leaving from two station 50 miles away from each other with constant speed of 60 miles per hour, approaches towards each other on different tracks. if length of each train is 1/6 mile. when they meet How much time they need to pass each other totally ?
(A) 277
(B) 87
(C) 27
(D) 10
(E) 72
Rationale: Explanation:
The trains are coming towards each other so their relative speed is 60 + 60 = 120 mph
In this case the distance would be addition of lengths of trains.i.e 1/6 + 1/6 = 1/3 m
T = dsds = 1/3 1/120 3/120 = 1/1360 h
Answer: D
Answer: (D) 10
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 22. Which of the following integers is the higher of the remaining two integers?
(A) 83
(B) 86
(C) 44
(D) 22
(E) 55
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 22
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -22 = 144
B = (144 + 22)/2 = 83
Answer:Option A
Answer: (A) 83
Question: What is the last digit in the product (3^65 x 6^59 x 7^71)
(A) 5
(B) 6
(C) 4
(D) 8
(E) 9
Rationale: Explanation:
Unit digit in 34 = 1 Unit digit in (34)16 = 1
Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3
Unit digit in 659 = 6
Unit digit in 74 Unit digit in (74)17 is 1.
Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3
Required digit = Unit digit in (3 x 6 x 3) = 4.
Answer is C
Answer: (C) 4
Question: Jim bought edging to go around a circular garden with a radius of 7 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
(A) 43.96' additional edging
(B) 48.84' additional edging
(C) 38.84' additional edging
(D) 18.84' additional edging
(E) 58.84' additional edging
Rationale: circumference of small garden = 2 x 3.14 x 7 = 43.96'
double of the circumference of small garden = 2 x 43.96' = 87.92'
More feet to be buy =87.92 - 43.96 = 43.96
Answer :A
Answer: (A) 43.96' additional edging
Question: Can you find the last term in the sequence that is given below ?
2, 12, 36, 80, 150, ?
(A) 252
(B) 199
(C) 416
(D) 312
(E) 521
Rationale: C
252
Explanation:
A unique pattern has been made into use in this series.
All numbers are (n^3 + n^2) where n is 1, 2, 3 and so on.
In first number, n = 1
1^3 + 1^2 = 1 + 1 = 2
In second number, n = 2
2^3 + 2^2 = 8 + 4 = 12
In third number, n = 3
3^3 + 3^2 = 27 + 9 = 36
In fourth number, n = 4
4^3 + 4^2 = 64 + 16 = 80
In fifth number, n = 5
5^3 + 5^2 = 125 + 25 = 150
Similarly for the sixth number, n = 6
6^3 + 6^2 = 216 + 36 = 252.
Answer: (A) 252
Question: The ratio 9 : 5 expressed as a percent equals
(A) 12.5%
(B) 40%
(C) 180%
(D) 125%
(E) None
Rationale: Solution
9 : 5	= 9/ 5
= (9 / 5 x 100)%.
= 180 %.
Answer C
Answer: (C) 180%
Question: A parking garage rents parking spaces for $10 per week or $35 per month. How much does a person save in a year by renting by the month rather than by the week?
(A)  $140
(B)  $100
(C)  $220
(D)  $240
(E)  $260
Rationale: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
30$ per month!
An year has 12 months.
Annual charges per year = 12 * 35 = 420$
520 - 420 = 100
Ans B
Answer: (B)  $100
Question: Out of 400 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
(A) 120
(B) 150
(C) 100
(D) 180
(E) 220
Rationale: n(A)=325,n(B)=175,n(AuB)=400-50=350.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-350=150.
Answer is B
Answer: (B) 150
Question: SHOW TIMER STATISTICS
To apply for the position of photographer at a local magazine, Veronica needs to include three or four of her pictures in an envelope accompanying her application. If she has pre-selected five photos representative of her work, how many choices does she have to provide the photos for the magazine?
(A) 5
(B) 10
(C) 12
(D) 15
(E) 50
Rationale: Veronica can choose 3 photos in 5C3 = 10 ways
She can choose 4 photos in 5C4 = 5 ways
Total number of ways = 10 + 5 = 15
Answer: D
Answer: (D) 15
Question: The sale price sarees listed for Rs.390 after successive discount is 14% and 15% is?
(A) 285
(B) 277
(C) 290
(D) 662
(E) 262
Rationale: 390*(86/100)*(85/100)
= 285
Answer: A
Answer: (A) 285
Question: Which of the following is closer to (26!+25!)/(26!-25!)?
(A) 1
(B) 36
(C) 25
(D) 16
(E) 49
Rationale: Notice that 26! = (26)(25!), so we can factor out 25! from top and bottom.
(26!+25!)/(26!-25!)=[25!(26+1)]/[25!(26-1)]
= (26+1)/(25-1)
= 27/25
≈ 1
Answer: A
Answer: (A) 1
Question: If a certain computer is capable of printing 4900 monthly credit card bills per hour, while a new model is capable of printing at a rate of 6600 per hour, the old model will take approximately how much longer than the new model to print 10000 bills?
(A) 31
(B) 76
(C) 88
(D) 26
(E) 81
Rationale: Explanation:
Old model is capable of printing at a rate of 4900 per hour
New model is capable of printing at a rate of 6600 per hour
Old model time taken to print 10000 cards = 10000/4900 = 100/49
New model time taken to print 10000 cards = 10000/6600 = 100/66
Old model – new model: 100/49 - 100/66 = 1700 /(49 × 66) = 850/(49 × 33) = 0.525 hrs => 31 mins
Therefore, the old model will take approximately 31 mins longer than the new model to print 10000 bills
Answer: A
Answer: (A) 31
Question: In how many different ways can the letters of the word ‘LOVE’ be arranged ?
(A) 24
(B) 120
(C) 720
(D) 40320
(E) 6
Rationale: A
24
Required number of arrangements = 4! = 24
Answer: (A) 24
Question: Robert borrows a certain amount at 15% p.a. simple interest. How many years will it take for the amount to become twice the principal?
(A) 4 years 4 months
(B) 5 years 2 months 3 days
(C) 6 years 5 months
(D) 3 years
(E) 8 years
Rationale: Solution: simple interest question
B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate
after putting the values 15
2= [1+(15t/100)]
t= 4/3 which is (4+1)/3= 4 + 1/3 means 4 years and (12*1)/3 = 4 months.
Total time is 4 years 4 months
Answer is A
Answer: (A) 4 years 4 months
Question: Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(3a) if a is even. Then (4#3) + (3#4) – (3#3) is equal to
(A) 64
(B) 82
(C) 128
(D) 512
(E) 4096
Rationale: Answer:
4^6 + 3^6 - 3^6 = 4^6=4096
ANs E
Answer: (E) 4096
Question: In a class everyone will play at least one sport viz table tennis, cricket and badminton. 73
students play table tennis, 79 play badminton, 75 play cricket and 25 students play both table
tennis and badminton, 27 play both table tennis and cricket 30 play. Badminton and cricket and
16 students play all the sports. How many students play only cricket ?
(A) 36
(B) 38
(C) 39
(D) 40
(E) 37
Rationale: PERSONS PLAY CRICKET ONLY=N(C)-N(B∩C)+N(C∩T)-2(N(B∩T∩C))
=75-30+27-(2*16)
=40
ANSWER:D
Answer: (D) 40
Question: A is twice as good a workman as B and they took 6 days together to do the work B alone can do it in?
(A) 25 days
(B) 18 days
(C) 21 days
(D) 11 days
(E) 13 days
Rationale: WC = 2:1
2x + x = 1/6
x = 1/18 => 18 days
Answer: B
Answer: (B) 18 days
Question: A train 220 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 12
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 220 * 3/55 = 12 sec.
Answer: Option A
Answer: (A) 12
Question: The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
(A) 8:3
(B) 7:5
(C) 4:3
(D) 2:3
(E) 3:1
Rationale: Explanation:
Milk in 1-liter mixture of A = 4/7 liter.
Milk in 1-liter mixture of B = 2/5 liter.
Milk in 1-liter mixture of C = 1/2 liter.
By rule of allegation we have required ratio X: Y.
X : Y
4/7 2/5
So Required ratio = X: Y = 1/10: 1/14 = 7: 5.
ANSWER IS B
Answer: (B) 7:5