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
19 table
19 1 19 19 2 38 19 3 57 19 4 76 19 5 95 19 6 114 19 7 133 19 8 152 19 9 171 19 10 190
20 table
20 1 20 20 2 40 20 3 60 20 4 80 20 5 100 20 6 120 20 7 140 20 8 160 20 9 180 20 10 200
What is the equation of vetical line which is 4 unit away from y axis
Similay what is the equation of horizontal line which is 2 units away from x axis
what is the equation of the x axis
What is the equation of the y axis
y = 4
X = 2
X = 0
Y = 0
what is the equation of a slope
Slope = rise / run ( y2-y1)/(x2/x1)
Always use the right most point as point 2.
Always use the triangle and do not rely too much on the formula
if slope is 1 then what is the angle that the line forms with the x axis
what is the difference between the rise and the run
what is the angles of the slope triangle
what is the slope between two parallel lines
what is the slope between two perpendicular line
rise = run
hence the line forms a angle of 45 degrees with the x axis.
The slope triangle is 45-45-90 triangle.
slope of parallel lines is equal
Slope of perpendicular lines is the negative respricol for example slope of a line is 3/2 then the slope of perpendicular line is -2/3
Magoosh: Practice Problem: Distance between two points
Find the distance between (-5,-1) and (3,3)
Draw a tringles on the coordinate plane with the points mentioned.
draw a tringle with the x run and y run. the triangle would have two sides of (3-(-5)) = 8 and (3-(-1)) = 4
Use pythogorus theorm to solve for the slope
X^2 = 64 + 16 = 80 = 4 root 5 which is thw answer.
6Magoosh : Practice Problem: Distance between two points
A circle in the xy plane has a center of (6,3) and radius of 5, Find the x - intercepts.
Irr,0) and (10,0)
GMAT Workbook
What is
- Rational Numbers
- Real Numbers
- Irrational Numbers
- Integers
- Rational Numbers: All integers and fractions
- All numbers on the number line both rational and irrational
- Irrational Numbers: All numbers what are not rational such as Pi, root 2 etc
- integers: not fractional or decimals
How to compare fractions
you compare fractions by drawing a circle and divinding it into the denominator number. then shade the number of numerators.
will give a visual representation of which one is larger.
Solve
13 + 5/16
13(5/16) simple
Gmat Workbook
which of the follosing is less than 1/6
- 0.1667
- 3/18
- 0.167
- 0.1666.
- 8/47
Answer : 0.1666
1/6 = 0.1666666. Hence 1, and 3 are already out
2 is out because 3/18 = 1/6
- is out cause 8*6 = 48. since the denominator is less than 47 hence the answer would be greater than 1/6.
the only answer is 4 which is less than 0.16667
which of the following fractions are in ascending order
- 9/26, 1/4, 3/10
- 9/26, 3/10, 1/4
- 1/4, 9/26, 3/10
- 1/4, 3/10, 9/26
- 3/10, 9/26, 1/4
we know that 1/4 = 0.25 and 3/10 = 0.30
now calculate 9/26 = 0.34
hence the correct order is 0.25, 030 and 034
i.e 1/4, 1/3, 9/26
Hence 4 is the answer
How to know if a number is divisible by 3
How to know if a number is divisible by 4
How to know if a number is divisible by 5
How to know if a number is divisible by 6
How to know if a number is divisible by 7
How to know if a number is divisible by 8
How to know if a number is divisible by 9
if the sum of all numbers is divisible by 3 then the number is divisible by 3
If any number ends in a two digit number that you know is divisible by 4 (e.g. 24, 04, 08, etc.), then the whole number will be divisible by 4 regardless of what is before the last two digits.
A number is divisible by 5 if the its last digit is a 0 or 5
So for a number to be divisible by 6, it must also be divisible by 2 and 3. Therefore, we need to check if a number is even and then check if the sum of the digits is divisible by 3.
Take the last digit of the number you’re testing and double it. Subtract this number from the rest of the digits in the original number. If this new number is either 0 or if it’s a number that’s divisible by 7, then you know that the original number is also divisible by 7.
Numbers are divisible by 8 if the number formed by the last three individual digits is evenly divisible by 8. For example, the last three digits of the number 3624 is 624, which is evenly divisible by 8 so 3624 is evenly divisible by 8.
A number is divisible by 9 if the sum of the digits are evenly divisible 9.
For how many positive integers x is 130/x an integer
- 8
- 7
- 6
- 5
- 3
the factors of 130 are
13, 5, and 2 hence the positive integers are as follows
1, 2, 5, 13, 10, 36, 65, 130
A laboratory has 55 rabbits some white and the rest brown. Which of the following could be the ratio of white rabbits to brown rabbits in the lab.
- 1:3
- 3:8
- 5:11
- 3:4
- 5:1
there are 55 rabbit so the factors are 5 and 11. hence the total sum of the parts must be able to divide 55
for 1. 3+1 = 4 does not divide 55 for 2. 3+ 8 = 11 . divides and is therefore the correct ans for 3. 5 + 11 = 16 does not divide 55 for 4. 4 = 3 = 7 does not divide 55 for 5. 5 + 1 = 6 does not divide 55
hence the answer is 2.
One - twenthieth of the entrants in a contest won prizes. If 30 prizes were won and no entrant won more than one prize, how many entrants did not win prizes
a. 30
b. 300
c. 540
d. 570
e. 600
(1/20) * X = 30 then
X = 30 *20 = 600
but this is the total number of prizes won hence you neeed to substract 30 from it.
X = 570
Hence C is the correct answer.
A recipe for the egg nog calls for 2 eggs for every 3 cups of milk If there are 4 cups in a quart, how many eggs would be needed to mix with 6 quarts of milk.
a. 12
b. 16
c. 24
d. 36
e. 48
total number of cups in 6 quarts are 6*4 = 24
then eggs/ milk = 2/3 = x/24
solve for x you get X = 16
hence b is the correct anwer
If Cement, gravel and sand are to be mixed in a ratio 3:5:7 respectively and 5 tons of cement are available, how many tons of the mixture can be made
a. 15
b. 20
c. 25
d. 30
e. 75
hence the total mixture is 3+5+7 = 15 therefore cement / total mixture = 3/15 = 5/X
therefore solve for x we get X = 25
Hence C is the answer
Bob finished the first half of an exam in two thirds the time it takes him to finish the second half. If the whole exam takes him an hour how many minutes does he spend on the first half of the exam
a. 20
b. 24
c. 27
d. 36
e. 40
Let the time it takes him to finish the second half be S then total time is
2S/3 + S = 5S/3
it takes him 60 minutes to finish then
5S/3 = 60 S = 36
But the time it takes to complete the 1st half is 2S/3 = 2 *36/3 = 24
Hence the answer is B
In a certain factory with 2,700 workers one-third of the workers are unskilled. If 600 of the unskilled workers are apprentices, what fraction of the unskilled workers are not appretices.
a. 1/9
b. 1/7
c. 1/5
d. 1/3
e. 1/2
1/3 of the workers are unskilled (i.e 1/3 of 2700 = 900)
if 600 of the unskilled workers are apprentices then 300 are not apprentices
300/900 = 1/3
Hence the answer is 1/3
A sporting goods store ordered an equal number of white and yellow tennis balls. The tennis ball company delivered 30 extra white balls making the ratio of white balls to yellow balls 6:5. How many tennis balls did the store originally ordered.
a. 120
b. 150
c. 180
d. 300
e. 330
If x is the total number of white balls then the store called for 2x of the total balls.
since there were 30 more white balls delivered therefore
x/(x+30) = 5/6 ( note that x + 30 will be the larger one)
solving for x we get x = 150
but the store called for 2x then the total ones are 300
hence D is the correct answer
Two hundred percent more than 30 is
a. 36
b. 60
c. 90
d. 120
e. 360
two hundred precent more is 300/100 of 30 then the answer is 90
hence c is correct answer.
What is 0.25 percent of 4/3
a. 1/3000
b. 1/300
c. 1/300
d. 1/20
e. 1/3
25/100 * 1/00 * 4/3 = 1/300
donot convert it into percentage as the answer is not in percentage.
The price of a newspaper rises from 5 cents to 15 cents. what is the percent increase in the price.
a. 2%
b. 50%
c. 150%
d. 200%
e. 300
15/5 = 3
hence substract by 1 = 3 -1 then 2
converting into percentage 200%
hence d is the correct answer.
If q343638 = 1718*19 then q =
a) 1/8
b) 1/6
c) 1/2
d) 2
e) 8
q = (17/34)*(18/36) *(19/38) = 1/8
Hence a is the correct answer.
(a^2+b)^2 - (a^2-b)^2 =
a) -4a^2b
b) 0
c) (2ab)^2
d) 4a^2b
e) b^4
(a^2+b)^2 = a^4 + 2a^2b + b^2
similarly (a^2-b)^2 = a^4 -2a^2b + b^2
substracting the two we get
4a^2b
Hence d is the correct answer
When does the direction of an unequality change.
> or
it changes when it is multiplied or divided by a -ve sign.
if 3m < 48 and 2m > 24 then m could equal which of the following
a) 10
b) 12
c) 14
d) 16
e) 18
m < 48/3 = 16
similarly m < 24/2 = 12
then m must be 14 hence c is the answer
if a<b></b>
the answer is d
a+b < 2c because we can view this as a+b< c +c
since both terms are greater on the right side then it must be true.
if a > b > c then all of the following could be true except
a) b + c < a
b) 2a > b + c
c) 2c > a + b
d) ab > bc
e) a + b > 2b +c
the answer is C
break it up
c + c > a + b
since c is smaller than both a and b then it cannot be true.
Between 1950 and 1960 the population of Country A increased by 3.5 million people. If the amount of increase between 1960 and 1970 was 1.75 million more than the increase from 1950 to 1960 what was the total amount of increase in population in County A between 1950 and 1970
a) 1.75 million
b) 3.5 million
c) 5.25 million
d) 7 million
e) 8.75 milion
the answer is 8.75 million (E)
between 1950 - 60 the population increased by 3.5 million
between 1960 - 70 the population increased by 3.5 + 1.75 = 5.25 million
adding both of them we get 3.5+5.25 = 8.75 million
At arecord store a record Is priced at 60 percent of the price of the compact disk of the same title. If a compact disk is priced at USD 15, how much less does the record cost.
a) 5
b) 6
c) 9
d) 10
e) 12
60% is 3/5
then 3/5 of 15 is 9
the question asks for how much less then 15 - 9 = 6
Hence B is the answer.
If Bill can mow 3/4 of his lawn in one hour, how many minutes does it take Bill to mow his entire lawn?
a) 45
b) 75
c) 80
d) 90
e) 100
3/4x = 60 minutes
then x = 60 * 4/3 = 80
Hence C is the correct answer
If it takes ten minutes to fill 5/12 of a hole how many minutes will it take to fill the rest of the hole at this rate
a) 12
b) 14
c) 16
d) 18
e) 24
5/12 x = 10
then x = 10 * 12/5 = 24
then it will take (24 minus 10) minutes to fill the hole i.e 14 minutes
Hence B is the answer.
The ratio of the sides in an isosceles triangle is
1 : 1 : root 2
Properties of Diagonals in a Parallalogram
in a parallelogram
- diagonals are not of equal length
- they biscet each other in half
- They create 4 triangle of equal area
- The angles at the vertices are not bisected
- the angles at the middle are not right angles.
Properties of Diagonals in a Rectangle
In a Rectangle
- diagonals are equal in length
- they biscect each other in half
- they create 4 triangles of equal area
- the angles at the vertices are not bisected
- the angles in the middle are not right
Properties of a Rhombus
In a Rhombus
- Diagonals are not equal in length
- they Biscet each other in half
- they create 4 triangles of equal area
- The angles at the vertices are biscected
- The angles in the middle where the diagonals are right
Properties of Square
In a Square
- Diagonals are equal
- They biscet each other
- They create 4 triangles of equal area
- The angles at the vertices are bisected
- the angles in the middle are right.
If rectangle with integer side lengths has perimeter 10. What is the greatest number of these rectangles that can be cut from a piece of paper with width 24 and length 0
a) 144
b) 180
c) 240
d) 360
e) 480
The answer is D (i.e 360)
since the perimeter is 2l + 2w = 10 then L + w = 5
the smallest area rectangle would be when L = 4 and w = 1
then the area of the rectangle is 4*1 = 4
area of the paper is 24*60 = 1440
divide this by 4 we get 360
hence 360 small rectangles can be formed.
Arc Length formula
Arc length = (n/360) * 2 pi r
Area of sector
Area of sector = (n/360) * pi r^2
rules for angles formed by cords
- All angles extended by the same chord on to the circumfrance are equal
- angles extended by a chord on the center of a circle is twice of the angle extended at the circumfrance
- angles extended by the same chord on the opposite sides of the circumference are supplementary
- Angles extended by the diameter on to Any point on the circumference are equal to 90
A light house emits a light which can be seen for 60 miles in all directions. If the intensity of the light is strengthened so that its visibility is increased by 40 miles in all directions by approx. how mnay square miles is its region of visibility increased
a) 6300
b) 10000
c) 10300
d) 20000
e) 31400
the answer is D (i.e 20000)
the new area is pi (100)^2 = 10,000 Pi squred
the old area is pi (60)^2 = 3600 pi squred
then the difference is 6400 pi squared
but pi is 3.14 therefore we get the the closest number is 20000
hence d is the answer
Volume of a Rectangular solid :
Volume of a Rectangular solid : LBW
Surface Area of a Rectangular Solid
Surface Area of a Rectangular Solid: 2LW+2LH+2WH
Volume of Cube
LWH
Surface Area of Cube
6L^3
Volume of Cylinder
Pir^2h
Lateral Surface Area of
2pir*h
Total surface area
2pir^2+2pir*h
Equation of line
y = mx + c
Equation of Slope
(Change in y ) / Change in x
Points P and Q lie on the same line and have coordinates (1,3) and (5,8) respectively, which of the following points lie on the same line as point P and Q?
a) (-4,-5)
b) (-3,-2)
c) -2,-3)
d) (-1,-4)
e) (0,-1)
C is the correct answer.
Calculate the slope of the line
slope = change in y / change in x slope = (8-1)/(5-3) = 5/4
now check slope of each point
a) Slope = (8+4)/(5+5) = 12/10 = 6/5
b) Slope = (8+3)/(5+2) = 11/7
c) slope = (8+2)/(5+3) = 10/8= 5/4
Hence C is the correct answer
1!
1
2!
2
3!
6
4!
24
5!
120
6!
720
7!
5040
Two questions
a) A new country needs to create a flag and has decided upon a three stipe design. Ig has five colors to choose from : blue, green, yellow, white and red and no color can be used more than once. How many different flags can be created.
b) you have four friends in town but only two extra tickets for the concert. How many ways can the tickets can be distributed if you want to keep atleast two friends
c) what is the difference between the two questions and why are two separate formulas used
a) order matters hence we use permutations : perfumtation formula is 5P3 = 5! / (5-3)! = 54321/(21) = 60
b) Since order does not matter hence combinations formula needs to be used. 4!C2! = 4!/((4-2)!(2!)) = 4321/(21)(21) = 6
0!
1
formula for permutations
nPk = N! / (N-k)!
formula for Combinations
nCk = N!/((N-k)!*(k!))
five fundamental rules of GMAT English
a) Verb usage (Agreement, correct tense)
b) Reference (Proper usage of Pronouns and modifiers)
c) Parallel Structure (Consistancy among items, or comparision)
d) Idioms
e) Style (Effective Expression)
Each of entertainers ….. (was, were)
was
A series of sightings of UFOs .. (has, have)
has
Neither …. Nor .. (was, were)
was
there (is, are) a number of delicious ways
there are a number of
so as…..
Never correct.
Although “so…as to be…” is correct structure.
Idiom: Estimated….
both…..
Estimated to be
both … and
and also….
never correct. Considered to be redundant.
Idiom: Credit
Credit with
between….
Between X and Y
Idiom: Capable…
Capable of
A new generation of (sophisticated copy machines, capable of unprecedented detail and accuracy, are) prompting the development of more complex currency design to prevent counterfeiting.
a) sophisticated copy machines, capable of unprecedented detail and accuracy, are
b) sophisticated copy machines, capable for unprecedented detail and accuracy, is
c) sophisticated copy machines, capable of unprecedented detail and accuracy, is
d) sophisticated copy machines, capable for unprecedented detail and accuracy, are
e) sophisticated copy machines that are capable of unprecedented detail and accuracy, are
Answer@ C
generation …. is (generation is singular)
idiom: Capable of.
Early derisive reactions from art critics and established painters (did not discourage the Primitivist painter Henri Rousseau to exhibit repeatedly, despite him completely lacking formal training and starting late) as a professional artist.
a) did not discourage the Primitivist painter Henri Rousseau to exhibit repeatedly, despite him completely lacking formal training and starting late
b) did not discourage the Primitivist painter Henri Rousseau exhibiting repeatedly, completely lacking formal training though he was and starting late
c) did not discourage the Primitivist painter Henri Rousseau to exhibit repeatedly, despite their complete lack of formal training and late start
d) did not discourage the Primitivist painter Henri Rousseau in exhibiting repeatedly, despite his complete lack of formal training and late start
e) did not discourage the Primitivist painter Henri Rousseau from exhibiting repeatedly, despite his complete lack of formal training and late start
Answer : E
Idiom: Discourage from
