mathewhe/aqua_rat huggingface dataset:
Question: A prison of 10,000 inmates has enough food to feed them all for 50 days. After 10 days some of the inmates leave and the food is now enough for the same period of 50 days as before. How many of them left?
(A) 3,000
(B) 2,200
(C) 2,000
(D) 1,000
(E) 200
Rationale: 10,000 --- 50
10,000 --- 40
x --- 50
x*50 = 10,000*40
x = 8,000
10,000
--------
2,000
Answer = C
Answer: (C) 2,000
Question: 7, 26, 63, 124, (....)
(A) 342
(B) 125
(C) 289
(D) 564
(E) 36
Rationale: Explanation:
Numbers are
2^3-1=7
3^3-1=26
4^3-1=63
5^3-1=124
6^3-1=342
ANSWER:A
Answer: (A) 342
Question: The present ages of three persons in proportions 4 : 5 : 9. Eight years ago, the sum of their ages was 30. Find their present ages (in years).
(A) 19, 20, 28
(B) 12, 15, 27
(C) 20, 35, 45
(D) 33,42,43
(E) 13, 23,34
Rationale: Let their present ages be 4x, 5x and 9x years respectively.
Then, (4x - 8) + (5x - 8) + (9x - 8) = 30
18x = 54
x = 3.
Their present ages are 4x = 12 years, 5x = 15 years and 9x = 27 years respectively.
ANSWER:B
Answer: (B) 12, 15, 27
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 144 grams of water?
(A) 16
(B) 72
(C) 112
(D) 128
(E) 142
Rationale: See H/O = 2 / 16
Add 1 to both sides:
H/O + 1 = 2/16 + 1
Take LCM
(H+O)/O = (2+16)/16
Water/O = 18/16
Now that we have the Water to Oxygen ratio, put in the amount of water i.e. 144 gm
=>O= 144*16/18 = 128
ANSWER:D
Answer: (D) 128
Question: At what rate of interest is an amount doubled in two years, when compounded annually?
(A) 41.7%
(B) 41.4%
(C) 49.4%
(D) 81.4%
(E) 31.4%
Rationale: Let the rate of interest be r. The amount gets doubled in two years => P(1 + r/100)2 = 2p => 1 + r/100 = √2 => r/100 = √2 - 1 = 0.414 => r = 100(0.414) = 41.4%.Answer: B
Answer: (B) 41.4%
Question: one out of ten employees are capable of doing a certain task. 40 percent of the five employees, including the one who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?
(A) 43.33%
(B) 75%
(C) 13.33%
(D) 38.33%
(E) 23.33%
Rationale: Given 40% of 10 employees including 1 who are capable of doing task.
40% of 10 employeees
= 40/100 * 10
= 4 employees
===> 1 employees who are capable of doing the task and three employee who is not capable.
percentage of employees assigned who are not capable
= 3/4 * 100
=75%
ANSWER:B
Answer: (B) 75%
Question: The radius of a cone is 10 m, height 21 m. The volume of the cone is:
(A) 2200
(B) 1100
(C) 5500
(D) 3300
(E) 1050
Rationale: 1/3 πrh = 1/3 × 22/7 × 100 × 21
= 2200 m(power3)
Answer is A.
Answer: (A) 2200
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8200. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) 2177
(B) 2876
(C) 4500
(D) 5700
(E) 6711
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8200 = 32800 ----(2)
(2)-(1) i.e. May - Jan = 800
Salary of May is Rs.6500
Salary of January = Rs.5700.Answer: D
Answer: (D) 5700
Question: [(3/2 ÷ 1/2 × 3/2)]/[(3/2 × 1/2 ÷ 3/2)] = ?
(A) 6
(B) 8
(C) 10
(D) 9
(E) 3
Rationale: Explanation:
[(3/2 ÷ 1/2 × 3/2)]/[(3/2 × 1/2 ÷ 3/2)]
= [3/2 × 2/1 × 3/2]/[3/2 × 1/2 × 2/3]
= (9/2)/(1/2) = (9/2) × (2/1) = 9
Answer: Option D
Answer: (D) 9
Question: Find the slope of the line perpendicular to the line y = (1/5)x - 7
(A) 1
(B) 2
(C) -5
(D) 4
(E) 5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 5. If m is the slope of the line perpendicular to the given line, then
m × (1/5) = -1
Solve for m
m = - 5
correct answer C) -5
Answer: (C) -5
Question: Six points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
(A) 4
(B) 5
(C) 6
(D) 15
(E) 20
Rationale: Let's start with the triangle: You have 6 points to choose from but only 3 points you will connect and 3 points you will not connect.
Hence number of possibilities for triangle: 6! / 3! * 3! = 20
Same goes for the quadrilateral: 6 points to choose from, 4 points which you will connect and 2 points which you won't connect.
Number of possibilities for quadrilateral: 6! / 4! * 2! = 15
Difference = 5
Answer B
Answer: (B) 5
Question: A train ride from Town P to Town Q costs $6.85 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.45. What is the cost of a bus ride from Town P to Town Q?
(A) $1.30
(B) $2.50
(C) $4.10
(D) $4.70
(E) $8.20
Rationale: Let x be the cost of a bus ride.
x + (x+685) = 945
2x = 260
x = $1.30
The answer is A.
Answer: (A) $1.30
Question: The sum of three consecutive integers is 102. Find the lowest of the three?
(A) 15
(B) 33
(C) 56
(D) 96
(E) 88
Rationale: Explanation:
Three consecutive numbers can be taken as (P - 1), P, (P + 1).
So, (P - 1) + P + (P + 1) = 102
3P = 102 => P = 34.
The lowest of the three = (P - 1) = 34 - 1 = 33.
Answer B
Answer: (B) 33
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 12 salespeople on staff, how many different arrangements of winners are possible?
(A) 1,728
(B) 1,440
(C) 1,320
(D) 220
(E) 6
Rationale: Choose 3 people out of 12 and arrange these 3 people between themselves.
12!/(3!x9!)x3!=12x11x10x9!/(3!x9!)x3!=12x11x10=1320
ANSWER:C
Answer: (C) 1,320
Question: The average of seven numbers is 21. The average of first three numbers is 19 and the average of last three numbers is 23. What is the middle number?
(A) 20
(B) 22
(C) 18
(D) 19
(E) 21
Rationale: The total of seven numbers = 7X21 = 147
The total of first 3 and last 3 numbers is = 3 X 19+3 X 23 = 126
So, the middle number is (147 - 126 ) = 21
E
Answer: (E) 21
Question: Which of the listed below number is the odd one out?
(A) 17642
(B) 36119
(C) 84129
(D) 67626
(E) 65612
Rationale: E
65612
All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.
Answer E
Answer: (E) 65612
Question: If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 7, inclusive?
(A) 1/4
(B) 1/8
(C) 3/8
(D) 3/16
(E) 5/16
Rationale: One case is rainy-rainy-rainy-not rainy.
The probability of this case is (1/2)^4 = 1/16
The number of possible cases is 4C3 = 4.
P(exactly 3 rainy days) = 4*1/16 = 1/4
The answer is A.
Answer: (A) 1/4
Question: 1: 3 = 1 2/3: x. The value of x is?
(A) 1
(B) 6
(C) 7
(D) 5
(E) 8
Rationale: x * 1 = 3 * 5/3
x = 5
Answer: D
Answer: (D) 5
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 2: 30 p.m., at what time were there 32 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 6: 00 a.m.
(D) 8: 30 a.m.
(E) 10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 2H30 PM, we get 8H30 AM as the answer.
Option D
Answer: (D) 8: 30 a.m.
Question: If A:B:C = 2:3:4, then find AB:BC:CA
(A) 5:9:24
(B) 6:9:24
(C) 7:9:24
(D) 8:9:24
(E) None of these
Rationale: Explanation:
Let A = 2x, B = 3x, C = 4x, then,
AB=2x3x=23BC=3x4x=34CA=4x2x=21=>AB:BC:CA=23:34:21=8:9:24
Answer: D
Answer: (D) 8:9:24
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 170, what is the least possible value of n?
(A) 14
(B) 13
(C) 15
(D) 17
(E) 16
Rationale: 17, since n needs to be the largest of the prime factors. Therefore, the answer is D.
Answer: (D) 17
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 27 7/8
(B) 27 9/9
(C) 28 7/9
(D) 27 7/9
(E) 21 7/9
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9
= 27 7/9 m.
Answer: D
Answer: (D) 27 7/9
Question: Find the one which does not belong to that group ?
(A) 27
(B) 66
(C) 88
(D) 65
(E) 11
Rationale: Explanation:
37, 47, 67 and 17 are prime numbers but not 27.
Answer: A
Answer: (A) 27
Question: A fill pipe can fill 2/3 of cistern in 40 minutes in how many minutes, it can fill full of the cistern?
(A) 60min
(B) 36min
(C) 25min
(D) 30min
(E) 50min
Rationale: 2/3 of the cistern can fill in 40 min
3/3 of the cistern can fill in = 40*3/2*3/3 = 60min
Answer is A
Answer: (A) 60min
Question: A man has some hens and cows. If the number of heads be 60 and the number of feet equals 200, then the number of hens will be:
(A) 22
(B) 25
(C) 24
(D) 20
(E) 28
Rationale: Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 60 .... (i)
and 2x + 4y = 200 x + 2y = 100 .... (ii)
Solving (i) and (ii) we get: x = 20, y = 40.
The required answer = 20.
Answer: D
Answer: (D) 20
Question: x is a positive integer less than 600. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=600
n=25.42
or n= 25
Answer:- E
Answer: (E) 25
Question: How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}
(A) 16
(B) 65
(C) 86
(D) 82
(E) 60
Rationale: The given digits are 1, 2, 3, 5, 7, 9
A number is even when its units digit is even. Of the given digits, two is the only even digit.
Units place is filled with only '2' and the remaining three places can be filled in ⁵P₃ ways.
Number of even numbers = ⁵P₃ = 60.
Answer: E
Answer: (E) 60
Question: There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number?
(A) 5
(B) 7
(C) 11
(D) 13
(E) 15
Rationale: (385/1001) = 5/13 First Number is 5
ANSWER:A
Answer: (A) 5
Question: A group of 4th graders and 5th graders is going on a field trip to the zoo. Only 20% of the students remembered to bring written permission from their parents. If 40% of the students are 4th graders and 25% if the 4th graders remembered to bring written permission, what percentage of the students are 5th graders who forgot to bring written permission?
(A) 10%
(B) 30%
(C) 50%
(D) 60%
(E) 80%
Rationale: Assume that the total number of students is 100.
=> 20 students got permission from their parents, 40 students are 4th graders, and 10 of the 4th graders got permission from their parents
=> 30 of the 5th graders got written permission
=> 30 of the 5th graders did not get written permission (there are 60 students who are 5th graders)
=> 50% of the 5th graders didn't get permission
Option (C)
Answer: (C) 50%
Question: If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?
(A) 1/32
(B) 2/25
(C) 5/16
(D) 8/25
(E) 3/4
Rationale: From July 4 to July 8, we have total of 5 days. Prob of raining on exactly 3 days = 5C3∗(1/2)3∗(1/2)25C3∗(1/2)3∗(1/2)2
= 5/16
ANS: C
Answer: (C) 5/16
Question: What is the percentage increase in area when a triangle is cloned (so that we have two triangles in total) and the resulting two triangles are joined on their bases to form a parallelogram ?
(A) 100%
(B) 150%
(C) 300%
(D) 120%
(E) 140%
Rationale: area of a triangle having base b and height h given by 1/2(b*h)
when two triangles are mounted onto their bases to form a parallelogram, then area would become b*h
percentage increase of area= (new area- area of original triangle)/(area of the original triangle) X 100%
=(b * h)-1/2(b*h) /1/2(b * h) * 100%
= (1-1/2) / (1/2)X100%
=100%
ANSWER:A
Answer: (A) 100%
Question: When a commodity is sold for Rs.34.80, there is a loss of 2%. What is the cost price of the commodity?
(A) Rs.26.10
(B) Rs.43
(C) Rs.43.20
(D) Rs.46.40
(E) None
Rationale: Solution
C.P	= Rs.(100 / 75×34.80)
= Rs.46.40.
Answer D
Answer: (D) Rs.46.40
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.1 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
(A) $1.62
(B) $1.85
(C) $2.00
(D) $2.15
(E) $2.30
Rationale: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $8.25 (a 10-cent increment) and the the difference in sequential prices of the pots is 10 cents, the largest pot PROBABLY has a price that is a 10-cent increment. From the answer choices, I would then TEST Answer A first
IF....
The largest pot = $1.625
1.125
1.225
1.325
1.425
1.525
1.625
Total = $8.25
So this MUST be the answer.
A
Answer: (A) $1.62
Question: Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?
(A) A16
(B) G4
(C) E4
(D) E3
(E) F2
Rationale: Answer: Option C
The letters decrease by 1; the numbers are multiplied by 2.
Answer: (C) E4
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 20 miles per gallon, and from Town B to Town C, the car averaged 24 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
(A) 40
(B) 30
(C) 42
(D) 33
(E) 35
Rationale: step 1) took LCM of 20 and 24.. came as 120.
step 2) 120 distance between B to C... do 120/24 hence 5 gallons used
step 3) twice distance.. hence 120*2= 240... do as above.. 240/20= 7 gallons used
step 4) total gallons.. 5+7= 12 gallons
step ) total miles= 120+240= 360 miles
hence.. average of whole journey = 360/12 which comes to 30
Answer : B
Answer: (B) 30
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
(A) 278
(B) 370
(C) 237
(D) 482
(E) 223
Rationale: 20000(11/10)4 - 20000(6/5)2
= 482
Answer:D
Answer: (D) 482
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 37 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
(A) 17 litres
(B) 24.67 litres
(C) 11 litres
(D) 24.07 litres
(E) 38.67 litres
Rationale: 262.85(37)+3,104.35x = 1,399.45(37 + x)
Solve the equation.
262.85(37)+3,104.35x = 1,399.45(37 + x)
9725.45+ 3,104.35x = 51779.65+ 1,399.45x
9725.45 + 1,704.9x = 51779.65
1,704.9x = 42054.2
x ≈ 24.67
Answer is B.
Answer: (B) 24.67 litres
Question: Rashmi can do a piece of work in 16 days. Ravina can do the same work in 12 days while Gitika can do it in 32 days. All of them started to work together but Rashmi leaves after 4 days. Ravina leaves the job 3 days before the completion of the work. How long the work last?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: x/3=x/6+3
x=18.
ANSWER:E
Answer: (E) 18
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $2200 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
(A) $3,750
(B) $19,800
(C) $8,100
(D) $15,000
(E) $22,500
Rationale: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $2200 triples to $6600, in 28 years, it will again triple to $6600*3=$19,800
Answer B
Answer: (B) $19,800
Question: a clock is such that it looses 4 min every day.the clock is set right on feb 25,2008 2 p.m.how many min should be added to get the right time when the clock shows 9 am on 3rd march 2008?
(A) 9:07am
(B) 9:17am
(C) 9:27am
(D) 9:37am
(E) 8:27am
Rationale: There are 6days from 25th feb to 2nd march i.e(25-26,26-27,27-28,28-29,29-1,1-2)
so (6*24)=144 hrs
and of 3rd march(24-5)=19hrs will be counted
so total hrs=163hrs
as mentioned in que clock looses 4 mins in 24hrs
In 24hrs clock looses =4mins
hence in 163 hrs clock looses=(4/24)*163=27 mins 16 secs
The Question is to calculate no. of minutes to be added when clock shows 9.00AM
Therefore,the correct time will be 9:27am
ANSWER:C
Answer: (C) 9:27am
Question: Tom bought 2 shares and sold them for $91 each. If he had a profit of 30% on the sale of one of the shares but a loss of 9% on the sale of the other share, then on the sale of both shares Tom had
(A)  a profit of $12
(B)  a loss of $10
(C)  a loss of $12
(D)  a profit of $10
(E)  neither a profit nor a loss
Rationale: total CP = 9100/130 + 9100/91 = 70 + 100=170
SP=91*2=182
profit= Rs 12/+
Answer: A
Answer: (A)  a profit of $12
Question: In 1991, there are 28 days in February and there are 365 days in the year. In 1992, there are 29 days in February and there are 366 days in the year. If the date September 15, 1995 is a Monday, then which one of the following would the date September 15, 1996 be?
(A) Tuesday
(B) Wednesday
(C) Thursday
(D) Friday
(E) Saturday
Rationale: From the information given,September 15, 1992 is 366 days after September 15, 1991.
366 days = 52 weeks and 2 more days. Therefore if March 15, 1995 is a Monday, then March 15, 1996 is Monday + 2 days = Wednesday
Answer: B
Answer: (B) Wednesday
Question: In the rectangular coordinate system, what is the x-intercept of a line passing through (10, 3) and (−8, −6)?
(A) 4
(B) 2
(C) 0
(D) −2
(E) −4
Rationale: slope = rise/run = 9/18 = 1/2
The equation of the line is y = (1/2)x + b
3 = (1/2)(10) + b
b = -2
The equation of the line is y = (1/2)x - 2
To find the x-intercept, let y = 0:
0 = (1/2)x - 2
x = 4
The answer is A.
Answer: (A) 4
Question: The edges of a cuboid are 4 cm, 5 cm and 7 cm. Find the volume of the cuboid?
(A) 140
(B) 278
(C) 378
(D) 368
(E) 367
Rationale: 4*5*7
= 120
Answer: A
Answer: (A) 140
Question: A box contains five bulbs out of which 2 are defective. If two bulbs are chosen at random, find the probability that all the two bulbs are defective?
(A) 1/12
(B) 1/10
(C) 1/19
(D) 1/13
(E) 1/16
Rationale: Out of five, three are good and two are defective. Required probability
= 2C2/5C2
= 1/10
Answer:B
Answer: (B) 1/10
Question: A and B are two circles. The radius of A is twice as large as the radius of B. What is the ratio between the areas of the circles?
(A) 1:8.
(B) 1:2.
(C) 1:4.
(D) 1:16.
(E) 1:6.
Rationale: Given : The radius of A is twice as large as the radius of B. => R(a) = 2*R(b). The radius are in ratio of 1:2 thus the area will be in the ratio of square of radius. 1:4. Hence C.
Answer: (C) 1:4.
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.12000. A's share is?
(A) s.4000
(B) s.7200
(C) s.6000
(D) s.5750
(E) s.6750
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 12000 = 4000
ANSWER:A
Answer: (A) s.4000
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
(A) 1.7
(B) 2.5
(C) 3.6
(D) 3.9
(E) 4.5
Rationale: Option 'C'
Answer: (C) 3.6
Question: If n = 10p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: If n = 10p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 10p have.
p = 3 --> 10p = 30--> 30 has 4 even divisors: 2, 6, 10,30.
Answer: C.
Answer: (C)  Four
Question: How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
(A) 14
(B) 13
(C) 12
(D) 11
(E) 10
Rationale: The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers.
The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form.
So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number.
We get a total of 19−5=1419−5=14 numbers.
Answer A
Answer: (A) 14
Question: As x increases from 151 to 152, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
(A) II only
(B) II,III only
(C) I,II only
(D) I only
(E) III only
Rationale: On Increasing the value of x from 151 to 152
I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit
II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)
III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)
Answer: C
Answer: (C) I,II only
Question: In what ratio must tea at Rs.64 per Kg be mixed with tea at Rs.74 per Kg so that the mixture must be worth Rs.69 per Kg?
(A) 1 : 1
(B) 3 : 2
(C) 4 : 3
(D) 5 : 3
(E) None
Rationale: Required ratio = 500 : 500 = 1 : 1
Answer A
Answer: (A) 1 : 1
Question: Max left from a Pvt Company. Management hold his salary Rs. 35000/- for one month. Earlier Robert borrowed Rs. 17280/- from company. But Robert forgot that. After one month Robert asked his salary and accountant gives Rs.28500/- to him. What is the incentive amount given to Robert?
(A) A)9500
(B) B)12500
(C) C)10780
(D) D)10500
(E) E)8600
Rationale: Total Salary = Rs.35000/-
Borrowed Money = 17280/-
Balance Salary = 35000-17280= 17720
Paid amount = 28500/-
Incentive amount = 28500-17720 = 10780/-
Answer is C
Answer: (C) C)10780
Question: In an examination, 32% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
(A) 975
(B) 1020
(C) 1100
(D) 1243
(E) 1525
Rationale: Failed in 1st subject = 32*2500/100 = 800
Failed in 2nd subject = 42*2500/100 = 1050
Failed in both = 15*2500/100 = 375
Failed in 1st subject only = 800-375 = 425
Failed in 2nd subject only = 1050-375 = 675
Passed in either subject but not in both = 675+425 = 1100
Answer is C
Answer: (C) 1100