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1

first prime numbers

2, 3, 5,7,11,13,17,19,23,29,31,37,41,43,53,59,61,67,71,79,83,89,97,101

2

If Jack had twice the amount of money that he has he would have exactly the amount necessary to buy 3 hamburgers at USD 0.96 apiece and 2 milkshakes at USD 1.28 apiece. How much money doe Jack have?
A) USD 1.60
B) USD 2.24
C) USD 2.72
D) USD 3.36
E) USD 5.44

Answer is C

2J = 3(0.96) + 2(1.28)
2J = 5.44
J = 2.72

3

Two hundred gallons of fuel oil are purchased at USD 0.91 per gallon and are consumed at a rate of of USD 0.70 worth of fuel per hour. At this rate how many hours are required to consume the 200 gallons of fuel oil
A) 140
B) 220
C) 260
D) 322
E) 330

Ans: C

Total price of Fuel = 200 * 0.91 = 182
total hours = 182 / 0.70 = 260

4

1 yard = ?? Feet
1 Mile = ?? Feet

1 Yard = 3 feet
1 Mile = 5280 feet

5

Squares

1*1=1
2*2=4
3*3=9
4*4=16
5*5=25
6*6=36
7*7=49
8*8=64
9*9=81
10*10=100
11*11=121
12*12=144
13*13=169
14*14=196
15*15=225
16*16=254
17*17=289
18*18=324
19*19=361
20*20=400

6

GMAT 10th Edition: PS : 64
Today Rose is twice as old as Sam and Sam is 3 years younger than TIna. If Rose, Sam and Tina are all alive 4 years from today. which of the following must be true.
1. Rose is twice as old as Sam
2. Sam is 3 years younger than Tina
3. Rose is older than Tina

A) 1 only
B) 2 only
C) 3 only
D) 1 and 2 only
E) 2 and 3 only

Answer: B

R=2S. put in numbers say S = 10 then R = 20. After 4 years R = 24 and S = 14. Therefore R = 12 / 7 of S. Hence statement 1 is not true.

Similarly for statement 2:
S = T-3. If S = 10 then T = 7
After 4 years S = 14 whereas T = 11. Difference is still 3 years. Hence Statement 2 is true.

For Statement 3: R = 2(T-3). Hence it cannot be ascertained if R is greater or less than T

7

The average (airthmatic mean) of 6, 8 and 10 equals the average of 7, 9 and
A) 5
B) 7
C) 8
D) 9
E) 11

Answer : C

since there is equal gap between 6,8 and 10 therefore the mean is the middle number i.e 8

Similaly the only way the average of 7,9,and X will be 8 is when X = 8. Note that gap between 7,8 and 9 is the same.

8

GMAT 10th Edition: PS 75
If there are 664,579 prime numbers among the first 10 million positive integers, approximately what percent of the first 10 million positive integers are prime numbers
A) 0.0066%
B) 0.066%
C) 066%
D) 6.6%
E) 66%

Answer : D

Divide 664,579 by 10,000,000 = 0.0664579

Multiply by 100 to get percentage = 6.64579%. Hence D is the answer

9

GMAT 10th Edition: PS : 103
Three machines, individually can do a certain job in 4,5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of the machines working togather at their respective rates.
a) 11/30
b) 9/20
c) 3/5
d) 11/15
e) 5/6

Answer : B

Hence each machine does 1/4, 1/5 and 1/6 part of the work.
Since the question asks for the greatest work therefore two of the highest are to be chosen.

1/4 + 1/5 = (5+4)/20 = 9/20

10

Gmat 10th Edition: PS :109
A corporation that had USD 115.19 billion in profits for the year paid our USD 230.10 million in employee benefits. Approximately what percent of the profits were the employee benefits?
a) 50%
b) 20%
c) 5%
d) 2%
e) 0.2%

Answer: E

remember 1 billion = 10^9 and 1 Million = 10^6

so the equation also calls for approx. hence round off the numbers

230 divided by 115 x 10^3 = 2/1000 = 0.2%
Hence E is the answer

11

GMAT: 10th Edition: PS: 110
For any positive integer n, n>1, the length of n is the number of positive primes (not necessary distinct) whoe product is n. For example the length of 50 is 3 since 50 = (2)*(5)*(5)

which of the following integers has length 3?
a) 3
b) 15
c) 60
d) 64
e) 105

Answer: E

3 = (3) only hence length is 1
15 = (3)*(5) hence length is 2
60 = (2) (2) (3) (5) hence length is 4
64= (2) (2) (2) (2) (2) (2) hence length is 6
105 = (5) (3) (7) hence length is 3

Hence answer is E

12

GMAT: 10th Edition: PS 113
Two Oil cans X and Y are right cylinders and the height and the radius of Y are each twice those of X. If the oil in can X which is filled to capctiy sells for USD 2 then at the same rate how much does the oil in can y sell for if y is filled to only half its capacity?
a) USD 1
b) USD 2
c) USD 3
d) USD 4
e) USD 8

Answer: E

The formula for calculating volume of a cylinder is Base X height.

where base is pi*r^2.
Hence volume of cylinder is pi*r^2*h where r is the radius and h is the height.

since radius of Y cylinder is twice that of X then Ry=2r and Hy = 2h
put this in the equation for calcualting volume of the cylinder Y is we get
8*pi*r^2*h.

But pi*r^2*h is the area of X. Hence volume of Y = 8* volume of X.

Since X volume sells for USD 2 then total volume of Y sells for 16.

But it is only half full then it must sell for 16/2 = 8

13

Area of Triangle:
Sum of all angles of a triangle:
Longest side of a triangle:
Equilateral triangle:
Perimeter of a triangle
Colinear points
Congurent points
Complement Angles
Supplement Angles
Isosoles triangle

Area of Triangle: 1/2*base*height
Sum of all angles of triangle = 180
Longest side of a triangle is opposite the largest angle
Equilateral: All sides are equal
Perimeter of a triangle = sum of all sides of the triangle
Colinear points are points that lie on the same line
Congurent points are points that lie on same plane
Complement Angles sum is 90
Supplement Angles sum is 180
Isosles triangles has two sides and two angles same

14

Cubes

1^3= 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
8^3 = 512
9^3 = 729
10^3 = 1000
11^3 = 1331
12^3 = 1728
13^3 = 2197
14^3 = 2744
15^3 = 3375
16^3 = 4096
17^3 = 4913
18^3 = 5832
19^3 = 6859
20^3 = 8000

15

Value of Pi in Decimal
Value of Pi in Fraction

Value of Pi in Decimal: 3.14
Value of Pi in Fraction : 22/7

16

Pythogroas theorem
Define Quadrilateral
3 types of Quadrilateral
circumference of a circle
Area of a circle:
Equation of a line
if slope is -ve, +ve or 0 then what happens
X^2-Y^2

Pythogroas theorem: x^2 + y^2 = z^2

Define Quadrilateral: has four sides

3 types of Quadrilateral: square, rectangle, and parralalogram

circumference of a circle; 2*pi*r or pi*d

Area of a circle = pi*r^2

Equation of a line: y = mx + b where m is slope and b is y intercept

if slope is -ve, +ve or 0 then what happens: if slope is -ve line tits from left to right. reverse is true for +ve and line is straight if slope is 0

X^2-Y^2 = (X-Y)*(X+Y)

17

if a triangle is placed in a circle such that all three points lie on the circle then

then it has to be right angle triangle.

18

1 feet = ?? inches
1 yard = ?? inches
1 yard = ?? feet
1 mile = ?? feet
1 mile = ?? yards

1 feet = 12 inches
1 yard = 36 inches
1 yard = 3 feet
1 mile = 5280 feet
1 mile = 1760 yards

19

GMAT: 10th Edition: PS: 125
If USD 1 were invested at 8 percent interest compounded annually, the total value of the investment , in dollars at the end of 6 years would be
a) (1.8)^6
b) (1.08)^6
c) 6 * (1.08)
d) 1+(0.08)^6
e) 1+6*(0.08)^6

Answer : B

Future Value = Present Value * (1+rate)^(number of periods)

therefore
FV = 1*(1+0.08)^6 = (1.08)^6. Hence b is the answer.

20

GMAT 10th edition: PS: 133

IF X and Y are sets of integers X & Y denoted the set of integers that belong to set X or set Y but not both. If X consists of 18 integers and 6 of the integers are in both X and Y then X & Y consists of how many integers?
a) 6
b) 16
c) 22
d) 30
e) 174

Answer: B

As per Venn diagram the equation for Union of two sets is X + Y -XY.

Therefore 10 +18 - 6 = 22. Hence the total number of integers are 22.

Out of which 6 are both in X and Y
Therefore X & Y = 22 - 6 = 16

21

GMAT: 10th Edition: PS : 136
if (0.0015 * 10^m) / (0.03 * 10^k) = 5 *10^7 then
m-k =
a) 9
b) 8
c) 7
d) 6
e) 5

Answer: A

lets simplify 0.0015*10^m
we can write this as (15/10000)*10^m
or 15 * 10^(m-4)

similarly the denominator can be written as 3 * 10^(k-2)

now m-4 - (k - 2) = 7
therefore m-k-2 = 7
therefore m -k = 9

22

GMAT: 10th Edition: PS: 154

Which of the following CANNOT yield an integer when divided by 10?
a) The sum of two odd integers
b) An integer less than 10
c) The product of two primes
d) The sum of three consecutive integers
e) An odd integer

Answer : E

A) the sum of two odd integers can be divided by 10 for example 7+3 = 10

B) Negative integer is an integer which is less than 10 bu divided by 10

C) the product of two primes for example 5*2 = 10

D) for example 9,10 and 11.

E) is the correct answer.

23

GMAT : 10th Edition: PS : 155

A certain clock marks every hour by striking a number of times equal to the hour and the time required for a stroke is exactly equal to the time interval between strokes . At 6:00 the time lapse between the beginning of the first stroke and the end of the last stroke is 22 seconds. At 12:00 how many seconds elaspse between the beginning of the first stroke and the end of the last stroke?
a) 72
b) 50
c) 48
d) 46
e) 44

Answer : D

At 6:00 there are 6 strokes and 5 intervals. that means there are 11 period.

hence 22/ 11 = 2 second for each period.

at 12:00 there are 12 strokes and 11 intervals. That means there are 23 period.

Multiply it by 2 we get 46 seconds.

24

GMAT : 10th Edition: PS : 173

if a square region has area x, what is the length of its diagonal in terms of x?
a) root x
b) root (2x)
c) 2* root x
d) x* root (2)
e) 2x

Answer: B

area of square is a^2 = x
then each side is a = root x

using pytohgoras theoreum
a^2 + a^2 = z^2
x +x = z^2
2x=z^2
z= root (2x)

25

GMAT: 10th Edition: PS 174

In a certain class consisting of 36 students, some boys and some girls, exactly 1/3 of the boys and exactly 1/4 of the girls walk to school. What is the greatest possible number of students in this class who walk to school.

a) 9
b) 10
c) 11
d) 12
d) 13

Answer: C

let x be the number of boys in the class then there are 36-x girls in the class .

then
1/3x + 1/4(36-x) = ??
9 + (1/12)x =??

now lets assume that x = 36 (i.e the class has only boys)
9 +36/12 = 12. So the maximum value can be 12 that walked. but there are some girls in the class so

x can be maximum 24
that is 9+24/12 = 11. Hence the answer is 11

Alternatively

26

GMAT: 10th Edition:PS 176

1234
1243
1324
.......
.......
4321
____

The addition problem above shows four of the 24 different integers that can be formed by suing each of the digits 1,2,3,4 exactly once in each integer. What is the sum of these 24 integers

a) 24,000
b) 26,664
c) 40,440
d) 60,000
e) 66,660

Answer : E

The number of options are 4*3*2*1 = 24 options
since there are 4 numbers therefore each digit would be repeated by 24/4 = 6

Hence the sum for each digit would be 6(4+3+2+1) = 60

now look at the answers
since E has 66,660 then it is the most likely.

27

GMAT: 10th Edition: PS 185

If the number n of calculators sold per week varies with the price p in dollars according to the equation n = 300 - 20p, what would be the total weekly revenue from the sale of USD 10 calculators

a) USD 100
b) USD 300
c) USD 1,000
d) USD 2,800
e) USD 3,000

Answer: C

put USD 10 in the equation.

n = 300 - 20 (10) = 100
Hence the number of calculators sold is 100
Therefore the sale from USD 10 is 100 * 10 = 1,000

Hence C is the answer

28

GMAT: 10 Edition: PS 189

If a positive integer n id divisible by both 5 and 7 the n must also be divisible by which of the following.
1: 12
2: 35
3: 70

a) None
b) 1 only
c) 2 only
d) 1 and 2 only
E) 2 and 3 only

Answer : C

Since n is divisible of 5 and 7 then then it must be minimum 7*5 = 35

Hence statement 1 is in correct as the n cannot be 12
Statement 2 is correct as it is minimum 35
statement 3 may or may not be correct as the answer calls for that it must be hence if n = 35 then it is not divisible by 70

Therefore C is the correct answer

29

GMAT: 10th Edition : PS 192

which of the following describes all values of x for which 1 - x^2 >= 0

a) x >= 1
b) x == 1
e) -1 =

Answer: E

break the equation as (1+x)(1-x) >=0

if equation is equal then 1+x = 0 then x = -1
similarly for the other factor 1-x = 0 then x = 1

if equation is greater then then 1+x > 0 then x > -1
similarly 1 - x > 0 then 1 >x or x

30

what is the solution of
X^2 > X

cannot be solved as we donot whether x is positive or negative.