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)
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
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 432*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.
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
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
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
what is the solution of
X^2 > X
cannot be solved as we donot whether x is positive or negative.
GMAT: 10th Edition : PS 224
If a cube has a volume of 64. What is tis total survace area?
a) 16
b) 24
c) 48
d) 64
e) 96
Answer: E
since the volume of the cube is X^3 = 64 then x = 4
surface area of one of the sides of the cube is x^2 = 4^2 = 16
A cube has 6 sides therefore the total surface area is 16*6 = 96
Hence answer is E
GMAT: 10th Editiosn : PS 225
Club : No of Student
Chess : 40
Drama: 30
Math: 25
The table above shows the number of student sin three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and rama, 5 students are in both chess and math and 6 students are in both drama and math. How many different students are in the three clubs.
a) 68
b) 69
c) 74
d) 79
e) 84
Answer : C
As per venn diagram
A+B+C+D+E+F+G+H = total number of students
As per the table
A+B +D+ E = 40
C+B+E+SF = 30
D+E+F = 25
As per the paragraph E=0 B = 10 D = 5 and E = 6
Put in the equation to get
A = 25
C+ 14
G = 14
Add A + B + C + D + E + F + G = 74
GMAT : 10th Edition : PS 226
If s, u and v are positive integers and 2^s = 2^u + 2 ^v. which of the following must be true.
- s = u
- u is not equal to v
- s > u
a) None
b) 1 only
c) 2 only
d) 3 only
e) 2 and 3
Answer : D
As per the equation
S = U + V
hence it is not necessary for the statement 1 and 2 to be correct.
But statement 3 is correct because the question already mentions that the integers are positive.
GMAT : 10th Edition : PS 227
In a nation wide poll, N people were interviewed. If 1/4 of them answered “yes” to question 1 and of those 1/3 answered “yes” to question 2, which of the following expressions represents the number of people interviewed who did not answer “yes” to both questions
a) N/7
b) 6N/7
c) 5N/12
d) 7N/12
e) 11N/12
Answer: E
As per the venn diagram
A + B + C + D = N
but A = N/4 = those who answered yes to question 1
B = (1/3)*(N/4) = N/12
Hence the people who did not answer yes to both questions is N - B
ie. N = N/12 = 11N/12
Hence E is the correct answer.
GMAT: 10th Edition: PS 247
If 3 and 8 are the lengths of two sides of a triangular region. which of the following can be the length of the third side?
1) 5
2) 8
3) 11
a) 2 only
b) 3 only
c) 1 and 2 only
d) 2 and 3 only
e) 1, 2 and 3
Answer: A
Since 8 and 3 are the lengths of the two sides then the max length has to be less than 8 + 3 = 11 (i.e if both are lines are on the same line.
Similarly the minimu would be less than 8 - 3 = 5.
Hence the answer has to be A
GMAT: 10th Edition : PS 252
AB
x BA
_____
The product of the two digits numbers above is the three digit number ACA where A,B and C are three different non zero digits. If AxB
Answer : D
Since the question asks that A,B and C are different digits therefore a) cannot be true
in case of B
multiplication is less than 10 and the 12 and 21 = 252 which doesn’t satisfies the equation as the answer should be 1C1 instead it is 2C2
In case of c 1x3
GMAT : 10th Edition: PS 263
If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 4 strokes
a) 15/16
b) 7/8
c) 1/4
d) 1/8
e) 1/16
Answer
in first stroke 1/2 of air is removed
In 2nd stroke 1/4 of air is removed
in 3rd stroke 1/8 of air is removed
in 4th stroke 1/16 of air is removed
Hence total air removed is 1/2 + 1/4 + 1/8 + 1/16 is removed.
Hence total air removed is
Neither ..... "Compared to" or "Comparing" Both...... Not X ... Choose to or Choose Known Attribute Depend .. The idea...
Neither .... Nor Compared to Both.....and Not X .. But Y Choose to Known for Attibute,...to Depend on The idea of
Aid ... Among / Between California, Utah and Arizona In Contrast to/for Such ... as / that is included in / includes able than.... (Parts) Compose / compose of (whole) (whole) compose / compose of (parts)
Aid in Among California, Utah and Arizona In contrast to Such.... that Includes able than .... to (Parts) Compose (whole) (Whole) composed of (parts)
because of / because (single noun) because of / because (action) fascination ... replace .... Based... not only.... works.... dated... comparing.... so powerful....
because of (single noun) because (action) fascination ...with replace....with Based on not only... but also works ..as dated...at comparing....to so powerful...that
separate….
constrast….
between…
allows…
because of / because there was
on account …
composed ..
prior….
consequence ….
separate from. constrast.. with between....and allows ... to because of on account of composed ..of prior ... to consequence of
What is the mean minus median for a normal distribution.
A normal distribution is where all the members have equal gaps for example. 5,10,15,20,25…..
in such cases mean is always equal to median.
GMAT 10th Edition PS 430
If m > 0 and x is m percent of y then in terms of m, Y is what percent of x
a) 100m
b) 1/(100m)
c) 1/m
d) 10/m
e) 10,000/ m
Answer : E
X/y = m/100 then y/x = 100/m converting this into percentage y/x = (100*100)/m = 10,000/m Hence E is the correct answer.
GMAT 10th edition PS 434
A certain musical scale has 13 notes each having a different frequency measured in cycles per second. In the scale the notes are ordered by increasing frequency and the highest frequency is twice the lowest. For each of the 12 lower frequencies the ratio of a frequency to the next higher frequency is a fixed constant. if the lowest frequency is 440 cycles per second. then the frequency of the 7th note in the scale is how many cycles per second. A) 440 root 2 b) 440 root (2^7) C) 440 root (2^12) D) 440 12 root (2^7) E) 440 7 root (2^12)
Answer : A
1st frequency = 440 2nd frequency = 440X 3rd frequency = 440X^2 so... 7th frequency = 440 X^6 13th frequency = 440X^12
Hence the 13th frequency = 440X^12 = 880
X^12 = 2
(X^6)^2 = 2
X^6 = root 2
putting that in 7th frequency equation
440X^6 = 440*root 2
Hence A is the answer.
GMAT 10th Edition PS 436
Equal amounts of water were poured into two empty jars of different capacities which made one jar 1/4 full and the other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with the greater capacity. What fractiosn of the larger jar will be filled with water
A) 1/7 B) 2/7 C) 1/2 D) 7/12 E) 2/3
Answer: C
since the larger capacity jar is the one which was filled the least. therefore first jar was filled only 25% (ie 1/4 = 25%) whereas the other jar was filled 33% (I.e 1/3 = 33%)
hence the lager jar will be filled twice
i.e 2 * 1/4 = 1/2 hence C is the answer
Table of 12
12*1 = 12 12*2 = 24 12*3 = 36 12*4 = 48 12*5 = 60 12*6 =72 12*7 = 84 12*8 = 96 12*9 = 108 12*10 = 120
13 table
13*1 = 13 13*2 =26 13*3= 39 13*4 = 54 13*5 = 65 13*6 = 78 13*7 = 96 13*8 = 104 13*9 = 117 13*10 = 130
14 table
14 1 14 14 2 28 14 3 42 14 4 56 14 5 70 14 6 84 14 7 98 14 8 112 14 9 126 14 10 140
15 table
15 1 15 15 2 30 15 3 45 15 4 60 15 5 75 15 6 90 15 7 105 15 8 120 15 9 135 15 10 150
16 table
16 1 16 16 2 32 16 3 48 16 4 64 16 5 80 16 6 96 16 7 112 16 8 128 16 9 144 16 10 160
17 table
17 1 17 17 2 34 17 3 51 17 4 68 17 5 85 17 6 102 17 7 119 17 8 136 17 9 153 17 10 170
18 table
18 1 18 18 2 36 18 3 54 18 4 72 18 5 90 18 6 108 18 7 126 18 8 144 18 9 162 18 10 180