Mathematics Question bank from Jagdish’s Page for International
Education
If you consider
applying to graduate school or business school, then you’ve already seen all
the mathematics concepts on Jagdish’s Page for International Education.
Here is a small question bank which might help you in the GRE, SAT and GMAT examinations . You would have covered the relevant
mathematics concepts in school. No surprises—it’s all material you’ve seen
before. The only problem is, you may not have seen it
lately.
No
matter how much your memories of school algebra classes have dimmed, don’t
panic. The GRE SAT and the GMAT test a limited number of core concepts in
predictable ways. Certain topics come up in every test, and, chances are that
these topics will be expressed in much the same way; even some of the words and
phrases appearing in the questions are predictable. Since the tests are so
formulaic, I have created a question bank similar to questions you may
encounter in actual exam.
I
am hereby providing a checklist of concepts you’ll need for the exams. These
concepts are vital, not only because they are tested directly on every exam,
but also because you need to know how to perform these simpler operations in
order to perform more complicated tasks. I know the mathematics operations
mentioned in the following list are pretty basic, but make sure you know how
to do them.
i. Algebraic
expressions.
ii. Add, subtract,
multiply and divide fractions.
iii. Conversion of fractions to decimals.
iv. Add, subtract,
multiply, and divide signed numbers.
v. Solve a simple algebraic equation.
vi. Find a percent using the percent formula.
vii. Find an average.
viii. Find the areas
of rectangles, triangles, and circles.
Important Fact
The GRE will give you a
scaled quantitative score from 200 to 800. (The average score is 500.) This
score reflects your performance on the math portion of the GRE compared to all
other GRE test takers.
The
GMAT will give you a scaled quantitative score from 0 to 60. (The average score
is 30.) This score reflects your performance on the math portion of the test
compared to all other GMAT test takers.You will also
receive an overall score that reflects your performance on both the math and
the verbal portions of the test. This is a scaled score from 200 to 800.
GMAT
Mathematics
There are 37 questions
to be done in 75 minutes. Approximately two-thirds of the questions will be in
the Problem Solving format, and the remaining questions will be in the Data
Sufficiency format. About 10 of the questions in the GMAT CAT math section will
be experimental questions. These are questions that are being tested for use in
future tests, and are not scored. However, there is no way of telling the
experimental questions from the scored questions around them, and so you should
treat all questions as if they are scored.
Arithmetic—About half of all
questions.
Algebra—About a quarter of all questions.
Geometry—About a sixth of all questions.
Graphs, logic questions, and other miscellaneous question types occur from time
to time.
About half of all questions are presented in the form of word problems.
Important fact- GRE Mathematics
There
are 28 questions to be done in 45 minutes. Approximately half of the questions
will be in the Quantitative Comparison format and the remaining questions will
be in the Problem Solving format. About a quarter of the Problem Solving questions will ask you to interpret a set of charts
or graphs.
Arithmetic—About a third of all
questions.
Algebra—About a sixth of all questions.
Geometry—About a third of all questions.
Graphs—About a sixth of all questions.
About a quarter of all questions are presented in the form of word problems.
Question bank
1. How many four digit numbers exist which can be
formed by using the digits 2, 3, 5 and 7 once only such that they are divisible
by 25?
A. 4! - 3! B. 4
C. 8 D. 6
2. A certain number when successfully divided by
8 and 11 leaves remainders of 3 and 7 respectively. What will be remainder
when the product of 8 and 11, viz 88, divides the
number?
A. 3 B. 21
C. 59 D. 68
3. a’ and ‘b’ are the
lengths of the base and height of a right-angled triangle whose hypotenuse is
‘h’. If the values of ‘a’ and ‘b’ are positive integers, which of the following
cannot be a value of the square of the hypotenuse?
A. 13 B. 23
C. 37 D. 41
4. What is the reminder when 91 + 92 + 93 + ... +
6 divide 99?
A. 0 B. 3
C. 4 D. None of these
5. What is the longest gap that any person will
have to wait between two birthdays?
A. 365 days
B. 366 days
C. 4 years
D. 8 years
6. The largest number amongst the following that
will perfectly divide 101100 - 1 is:
A. 100
B. 10,000
C. 100,100
D. 100,000
7. What is the highest power of 7 in 5000? (5000!
means factorial 5000):
A. 4998 B. 714
C. 832 D. 816
8. What is the total number of different divisors
including 1 and the number that can divide the number 6400?
A. 24 B. 27
C. 54 D. 68
9. How many times will the digit ‘0’ appear
between 1 and 10,000?
A. 4000 B. 4003
C. 2893 D. 3892
10. What is the total number of different divisors
of the number 7200?
A. 20 B. 4
C. 54 D. 32
11. What is the least number that should be
multiplied to 100! To make it perfectly divisible by 350?
A. 144 B. 72
C. 108 D. 216
12. Two
numbers when divided by a certain divisor leave remainders of 431 and 379
respectively. When the sum of these two numbers is divided by the same divisor,
the remainder is 211. What is the divisor?
A. 599
B. 1021
C. 263
D. Cannot be determined
13. The question for the day is from the topic of
Number Systems. How many zeros contained in 100!?
A. 100
B. 24
C. 97
D. Cannot be determined
14. A trader buys goods at a 19% discount on the
label price. If he wants to make a profit of 20% after allowing a discount of
10%, by what % should his marked price be greater than the original label
price?
A. +8%
B. -3.8%
C. +33.33%
D. None of these
15. If apples are bought at the rate of 30 for a
rupee. How many apples must be sold for a rupee so as to gain 20%?
A. 28 B. 25
C. 20 D. 22
16. One-year payment to
the servant is Rs. 200 plus one shirt. The servant
leaves after 9 months and receives Rs. 120 and a
shirt. Then find the price of the shirt.
A. Rs. 80
B. Rs. 100
C. Rs. 120
D. Cannot be determined
17. A merchant marks his goods in such a way that
the profit on sale of 50 articles is equal to the selling price of 25 articles.
What is his profit margin?
A. 25% B. 50%
C. 100% D. 66.67%
18. Which is greater of the two:
A. 2300
B. 3200
C. Both are equal
D. Cannot be determined
19. What is the value of M and N respectively? If
M39048458N is divisible by 8 & 11; where M & N are single digit
integers?
A. 7, 8 B. 8, 6
C. 6, 4 D. 5, 4
20. A number when divided by a divisor leaves a
remainder of 24. When twice the original number is divided by the same divisor,
the remainder is 11. What is the value of the divisor?
A. 13 B. 59
C. 35 D. 37
21. When 26854 and 27584 are divided by a certain
two-digit prime number, the remainder obtained is 47. Which of the following
choices is a possible value of the divisor?
A. 61 B. 71
C. 73 D. 89
22. What is the value of M and N respectively? If
M39048458N is divisible by 8 and 11; where M and N are single digit integers?
A. 7, 8 B. 8, 6
C. 6, 4 D. 5, 4
23. A candidate who gets 20% marks fails by 10
marks but another candidate who gets 42% marks gets 12% more than the passing
marks. Find the maximum marks.
A. 50 B. 100
C. 150 D. 200
24. A trader makes a profit equal to the selling
price of 75 articles when he sold 100 of the articles. What % profit did he
make in the transaction?
A. 33.33% B. 75%
C. 300% D. 150%
25. A merchant buys two articles for Rs.600. He
sells one of them at a profit of 22% and the other at a loss of 8% and makes no
profit or loss in the end. What is the selling price of the article that he
sold at a loss?
A. Rs. 404.80
B. Rs. 440
C. Rs. 536.80
D. Rs. 160
26. When 36 divide a number, it leaves a remainder
of 19. What will be the remainder when 12 divide the number?
A. 10 B. 7
C. 11 D. None of these
27. Anita had to do a multiplication. Instead of
taking 35 as one of the multipliers, she took 53. As a result, the product went
up by 540. What is the new product?
A. 1050 B. 540
C. 1440 D. 1590
28. Let n be the number of different 5 digit
numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being
repeated in the numbers. What is the value of n?
A. 144 B. 168
C. 192 D. None of these
29. When 242 is divided
by a certain divisor the remainder obtained is 8. When the same divides 698
divisor the remainder obtained is 9. However, when the sum of the two numbers 242
and 698 is divided by the divisor, the remainder obtained is 4. What is the
value of the divisor?
A. 11 B. 17
C. 13 D. 23
30. When 26854 and 27584 are divided by a certain
two-digit prime number, the remainder obtained is 47. Which of the following
choices is a possible value of the divisor?
A. 61 B. 71
C. 73 D. 89
31. 30% of the men are more than 25 years old and
80% of the men are less than or equal to 50 years old. 20% of all men play
football. If 20% of the men above the age of 50 play football, what percentage
of the football players are less than or equal to 50 years?
A. 15% B. 20%
C. 80% D. 70%
32. Peter got 30% of the maximum marks in an
examination and failed by 10 marks. However, Paul who took the same examination
got 40% of the total marks and got 15 marks more than the passing marks. What
were the passing marks in the examination?
A. 35 B. 250
C. 75 D. 85
33. If the price of petrol increases by 25%, by
how much must a user cut down his consumption
so that his expenditure on petrol remains constant?
A. 25% B. 16.67%
C. 20% D. 33.33%
34. If
the cost price of 20 articles is equal to the selling price of 16 articles,
what is the percentage of profit or loss that the merchant makes?
A. 20% Profit B. 25% Loss
C. 25% Profit D. 33.33% Loss
35. A trader professes to sell his goods at a loss
of 8% but weights 900 grams in place of a kg weight. Find his real loss or gain
percent.
A. 2% loss
B. 2.22% gain
C. 2% gain
D. None of
these
36. Ronald sold an article for Rs.
56, which cost him Rs. x. If he had
gained x% on his outlay, what was his cost?
A. Rs. 40 B. Rs. 45
C. Rs. 36 D. Rs. 28
37. What is the angle between the minute hand and
the hour hand when the time is 1540 hours?
A. 150 B. 160
C. 140 D. 130
38. A merchant marks his goods up by 75% above his
cost price. What is the maximum % discount that he can offer so that he ends
up selling at no profit or loss?
A. 75% B. 46.67%
C. 300% D. 42.85%
39. A merchant marks his goods up by 60% and then
offers a discount on the marked price. If the final selling price after the
discount results in the merchant making no profit or loss, what was the
percentage discount offered by the merchant?
A. 60%
B. 40%
C. 37.5%
D. Depends
on the cost price
40. Given A = 265 and B = (264+263+262+...+20)
A. B is 264 larger than A
B. A and B are equal
C. B is larger than A by 1
D. A is larger than B by 1
41. The sum of third and ninth term of an A.P is
8. Find the sum of the first 11 terms of the progression.
A. 44
B. 22
C. 19
D. None of
these
42. If (x + 2) 2 = 9 and (y + 3) 2 = 25, then the
maximum value of x/y is.
A. 1/2 B. 5/2
C. 5/8 D. 1/8
43. The sum of the three numbers in A.P is 21 and
the product of their extremes is 45. Find the numbers.
A. 5, 7 and 9
B. 9, 7 and 5
C. Both (1) and
(2)
D. None of
these
44. Obtain the sum of all positive integers up to
1000, which are divisible by 5 and not divisible by 2.
A. 10050 B. 5050
C. 5000 D. 50000
45. A 4 cm cube is cut into 1 cm cubes. What is
the percentage increase in the surface area after such cutting?
A. 4% B. 300%
C. 75% D. 400%
46. If the diagonal and the area of a rectangle
are 25 m and 168 m2, what is the length of the rectangle?
A. 17 m B. 31 m
C. 12 m D. 24 m
47. A regular hexagon is inscribed in a circle of
radius r cms. What is the perimeter of the regular
hexagon?
A. 3r B. 6r
C. r D. 9r
48. The surface area of
the three coterminous faces of a cuboid are 6, 15, 10
sq.cm respectively. Find the volume of the cuboid.
A. 30 B. 20
C. 40 D. 35
49. The time in a clock is 20 minute past 2. Find
the angle between the hands of the clock.
A. 60 degrees
B. 120 degrees
C. 45 degrees
D. 50 degrees
50. How often between 11 O’clock and 12 O’clock
are the hands of the clock together at an integral number value?
A. 55 B. 56
C. 4 D. 5
51. At how many points between 10 O’clock and 11
O’clock are the minute hand and hour hand of a clock at an angle of 30 degrees
to each other?
A. 2 B. 4
C. 1 D. 3
52. Four dice are rolled simultaneously. What is
the number of possible outcomes in which at least one of the die shows 6?
A. 6!/4! B. 625
C. 671 D. 1296
53. There are 2 brothers among a group of 20
persons. In how many ways can the group be arranged around a circle so that
there is exactly one person between the two brothers?
A. 2 * 19! B. 18! * 18
C. 19! * 18 D. 2 * 18!
54. There are 12 yes or no questions. How many
ways can these be answered?
A. 1024 B. 2048
C. 4096 D. 144
55. The angle of
elevation of the top of a tower 30 m high, from two points on the level ground
on its opposite sides are 45 degrees and 60 degrees. What is the distance
between the two points?
A. 30 B. 51.96
C. 47.32 D. 81.96
56. A person starts multiplying consecutive
positive integers from 20. How many numbers should he multiply before the will
have result that will end with 3 zeroes?
A. 11 B. 10
C. 6 D. 5
57. 1025–7 is divisible by:
A. 2 B. 3
C. 9 D. Both (b) and (c)
58. The sum of the first
100 numbers, 1 to 100 is divisible by:
A. 2, 4 and 8
B. 2 and 4
C. 2 only
D. None of
these
The question for the day is from the topic of Number Systems.
59. How many zeros contained in 100!?
A. 100
B. 24
C. 97
D. Cannot be determined
60. In how many ways can
the letters of the word MANAGEMENT be rearranged so that the two As do not
appear together?
A. 10! - 2!
B. 9! - 1!
C. 10! - 9!
D. None of
these
The question for the day is from the topic permutation and
combination. Permutation and Combination is one area which if you are
reasonably comfortable, you will be able to answer questions in minimum time.
61. How many alphabets need to be there in a
language if one were to make 1 million distinct 3-digit initials using the
alphabets of the language?
A. 26 B. 50
C. 100 D. 1000
62. Which is greater of the two?
A. 2300
B. 3200
C. Both are equal
D. Cannot be determined
63. A vendor sells 60 percent of apples he had and
throws away 15 percent of the remainder. Next day he sells 50 percent of the
remainder and throws away the rest. What percent of his apples does the vendor
throw?
A. 17 B. 23
C. 77 D. None of these
65. Four horses are tethered at 4 corners of a
square field of side 70 meters so that they just cannot reach one another. The
area left ungrazed by the horses is:
A. 1050 sq.m B. 3850
sq.m
C. 950 sq.m D. 1075
sq.m
66. If each interior angle of a regular polygon is
150 degrees, then it is
A. Octagon B. Decagon
C. Dodecagon D. Tetrahedron
67. A 5 cm cube is cut into as many 1 cm cubes as
possible. What is the ratio of the surface area of the larger cube to that of
the sum of the surface areas of the smaller cubes?
A. 1: 6 B. 1: 5
C. 1: 25 D. 1: 125
68. If the sides of a triangle measure 72, 75 and
21, what is the measure of its in radius?
A. 37.5 B. 24
C. 9 D. 15
69. The area of a square field is 24200 sq m. how
long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?
A. 3 minutes
B. 2 minutes
C. 2.4 minutes
D. 2 minutes 40 seconds
70. Rs. 432 is divided
amongst three workers A, B and C such that 8 times A’s share is equal to 12
times B’s share which is equal to 6 times C’s share. How much did A get?
A. Rs.192 B. Rs.133
C. Rs.144 D. Rs.128
71. If 20 men or 24 women or 40 boys can do a job
in 12 days working for 8 hours a day, how many men working with 6 women and 2
boys take to do a job four times as big working for 5 hours a day for 12 days?
A. 8 men B. 12 men
C. 2 men D. 24 men
72. Two cogged wheels of which one has 32 cogs and
other 54 cogs, work into each other. If the latter turns 80 times in three
quarters of a minute, how often does the other turn in 8 seconds?
A. 48 B. 135
C. 24 D. None of these
73. The monthly salaries of two persons are in the
ratio of 4:7. If each receives an increase of Rs.25 in the salary, the ratio is
altered to 3: 5. Find their respective salaries.
A. 120 and 210
B. 80 and 140
C. 180 and 300
D. 200 and 350
74. The ratio of marks obtained by vini and
A. 150
B. 200
C. 400
D. None of
these
75. The present ages of A and B are as 6: 4. Five
years ago their ages were in the ratio 5: 3. Find their present ages.
A. 42, 28 B. 36, 24
C. 30, 20 D. 25, 15
76. A, B and C, each of them working alone can
complete a job in 6, 8 and 12 days respectively. If all three of them work
together to complete a job and earn Rs. 2340, what
will be C’s share of the earnings?
A. Rs. 520
B. Rs. 1080
C. Rs. 1170
D. Rs. 630
77. An express train traveling at 72 km/hr speed
crosses a goods train traveling at 45 km/hr speed in the opposite direction in
half a minute. Alternatively, if the express train were to overtake the goods
train, how long will it take to accomplish the task? Assume that the trains
continue to travel at the same respective speeds as mentioned in case 1.
A. Cannot be determined
B. 30 seconds
C. 150 seconds
D. 130 seconds
78. A boat travels from point A to point B
upstream and returns from point B to point A downstream. If the round trip
takes the boat 5 hours and the distance between point A and point B is 120 kms and the speed of the stream is 10 km/hr, how long did
the upstream journey take?
A. 2 hours 40 minutes
B. 2 hours 24 minutes
C. 3 hours
D. 2 hours
79. A train travels at an average speed of 90
km/hr without any stoppages. However, its average speed
decrease to 60km/hr on account of stoppages. On an average, how many
minutes per hour does the train stop?
A. 12 minutes
B. 18 minutes
C. 24 minutes
D. 20 minutes
80. Two trains A and B start simultaneously from
stations X and Y towards each other respectively. After meeting at a point between X and Y,
train A reaches station Y in 9 hours and train B reaches station X in 4 hours
from the time they have met each other. If the speed of train A is 36 km/hr,
what is the speed of train B?
A. 24 km/hr
B. 54 km/hr
C. 81 km/hr
D. 16 km/hr
81. A, B and C enter into a partnership by
investing Rs. 3600, Rs. 4400 and Rs. 2800. A is a working partner and gets a fourth
of the profit for his services and the remaining profit is divided amongst the
three in the rate of their investments. What is the amount of profit that B
gets if A gets a total of Rs. 8000?
A. 4888.88
B. 9333.33
C. 4000
D. 3666.66
82. The marks scored by a student in three subjects
are in the ratio of 4: 5: 6. If the candidate scored an overall aggregate of
60% of the sum of the maximum marks and the maximum marks in all three subjects
are the same, in how many subjects did he score more than 60%?
A. 1
B. 2
C. 3
D. None of the
subjects
83. How much number of times will the digit ‘7’ be written when listing the integers from 1 to 1000?
A. 271 B. 300
C. 252 D. 304
84. There are 5 Rock songs, 6
Fanatic songs and 3 Indy pop songs. How many different albums can be
formed using the above repertoire if the albums should contain at least 1 Rock
song and 1 Fanatic song?
A. 15624 B. 16384
C. 6144 D. 240
85. The monthly incomes of A and B are in the
ratio 4: 5; their expenses are in the ratio 5: 6. If ‘A’ saves Rs.25 per month
and ‘B’ saves Rs.50 per month, what are their respective incomes?
A. Rs. 400 and Rs. 500
B. Rs. 240 and Rs. 300
C. Rs. 320 and Rs. 400
D. Rs. 440 and Rs. 550
86. The proportion of
milk and water in 3 samples is 2:1, 3:2 and 5:3. A mixture comprising of equal
quantities of all 3 samples is made. The proportion of milk and water in the
mixture is
A. 2:1 B. 5:1
C. 99:61 D. 227:133
87. A group of workers can do a piece of work in
24 days. However as 7 of them were absent it took 30
days to complete the work. How many people actually worked on the job to
complete it?
A. 35 B. 30
C. 28 D. 42
88. A, B and C play cricket. A’s runs are to B’s
runs and B’s runs are to C’s as 3 : 2. They get
altogether 342 runs. How many runs did A make?
A. 162 B. 108
C. 72 D. None of these
89. How many five digit numbers can be formed
using the digits 0, 1, 2, 3, 4 and 5, which are divisible by 3, without
repeating the digits?
A. 15 B. 96
C. 216 D. 120
90. How many words can be formed by re-arranging
the letters of the word PROBLEMS such that P and S occupy the first and last
position respectively?
A. 8!/2!
B. 8! - 2!
C. 6!
D. 8! - 2*7!
91. How many ways can 4 prizes be given away to
3 boys, if each boy is eligible for all the prizes?
A. 256
B. 12
C. 81
D. None of
these
92. A team of 8 students goes on an excursion, in
two cars, of which one can seat 5 and the other only 4. In how many ways can
they travel?
A. 9 B. 26
C. 126 D. 3920
93. A team of 8 students goes on an excursion, in
two cars, of which one can seat 5 and the other only 4. In how many ways can
they travel?
A. 9 B. 26
C. 126 D. 3920
94. How many numbers are there between 100 and
1000 such that at least one of their digits is 6?
A. 648 B. 258
C. 654 D. 252
95. In how many ways can 15 people be seated
around two round tables with seating capacities of 7 and 8 people?
A. 15! /(8!)
B. 7! *8!
C. (15C8)*6!
*7!
D. 2*(15C7)*6!
*7!
96. When four fair dice are rolled simultaneously,
in how many outcomes will at least one of the dice show
3?
A. 155
B. 620
C. 671
D. 625
97. How many words of 4 consonants and 3 vowels
can be made from 12 consonants and 4 vowels, if all the letters are different?
A. 16C7 * 7!
B. 12C4 * 4
C. 3 * 7!
D. 12C4 * 4C3
98. In how many ways can
5 letters be posted in 3 post boxes, if any number of letters can be posted in
all of the three post boxes?
A. 5C3
B. 5P3
C. 53
D. 35
99. Train A traveling at 60 km/hr leaves Mumbai
for Delhi at 6 p.m. Train B
traveling at 90 km/hr also leaves Mumbai for Delhi at 9 p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all three trains meet at the
same time between Mumbai and
A. 60 km/hr
B. 90 km/hr
C. 120 km/hr
D. 135 km/hr
100. Two trains, 200 and 160 meters long take a
minute to cross each other while traveling in the same direction and take only
10 seconds when they cross in opposite directions. What are the speeds at which
the trains are traveling?
A. 21 m/s; 15 m/s
B. 30 m/s; 24 m/s
C. 18 m/s; 27 m/s
D. 15 m/s; 24 m/s
101. A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven 25%
faster on an average he would have reached 4 minutes earlier than the scheduled
time. How far is his office?
A. 24 km
A. 72 km
C. 18 km
D. Data
Insufficient
102. If the wheel of a bicycle makes 560 revolutions
in traveling 1.1 km, what is its radius?
A. 31.25 cm
B. 37.75 cm
C. 35.15 cm
D. 11.25 cm
103. A man and a woman 81 miles apart from each
other, start traveling towards each other at the same time. If the man covers 5
miles per hour to the women’s 4 miles per hour, how far will the woman have
traveled when they meet?
A. 27
B. 36
C. 45
D. None of
these
103. The speed of a motorboat itself is 20 km/h and
the rate of flow of the river is 4 km/h. moving with the stream the boat went
120 km. What distance will the boat cover during the same time going against
the stream?
A. 80 km
B. 180 km
C. 60 km
D. 100 km
104. A passenger train covers the distance between
stations X and Y, 50 minutes faster than a goods train. Find this distance if
the average speed of the passenger train is 60 kmph and that of goods train is 20 kmph.
A. 20 kms
B. 25 kms
C. 45 kms
D. 40 kms
105. I travel the first part of my journey at 40 kmph and the second part at 60 kmph
and cover the total distance of 240 km to my destination in 5 hours. How long
did the first part of my journey last?
A. 4 hours
B. 2 hours
C. 3 hours
D. 2 hours 24
minutes
106. Three friends A, B and C run around a circular
track of length 120 meters at speeds of 5 m/s, 7 m/sec and 15 m/sec, starting
simultaneously from the same point and in the same direction. How often will
the three of them meet?
A. Every 60 seconds
B. Every 120 seconds
C. Every 30 seconds
D. None of these
107. Jim travels the first 3 hours of his journey at
60 mph speed and the remaining 5 hours at 24 mph speed. What is the average
speed of Jim’s travel in mph?
A. 42 mph
B. 36 mph
C. 37.5 mph
D. 42.5 mph
108. A man can row 50 km upstream and 72 km
downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in
12 hours. Find the rate of current.
A. 3 km/hr
B. 8 km/hr
C. 4 km/hr
D. None of
these
109. A circle of maximum possible size is cut from a
square sheet of board. Subsequently, a square of maximum possible size is cut
from the resultant circle. What will be area of the final square?
A. 75% of the of the original square
B. 50% of the size of the original square
C. 75% of the size of the circle
D. 25% of the size of the original square
110. Each interior angle of a regular polygon is 120
degrees greater than each exterior angle. How many sides are there in the
polygon?
A. 6 B. 8
C. 12 D. 3
111. What is the area of the largest triangle that
can be fitted into a rectangle of length ‘l’ units and width ‘w’ units?
A. l w/3
B. (2l w)/3
C. (3l w)/4
D. (l w)/2
112. A stairway 10ft high is such that each step
accounts for half a foot upward and one-foot forward. What distance will an ant
travel if it starts from ground level to reach the top of the stairway?
A. 30 ft B. 33 ft
C. 10 ft D. 29 ft
113. Find the equation of a line whose intercepts
are twice of the line 3x – 2y – 12 = 0
A. 3x – 2y = 24
B. 2x – 3y = 12
C. 2x – 3y = 24
D. None of
these
114. Find the area of the sector covered by the hour
hand after it has moved through 3 hours and the length of the hour hand is 7cm.
A. 77 sq. cm
B. 38.5 sq. cm
C. 35 sq. cm
D. 70 sq. cm
115. Find the area of the triangle whose vertices
are (-6, -2), (-4, -6), (-2, 5).
A. 36
B. 18
C. 15
D. 30
116. Find the coordinates of the point which divides
the line joining (5, -2) and (9, 6) internally in the ratio 1: 3.
A. (6, 0)
B. (6, 3)
C. (0, 6)
D. (3, 6)
117. What is the circum radius
of a triangle whose sides are 7, 24 and 25 respectively?
A. 18
B. 12.5
C. 12
D. 14
118. If the sum of the interior angles of a regular
polygon measures up to 1440 degrees, how many sides does the polygon have?
A. 10 sides
B. 8 sides
C. 12 sides
D. 9 sides
119. In a km race, A gives
B a start of 20 seconds and beats him by 40 m. However, when he gives B a start
of 25 seconds they finish in a dead heat. What is A’s speed in m/sec?
A. 12.5 m/sec
B. 20 m/sec
C. 8 m/sec
D. 10 m/sec
120. A takes 3 min 45 seconds to complete a
kilometer. B takes 4 minutes to complete the same 1 km track. If A and B were to participate in a race of 2 kms, how much start can A give B in terms of distance?
A. 30 m B. 62.5 m
C. 125 m D. 250 m
121. In a kilometer race, A
can give B a start of 100 m or 15 seconds. How long does A
take to complete the race?
A. 150 seconds
B. 165 seconds
C. 135 seconds
D. 66.67
seconds
122. A gives B a start of 10 meters in a 100-meter
race and still beats him by 1.25 seconds. How long does B take to complete the
100-meter race if a runs at the rate of 10 m/sec?
A. 8 seconds
B. 10 seconds
C. 16.67
seconds
D. 12.5 seconds
123. A skating champion moves along the circumference
of a circle of radius 21 meters in 44 seconds. How many seconds will it take
her to move along the perimeter of a hexagon of side 42 meters?
A. 56 B. 84
C. 64 D. 48
124. A runs 13/5 times as fast as B. If A gives a start of 240m, how far must the post be so that A
and B might reach at the same time.
A. 390 m
B. 330 m
C. 600 m
D. 720 m
125. P can give Q a start of 20 seconds in a
kilometer race. P can give R a start of 200 meters in the same kilometer race.
And Q can give R a start of 20 seconds in the same kilometer race. How long
does P take to run the kilometer?
A. 200 seconds
B. 240 seconds
C. 160 seconds
D. 140 seconds
126. A gives B a start of 30 seconds in a km race
and still beats him by 20 m. However, when he gives B a start of 35 seconds,
they finish the race in a dead heat. How long does A take
to run the km?
A. 250 seconds
B. 285 seconds
C. 220 seconds
D. 215 seconds
Three runners A, B and C run a race, with runner A finishing 12 meters
ahead of runner B and 18 meters ahead of runner C, while runner B finishes 8
meters ahead of runner C. Each runner travels the entire distance at a constant
speed.
127. What was the length of the race?
A. 36 meters
B. 48 meters
C. 60 meters
D. 72 meters
128. A can give B a start of 50 meters or 10 seconds
in a kilometer race. How long does A take to complete
the race?
A. 200 seconds
B. 140 seconds
C. 220 seconds
D. 190 seconds
129. A can give B 20 points, A can give C 32 points
and B can give C 15 points. How many points make the game?
A. 150
B. 200
C. 100
D. 170
130. What is the probability of getting at least one
six in a single throw of three unbiased dice?
A. 1/6
B. 125/216
C. 1/36
D. 91/216
131. What is the probability that a two-digit number
selected at random will be a multiple of ‘3’ and not a multiple of ‘5’?
A. 2/15
B. 4/15
C. 1/15
D. 4/90
132. Two
squares are chosen at random on a chessboard. What is the probability that
they have a side in common?
A. 1/18
B. 64/4032
C. 63 / 64
D. 1/9
133. When two dice are thrown simultaneously, what
is the probability that the sum of the two numbers that turn up is less than
11?
A. 5/6
B. 11/12
C. 1/6
D. 1/12
134. An anti aircraft gun can fire four shots at a
time. If the probabilities of the first, second, third and the last shot
hitting the enemy aircraft are 0.7, 0.6, 0.5 and 0.4, what is the probability
that four shots aimed at an enemy aircraft will bring the aircraft down?
A. 0.084
B. 0.916
C. 0.036
D. 0.964
135. A number is selected at random from first
thirty natural numbers. What is the chance that it is a multiple of either 3 or
13?
C. 17/30
B. 2/5
C. 11/30
D. 4/15
137. In what ratio must a person mix three kinds of
tea costing Rs. 60/kg, Rs.
75/kg and Rs. 100/kg so that the resultant mixture
when sold at Rs. 96/kg yields a profit of 20%?
A. 1: 2: 4
B. 3: 7: 6
C. 1: 4: 2
D. None of
these
138. A 20-liter mixture of milk and water contains
milk and water in the ratio 3: 2. 10 liters of the mixture is removed and
replaced with pure milk and the operation is repeated once more. At the end of
the two removals and replacement, what is the ratio of milk and water in the
resultant mixture?
A. 17: 3
B. 9: 1
C. 3: 17
D. 5: 3
139. How many liters of water should be added to a
30-liter mixture of milk and water containing milk and water in the ratio of 7:
3 such that the resultant mixture has 40% water in it?
A. 7 liters
B. 10 liters
C. 5 liters
D. None of
these
140. A merchant mixes three varieties of rice
costing Rs. 20/kg, Rs.
24/kg and Rs. 30/kg and sells the mixture at a profit
of 20% at Rs. 30/kg. How many kgs
of the second variety will be in the mixture if 2 kgs
of the third variety is there in the mixture?
A. 1 kg
B. 5 kgs
C. 3 kgs
D. 6 kgs
141. A sample of x liters from a container having a
60 liter mixture of milk and water containing milk and water in the ratio of 2:
3 is replaced with pure milk so that the container will have milk and water in
equal proportions. What is the value of x?
A. 6 liters
B. 10 liters
C. 30 liters
D. None of
these
142. How many liters of a 12-liter mixture containing
milk and water in the ratio of 2: 3 are replaced with pure milk so that the
resultant mixture contains milk and water in equal proportion?
A. 4 liters B. 2 liters
C. 1 liter D. 1.5 liters
143. From a cask of milk
containing 30 liters, 6 liters are drawn out and the cask is filled up with
water. If the same process is repeated a second, then a third time, what will
be the number of liters of milk left in the cask?
A. 0.512 liters
B. 12 liters
C. 14.38 liters
D. 15.36 liters
144. A zookeeper counted the heads of the animals in
a zoo and found it to be 80. When he counted the legs of the animals he found
it to be 260. If the zoo had either pigeons or horses, how many horses were
there in the zoo?
A. 40 B. 30
C. 50 D. 60
145. A father left a will of Rs.
35 lakhs between his two daughters aged 8.5 and 16
such that they may get equal amounts when each of them reach the age of 21
years. The original amount of Rs. 35 lakhs has been instructed to be invested at 10% p.a. simple
interest. How much did the elder daughter get at the time of the will?
A. Rs. 17.5 lakhs
B. Rs. 21 lakhs
C. Rs. 15 lakhs
D. Rs. 20 lakhs
146. What will Rs.1500 amount to in three years if
it is invested in 20% p.a. compound interest, interest being compounded
annually?
A. 2400
B. 2592
C. 2678
D. 2540
147. If a sum of money grows to 144/121 times when
invested for two years in a scheme where interest is compounded annually, how
long will the same sum of money take to treble if invested at the same rate of
interest in a scheme where interest is computed using simple interest method?
A. 9 years
B. 22 years
C. 18 years
D. 33 years
148. The population of a town was 3600 three years
back. It is 4800 right now. What will be the population three years down the
line, if the rate of growth of population has been constant over the years and
has been compounding annually?
A. 6000
B. 6400
C. 7200
D. 9600
149. A man invests Rs.5000 for 3 years at 5% p.a.
compound interest reckoned yearly. Income tax at the rate of 20% on the
interest earned is deducted at the end of each year. Find the amount at the end
of the third year.
A. 5624.32
B. 5630.50
C. 5788.125
D. 5627.20
150. Vijay invested Rs.
50, 000 partly at 10% and partly at 15%. His total income after a year was Rs. 7000. How much did he invest at the rate of 10%?
A. Rs. 30, 000
B. Rs. 40, 000
C. Rs. 12, 000
D. Rs. 20, 000
151. The difference between the compound interest
and the simple interest on a certain sum at 12% p.a. for two years is Rs. 90. What will be the value of the amount at the end of
3 years?
A. 9000
B. 6250
C. 8530.80
D. 8780.80
152. A sum of money invested for a certain number of
years at 8% p.a. simple interest grows to Rs.180. The same sum of money
invested for the same number of years at 4% p.a. simple interest grows to
Rs.120 only. For how many years was the sum invested?
A. 25 years
B. 40 years
C. 33 years and 4 months
D. Cannot be determined
153. How long will it take for a sum of money to
grow from Rs.1250 to Rs.10, 000, if it is invested at 12.5% p.a
simple interest?
A. 8 years
B. 64 years
C. 72 years
D. 56 years
154. The average age of a board of 10 advisors of a
company is the same as it was 3 years back on account of the replacement of one
of the older advisors by a younger man. How much younger was the new man than
the director whom he replaced?
A. 3 years
B. 15 years
C. 30 years
D. 24 years
155. If the average of three numbers a, b, and c is
A. What is the average of the four numbers a, b, c and A?
A. A/4
B. A/2
C. 2A
D. None of
these
156. The average monthly salary of 12 workers and 3
managers in a factory was Rs. 600. When one of the
manager whose salary was Rs. 720, was replaced with a
new manager, then the average salary of the team went down to 580. What is the
salary of the new manager?
A. 570
B. 420
C. 690
D. 640
157. Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. Find the total cost of 24 apples and 24 mangoes.
A. 1044
B. 2088
C. 720
D. 324
158. A student finds the average of 10 positive
integers. Each integer contains two digits. By mistake, the boy interchanges
the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the
previous one. What was the difference of the two digits a and
b?
A. 8 B. 6
C. 2 D. 4
159. The average age of a family of 5 members is 20
years. If the age of the youngest member were 10 years then what was the
average age of the family at the time of the birth of the youngest member?
A. 13.5
B. 14
C. 15
D. 12.5
160. The average of 5 quantities is 10 and the average of
3 of them is 9. What is the average of the remaining 2?
A. 11
B. 12
C. 11.5
D. 12.5
161. The average weight of a class of 24 students is
36 years. When the weight of the teacher is also included, the average weight
increases by 1kg. What is the weight of the teacher?
A. 60 kgs
B. 61 kgs
C. 37 kgs
D. None of
these
162. When a student weighing 45 kgs
left a class, the average weight of the remaining 59 students increased by
200g. What is the average weight of the remaining 59 students?
A. 57 kgs
B. 56.8 kgs
C. 58.2 kgs
D. 52.2 kgs
163. The average temperature on Wednesday, Thursday
and Friday was 250. The average temperature on Thursday, Friday and Saturday
was 240. If the temperature on Saturday was 270, what was the temperature on
Wednesday?
A. 240
B. 210
C. 270
D. 300
164. A tank is fitted with 8 pipes; some of them
that fill the tank and others that are waste pipe meant to empty the tank. Each
of the pipes that fill the tank can fill it in 8 hours, while each of those
that empty the tank can empty it in 6 hours. If all the pipes are kept open
when the tank is full, it will take exactly 6 hours for the tank to empty. How many
of these are fill pipes?
A. 2
B. 4
C. 6
D. 5
165. If A and B work together, they will complete a
job in 7.5 days. However, if A works alone and completes half the job and then
B takes over and completes the remaining half alone, they will be able to
complete the job in 20 days. How long will B alone take to do the job if A is
more efficient than B?
A. 20 days
B. 40 days
C. 30 days
D. 24 days
166. There are 12 pipes that are connected to a
tank. Some of them are fill pipes and the others are drainpipes. Each of the
fill pipes can fill the tank in 8 hours and each of the drainpipes can drain
the tank completely in 6 hours. If all the fill pipes and drain pipes are kept
open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill
pipes?
A. 6 B. 8
C. 7 D. 5
167. Four men and three women can do a job in 6
days. When five men and six women work on the same job, the work gets completed
in 4 days. How long will a woman take to do the job, if she works alone on it?
A. 18 days
B. 36 days
C. 54 days
D. None of
these
168. Shim can do a job in 20 days, Ram in 30 days
and Singh in 60 days. If Ram and Singh help Shim every 3rd day, how long will
it take for them to complete the job?
A. 12 days
B. 16 days
C. 15 days
D. 10 days
169. Pipe A usually fills a tank in 2 hours. On
account of a leak at the bottom of the tank, it takes pipe A
30 more minutes to fill the tank. How long will the leak take to empty a full
tank if pipe A is shut?
A. 2 hours 30 minutes
B. 5 hours
C. 4 hours
D. 10 hours
170. Two workers A and B manufactured a batch of
identical parts. A worked for 2 hours and B worked for 5 hours and they did
half the job. Then they worked together for another 3 hours and they had to do
(1/20)th of the job. How
much time does B take to complete the job, if he worked alone?
A. 24 hours
B. 12 hours
C. 15 hours
D. 30 hours
171. Pipe A can fill a tank in ‘a’
hours. On account of a leak at the bottom of the tank it takes thrice as long
to fill the tank. How long will the leak at the bottom
of the tank take to empty a full tank, when pipe A is kept closed?
A. (3/2) a
hours
B. (2/3) a
hours
C. (4/3) a
hours
D. (3/4) a
hours
172. A man can do a piece of work in 60 hours. If he
takes his son with him and both work together then the work is finished in 40
hours. How long will the son take to do the same job, if he worked alone on the
job?
A. 20 hours
B. 120 hours
C. 24 hours
D. None of
these
173. X
alone can do a piece of work in 15 days and Y alone can do it in 10 days. X and
Y undertook to do it for Rs. 720. With the help of Z
they finished it in 5 days. How much is paid to Z?
A. Rs. 360
B. Rs. 120
C. Rs. 240
D. Rs. 300
174. A, B and C can do a work in 5 days, 10 days and
15 days respectively. They started together to do the work but after 2 days A
and B left. C did the remaining work (in days)
A. 1 B. 3
C. 5 D. 4
175. A red light flashes 3 times per minute and a
green light flashes 5 times in two minutes at regular intervals. If both lights
start flashing at the same time, how many times do they flash together in each
hour?
A. 30 B. 24
C. 20 D. 60
Answers
1 B 2 C 3 b 4 B 5 D 6 B 7 C 8 B 9 C 10 C
11 B 12 A 13 B 14 A 15 B 16 C 17 C 18 B 19 C 20 D
21 C 22 C 23 B 24 B 25 A 26 B 27 D 28 C 29 C 30 C
31 C 32 D 33 C 34 C 35 B 36 A 37 D 38 D 39 C 40 D
41 A 42 C 43 C 44 D 45 B 46 D 47 B 48 A 49 D 50 D
51 C 52 C 53 D 54 C 55 C 56 C 57 B 58 C 59 B 60 D
61 C 62 B 63 B 64 A 65 C 66 B 67 C 68 B 69 C 70 C
71 C 72 D 73 B 74 C 75 A 76 D 77 C 78 D 79 B 80 A
81 A 82 B 83 A 84 A 85 D 86 C 87 A 88 C 89 C 90 C
91 C 92 C 93 D 94 C 95 C 96 B 97 D 98 C 99 A 100 C
101 A 102 B 103 A 104 B 105 C 106 A 107 C 108 C 109 B 110 C
111 D 112 D 113 A 114 B 115 C 116 A 117 B 118 A 119 D 120 C
121 C 122 D 123 B 124 A 125 c 126 d 127 b 128 d 129 c 130 d
131 b 132 a 133 b 134 d 135 b 136 c 137 b 138 c 139 b 140 b
141 b 142 d 143 c 144 b 145 b 146 b 147 b 148 a 149 b 150 d
151 a 152 d 153 c 154 d 155 b 156 b 157 c 158 d 159 c 160 b
161 a 162 d 163 b 164 c 165 c 166 c 167 c 168 d 169 c 170 a 171 b 172 b 173 d 174 a
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