Daily Practice Flashcards
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
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
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
1 yard = ?? Feet
1 Mile = ?? Feet
1 Yard = 3 feet
1 Mile = 5280 feet
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
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
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.
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
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
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
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
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 pir^2.
Hence volume of cylinder is pir^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
8pir^2*h.
But pir^2h 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
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: 1/2baseheight
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
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
Value of Pi in Decimal
Value of Pi in Fraction
Value of Pi in Decimal: 3.14
Value of Pi in Fraction : 22/7
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; 2pir 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)
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.
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
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.
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
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 0.001510^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
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.
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.
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)