divelab/Sys2Bench huggingface dataset:
Question: A man took some money for borrowed, for 3 years the total will be Rs.6000 and 5 years it will be Rs.7000/-. Then how much amount he borrowed?
Options:
A)s.4000/-
B)s.4500/-
C)s.4770/-
D)s.4800/-
E)s.4820/-
Rationale: 3 years --------> Rs.6000/-
5 years --------> Rs.7000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.6000/- - Rs.1500/- = Rs.4500/-
P = Rs.4500/-
B
Answer: B
Question: If 1/a + 3/a + 3/a is an integer, which of the following must also be an integer?
Options:
A)12/a
B)3/a
C)7/a
D)9/a
E)15/a
Rationale: 1/a + 3/a + 3/a
=7/a
Answer C
Answer: C
Question: The H.C.F. of two numbers is 63 and the other two factors of their L.C.M. are 11 and 17. The larger of the two numbers is:
Options:
A)3421
B)2132
C)1111
D)4323
E)1071
Rationale: :	Explanation:
Clearly, the numbers are (63 x 11) and (63 x 17).
{\color{Blue} \therefore } Larger number = (63 x 17) = 1071.
Answer: E)1071
Answer: E
Question: At a local supermarket, a box of cereal usually costs 13 dollars. This week, the supermarket sells the box of cereal for 7 dollars. How much money will you save if you buy this cereal at this supermarket?
Options:
A)5 dollars
B)3 dollars
C)4 dollars
D)2 dollars
E)6 dollar
Rationale: Solution:
In this situation, there is a decrease in the price.
Saving = 13 - 7 = 6 dollars
Option E
Answer: E
Question: A is twice as good a workman as B and together they finish a piece in 18 days. In how many days will A alone finish the work?
Options:
A)25 days
B)26 days
C)23 days
D)45 days
E)27 days
Rationale: Sol. (A’s 1 day’s work):)(B’s 1 days work) = 2 : 1.
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1.
:. A’s 1 day's work =(1/18*2/3)=1/27
Hence, A alone can finish the work in 27 days.
Ans: E
Answer: E
Question: For four days of work, a clerk had daily earnings of $160, $150, $160, and $160 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
Options:
A)Between $10 and $50
B)Between $0 and $10
C)Between $20 and $25
D)Between $50 and $100
E)Between $50 and $65
Rationale: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(150-(160*3+150)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : B
Answer: B
Question: Sophia finished 2/3 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
Options:
A)270
B)260
C)250
D)230
E)None
Rationale: Solution:
Let x be the total number of pages in the book, then she finished 2/3⋅x pages.
Then she has x−2/3⋅x=1/3.x pages left.
2/3⋅x - 1/3.x=90
1/3.x=90
x=270
So the book is 270 pages long.
Answer A
Answer: A
Question: The average score of a cricketer for six matches is 36 runs. If the average for first four matches is 32, then average for last 2 matches is
Options:
A)48
B)46
C)44
D)34.5
E)35.5
Rationale: Explanation:
=(36×6)−(32×4)/2
=(216−128)/2=44
Answer: Option C
Answer: C
Question: A group of 11 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
Options:
A) E/(12 - n)
B) (12 - n)/E
C) E/[12(12-n)]
D) nE / [11(11-n)]
E) (12-n)E/(12n)
Rationale: total cost =E
no of people willing to participate initially =11
initial cost for each =E/11
when n people decided not to participate
Cost for each =E/11-n
D
Answer: D
Question: The cost price of 17 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)58 2/91%
B)54 6/11%
C)58 9/11%
D)58 2/91%
E)52 2/11%
Rationale: 17 CP = 11 SP
11 --- 2 CP
100 --- ? =>54 6/11%
Answer:B
Answer: B
Question: 10 men, working 7 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ?
Options:
A)4 hours a day
B)5 hours a day
C)6 hours a day
D)7 hours a day
E)8 hours a day
Rationale: Explanation:
More Men, Less Hours {Indirect Proportion}
Less Days, More Hours {Indirect Proportion}
[men 15 10
days 12 18] ::7:x
=>xâˆ—15âˆ—12=10âˆ—18âˆ—7
=>x=10âˆ—18âˆ—7/ 15âˆ—12
=>x=7
Option D
Answer: D
Question: Consider the sets Tn = {n, n + 1, n + 2, n + 3, n + 4}, where n = 1, 2, 3,...., 72. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, ...)?
Options:
A)(a) 80
B)(b) 81
C)(c) 60
D)(d) 83
E)(e) 84
Rationale: T1: 1,2,3,4,5
T2: 2,3,4,5,6
T3: 3,4,5,6,7
etc.
means that every multiple of 6 will be involved in 5 sets. We have (72-6)/6+1=12 such multiples.
So, final number of sets is 12*5=60
Answer : C
Answer: C
Question: Lloyd normally works 7.5 hours per day and earns $5.50 per hour. For each hour he works in excess of 7.5 hours on a given day, he is paid 1.5 times his regular rate. If Lloyd works 10.5 hours on a given day, how much does he earn for that day?
Options:
A)$33.75
B)$47.25
C)$51.75
D)$54.00
E)$66.00
Rationale: Daily working hour*Regular Rate + Overtime*Increased Rate
7.5*5.5+ 3*5.5*1.5=66.00
Answer E
Answer: E
Question: The forth proportional to 100,200,300 is?
Options:
A)200
B)600
C)750
D)450
E)1000
Rationale: Let the fourth proportional to 100,200,300 be x
then 100:200::300:x
100x = 200*300
x = 600
Answer is B
Answer: B
Question: If the speed of X meters per second is equivalent to the speed of Y kilometers per minute, what is Y in terms of X? (1 kilometer=1000 meters)
Options:
A)0.06x
B)6x/5
C)18x/5
D)60x
E)3600000x
Rationale: x=1000y/60
y = 0.06x
Answer : A
Answer: A
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
Options:
A)1
B)5
C)4
D)8
E)9
Rationale: C
Four
three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: C
Question: If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true?
I.	The slope of L is positive
II.	L exactly passes through origin
III.	The slope of L is negative
Options:
A)III only
B)II only
C)I only
D)I and II only
E)II and III only
Rationale: Let (m,n) = (2,3)
(-m,-n) = (-2,-3)
Slope = (3+3)/(2+2) = 6/4 = 3/2
So III may not be true
Let (m,n) = (2,-3) then (-m,-n) = (-2,3)
So slope = (3 +3)/(-2-2) = -3/2
so I may not be true
So such a line would be -> (y - 3) = 3/2(x - 2)
=> 2y - 6 = 3x - 6
=> 2y - 3x = 0, hence no x or y intercept, so it passes through origin.
II is true.
Answer - B
Answer: B
Question: 85% of a number is added to 24, the result is the same number. Find the number?
Options:
A)28
B)288
C)279
D)160
E)232
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: D
Question: There are 5 boxes of different weights. They are weighed in pairs taken 2 at a time and the weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121. What is the sum of the weights of the 5 boxes ?
Options:
A)250
B)289
C)290
D)295
E)305
Rationale: Let the 5 boxes be a, b, c, d and e. The ten weights correspond to all the possible combinations of 2 weights out of 5.
On adding all the given weights, each boxes weight gets added 4 times:
a+b, a+c, a+d, a+e.
Similarly for b:
b+c, b+d, b+e and a+b (already included above)
Similarly for c, d and e.
Therefore, 110+112+113+114 .....+120+121 = 4* (a+b+c+d+e)
or, 4* (a+b+c+d+e) = 1156
or, (a+b+c+d+e) = 1156/4 = 289
ANSWER:B
Answer: B
Question: The average of 5 quantities is 10. The average of 3 of them is 4. What is the average of remaining 2 numbers?
Options:
A)19
B)14
C)8
D)9.5
E)None of these
Rationale: ANSWER: A
(5x10-3x4)/2=19
Answer: A
Question: John needs 4 balls out of 10 balls.How many ways are possible?
Options:
A)1050
B)220
C)630
D)540
E)720
Rationale: The possible way is 10C4
10C4=10!/6!*4!=10*9*8*7*6!/6!*4*3*2*1
=630 ways
Ans:option C
Answer: C
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Options:
A)4800
B)4991
C)5004
D)5000
E)5002
Rationale: Explanation:
Let the sale in the sixth month =x=x
Then 6435+6927+6855+7230+6562+x/6=6500
=> 6435+6927+6855+7230+6562+ =6×6500
=> 34009+x=39000
=> x=39000−34009=4991
Answer: Option B
Answer: B
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
Options:
A)2:3:5
B)3:4:7
C)4:5:9
D)6:5:9
E)None of these
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336 = 3:4:7
ANSWER:B
Answer: B
Question: What is the greatest value of n such that 30!/6^n is an integer?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: 30/2 + 30/(2^2)+30/(2^3)+30(2^4) = 15+7+3+1=26
How many 3's are there ? so that the division leads to be an integer
30/3 + 30/(3^2)+30/(3^3)= 10+3+1=14
How many 3's and 2's are there so that the division leads to be an integer
Minimum or common between 26 and 14.
Answer is 14.
ANSWER:D
Answer: D
Question: Each of the dogs in a certain kennel is a single color. Each of the dogs in the kennel either has long fur or does not. Of the 45 dogs in the kennel, 26 have long fur, 30 are brown, and 8 are neither long-furred nor brown. How many long-furred dogs are brown?
Options:
A)26
B)19
C)11
D)8
E)6
Rationale: No of dogs=45
Long fur=26
Brown=30
Neither long fur nor brown=8
Therefore, either long fur or brown=45-8=37
37=26+30-Both
Both=19
Answer B
Answer: B
Question: If v persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
Options:
A)z
B)x
C)x/y
D)z/x
E)y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
v person can do z jobs in y days..
so v person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: E
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent F of the gasoline in the tank is brand Z?
Options:
A)50%
B)40%
C)37.5%
D)331⁄3%
E)25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) F= 3/8 = 37.5%
Answer (C)
Answer: C
Question: If 6887 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?
Options:
A)1 books
B)2 books
C)3 books
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 6887.
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 6887 = 29 and 27 is divisible by 9.
Hence, we need to remove 2 to this number for it to be divisible by 9
Correct Option: B
Answer: B
Question: Using all the letters of the word "SULOCHANA", how many words can be formed, which begin with M and end with M?
Options:
A)5040
B)2010
C)3028
D)6078
E)1025
Rationale: There are five letters in the given word.
Consider 9 blanks ....
The first blank and last blank must be filled with S and A all the remaining three blanks can be filled with the remaining 7 letters in 7! ways.
The number of words = 7! = 5040.
Answer:A
Answer: A
Question: If Ben's income is Rs 35000, calculate his savings given that his income and expenditure are in the ratio 7:4.?
Options:
A)Rs 4900
B)Rs 9800
C)Rs 9000
D)Rs 7000
E)Rs.15000
Rationale: Let the income and the expenditure of the person be Rs.7x and Rs.4x respectively.
Income, 7x = 35000 => x = 5000
Savings = Income - expenditure = 7x - 4x = 3x
So, savings = Rs.15000
Answer: E
Answer: E
Question: What is the perimeter of a regular polygon with sides of length 13 cm and internal angles measuring 144° each?
Options:
A)96 cm
B)108 cm
C)120 cm
D)130 cm
E)144 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 144*n
from here
n = 10
So perimeter becomes 13*10= 130
answer D
Answer: D
Question: Water is poured in a bath tub at a rate of 11 cubic meters per hour, the level of water in the bath tub rises at a rate of .3 meters per hour. Which of the following best approximates the diameter of the tank in meters?
Options:
A)√33
B)√10/2
C)2√35/3
D)5
E)7
Rationale: Here's my re-worked solution:
volume = 11 = pi (r^2)(0.3)
11 = 22/7 (3/10)(r^2)
10 = r^2
r = sqrt(35/3)
Diameter=2*sqrt(35/3)
Ans: C
Answer: C
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 8 m wide at the top and 2 m wide at the bottom and the area of cross-section is 770 sq m, the depth of cannel is?
Options:
A)150
B)152
C)154
D)156
E)158
Rationale: 1/2 * d (8+2)
= 770
d = 154
Answer: C
Answer: C
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
Options:
A)388
B)2998
C)277
D)500
E)271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85
5x/100 + 90 – 6x/100 = 85
x/100 = 5
=> x = 500.Answer: D
Answer: D
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options:
A)10/21
B)15/21
C)09/21
D)11/21
E)13/21
Rationale: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5×4/2×1)(7×6/2×1)=5×47×6=10/21
Answer is A.
Answer: A
Question: A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey ?
Options:
A)1 kmph
B)5 kmph
C)6 kmph
D)4 kmph
E)7 kmph
Rationale: Explanation:
Speed of Man = 5.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 7 kmph
Speed in UpStream = 4 kmph
Average Speed = (2 x 7 x 4)/11 = 5 kmph.
Answer: B
Answer: B
Question: In Town P, 60 percent of the population are employed, and 42 percent of the population are employed males. What percent of the employed people in Town P are females?
Options:
A)20%
B)25%
C)30%
D)35%
E)40%
Rationale: The percent of the population who are employed females is 60-42 = 18%
The percent of employed people who are female is 18% / 60% = 30%.
The answer is C.
Answer: C
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
Options:
A)36
B)232
C)216
D)484
E)112
Rationale: number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216 Answer: C
Answer: C
Question: If F is the product of all positive integers less than 31, than what is the greatest integer k for which F/18^k is an integer?
Options:
A)3
B)6
C)7
D)14
E)26
Rationale: 30! F must be divisible by (3*3*2)^k.
As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18).
Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly.
3 6 9*
12 15 18*
21 24 27**
30
The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively.
3=3 (occurs 10 times) +10
3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3)
3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted)
Total: 14.
For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result.
Answer: 7 -> Answer choice: C.
Answer: C
Question: A and B together can complete a piece of work in 4days. If A alone can complete the same work in 12days, in how many days, in how many days can B alone complete that work?
Options:
A)6
B)8
C)10
D)12
E)5
Rationale: (A+B)'s 1day's work = 1/4
A's 1day's work = 1/12
B's 1days's work = (1/4)-(1/12) = 1/6
Hence, B alone can complete the work in 6days.
Answer is A
Answer: A
Question: If f(x)= 5x^3- 2x+8 and g(y)= 5y-4, then g(f(x)) =
Options:
A)11x^2+4x+4
B)11x^2-12x+44
C)8x^3-8x+32
D)25x^3-10x+36
E)30x^3-12x+44
Rationale: g(f(x)) = 6(f(x)) -4 = 5(5x^3- 2x+8) - 4 = 25x^3-10x+36 =>D
Answer: D
Question: The sum of two consecutive number is 87. Which is the larger number?
Options:
A)42
B)43
C)44
D)45
E)46
Rationale: Let consecutive number be x, x+1
Therefore sum of the consecutive number is x + x+1=87
2x+1=87
2x=86
x=43
Therefore larger number is x+1=44
ANSWER:C
Answer: C
Question: A man can row upstream at 27 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)31
B)92
C)30
D)32
E)23
Rationale: US = 27
DS = 35
M = (35 + 27)/2 = 31
Answer:A
Answer: A
Question: In a certain circle there are 9 points. What is the number of the triangles connecting 4 points of the 9 points?
Options:
A)80
B)96
C)108
D)126
E)132
Rationale: IMO : D
HERE we have to select 4 points out of 9 points. Order is not important
So the answer will be 9c4 = 126
Answer D
Answer: D
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day?
Options:
A)$0.15
B)$0.20
C)$0.30
D)$0.40
E)$0.45
Rationale: We are given that orangeade is made on Day 1 with an EQUAL AMOUNT of water and orange juice. We can set this information up into a ratio using a variable multiplier:
W : OJ = x : x
Thus, orangeade quantity = amount of water + amount of OJ = x + x = 2x
We are next given that orangeade on Day 2 was made by mixing the SAME AMOUNT of orange juice with TWICE THE AMOUNT of water. We can set this information up into a ratio using a variable multiplier:
W : OJ = 2x : x
Thus, orangeade quantity = amount of water + amount of OJ = 2x + x = 3x
We also know that all orangeade made was sold and that the revenue on both days was the same. We can therefore set up the following equation:
Day 1 Revenue = Day 2 Revenue
That is,
(quantity sold Day 1)(price per glass Day 1) = (quantity sold Day 2)(price per glass Day 2)
Let a be the amount of orangeade a glass can hold, then
quantity sold Day 1 = the number of glasses of orangeade sold on Day 1 = 2x/a
Similarly,
quantity sold Day 2 = the number of glasses of orangeade sold on Day 2 = 3x/a
We also know that the price per glass on day 1 = $0.6
But we don’t know the price per glass on day 2, so let’s label it as variable p.
We now have:
(2x/a)(0.6) = (3x/a)(p)
Multiplying both sides by a, we have:
(2x)(0.6) = (3x)(p)
1.2x = 3xp
1.2 = 3p
p = 0.4
Thus, each glass of orangeade was sold for $0.40 on Day 2.
Answer D.
Answer: D
Question: There are 7 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set?
Options:
A)16
B)31
C)48
D)79
E)90
Rationale: We can select from 0 to 7 pens and from 0 to 9 books.
Thus the total possible ways to select objects is 8*10 = 80
We must subtract 1 for the case with 0 pens and 0 books.
The answer is D.
Answer: D
Question: X, Y and Z started a business X's investment is 2 times of Y's investment is 5 times of Z's investment. Find the profit of Y in the total profit of Rs. 3200
Options:
A)Rs. 25600
B)Rs. 8500
C)Rs. 1000
D)Rs. 8000
E)None of these
Rationale: Explanation:
X = 2Y and Y = 5Z
=> X : Y = 2:1 and Y : Z = 5 : 1
=> X : Y : Z = 10 : 5 : 1
Ratio of capitals of X, Y and Z = 10 : 5 : 1
Y's share = Rs.[(5/16) × 3200] = Rs. 1000
Answer: Option C
Answer: C
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
Options:
A)Rs.2589
B)Rs.2380
C)Rs.8868
D)Rs.2477
E)Rs.6271
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs. 2380.
Answer:B
Answer: B
Question: How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)3.5 years
B)4 years
C)4.5 years
D)5 years
E)6 years
Rationale: Time = (100 * 81) / (450 * 4.5) = 4 years
ANSWER:B
Answer: B
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 6 days. B can do the work alone in?
Options:
A)19
B)36
C)11
D)19
E)114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/6
6/x = 1/6 => x = 36
So, B takes 18 hours to finish the work.
Answer: B
Answer: B
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)26%
C)42%
D)27%
E)22%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: A
Question: If x^2 + 9/x^2 = 7, what is the value of x - 3/x
Options:
A)1
B)25
C)9
D)5
E)3
Rationale: To find : x-3/x. Let it be t.
=> x-3/x = t
=> (x^2 + 9/x^2) - 2*x*3/x = t^2 (Squaring both sides).
=> (7) - 2*3 = 1
=> t^2 = 1. Thus t=1 or t=-1.
Answer A
Answer: A
Question: If p is a natural number and p! ends with y trailing zeros, then the number of zeros that (5p)! ends with will be
Options:
A)(p+y) trailing zeros
B)(5p+y) trailing zeros
C)(5p+5y) trailing zeros
D)(p+5y) trailing zeros
E)none of them above
Rationale: for p = 10 trailing 0's =
10/5 = 2
for 5p,
50/5 = 10, 50/25 = 2 hence total is 12
Similarly,
for p = 20 trailing 0's = 20/5 = 4
for 5p, trailing 0's = 50/5 = 10, 50/25 = 2 hence total is 10 + 2 = 12
thus we observe,
number of 0's = p + y
example p = 20, y = 4 giving 24.
Hence A.
Answer: A
Question: Find out the next word in the series below...
FAG, GAF, HAI, IAH, ...?
Options:
A)GAK
B)JAK
C)HGF
D)JAH
E)KHG
Rationale: In first FAG it was reodering the first and last letters and these are the continuous alphabets
ANSWER:B
Answer: B
Question: If S=x^4 + y^4 = 100, then the greatest possible value of x is between
Options:
A)0 and 3
B)3 and 6
C)6 and 9
D)9 and 12
E)12 and 15
Rationale: My attempt:
If S=x^4+y^4=100, then the greatest possible value of x would be when y is minimum.
Let y^4 be 0. Now x^4 = 100. x should be definitely greater than 3 but less than 4. The only option that fits this range is B
Hence answer is --
b) 3 and 6.
Answer: B
Question: In a mixture of 60 litres, the ratio of acid to base is 2 : 1. If this ratio is to be 1 : 2, then the quantity of base (in litres) to be further added is
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Acid = 40 lts
Base = 20 lts
to make the ratio A:B = 1:2 ,
60 lts of base should be added
ANSWER:E
Answer: E