GRE Math Problem Types

The total number of recording titles distributed by music distributors L and M is 9,300. The number of recording titles distributed by L is 7,100, and the number of recording titles distributed by M is 5,200. Which of the following statements must be true?

Add the two individuals and subtract by the total to get the overlap.

Compare: Std deviation of set of five numbers between 0-10; Std deviation of set of five numbers between 10-20

Don't know which 5 numbers were used in each set. Could be same could be different.

Graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?

Draw Venn Diagram. X cannot be greater than 142 OR 121 so it must be 121.

In triangle ABC, AB=AC=2, which could be the area?

Draw a right, acute and obtuse triangle

If A is 6km east of B which is 8km north of C....

Draw diagram, solve using pythagorean

In the xy-plane, line k is a line that does not pass through the origin. Which of the following statements individually provide(s) sufficient additional information to conclude that the slope of line k is negative?

Draw each scenario out on a grid

What information is necessary to find the area of a triangle?

Either two angles and a side or two sides and an angle (3 total)

How far away are points on a bisecting perpendicular line from two points on the original line?

Equidistant

On a radio tower, a red light flashes every 6 seconds and a blue light flashes every 10 seconds. If both lights flash together at a certain time, how many seconds later will both lights flash together the next time?

Find the LCM. DO NOT ASSUME that it's a x b. In this case, it is NOT 60. It is 30 seconds.

A car dealer received a shipment of cars, half of which were black, with the remainder being blue, silver and white. During the next month, 70% of the black cars, 80% of the blue cars, 30% of the silver cars and 40 percent of the white cars were sold. What percent of the shipment of cars were sold during that month?

(1/2)(70%)+(1/6)(80%)+(1/6)(30%)+(1/6)(40%)=60%

If j and k are integers and j-k is even, which of the following must be even?

(Choose One) Two even plugs will result in every answer choice so try using odd plugs first. READ DIRECTIONS CAREFULLY!

Compare: slope of line that goes through origin and (3,4); 1

(Y2-Y1)/(X2-X1) RISE(y) OVER RUN(x)

(1-x)/(x-1)=1/x; what is greater: x or -1/2

(y-x)/(x-y)=-1 ALWAYS. Or cross multiply. 0 CANT BE IN DENOMINATOR.

What is the least integer n such that the fraction 1/2^n is less than 0.001 ?

.001=1/1,000; what power of 2 is just over 1,000?

What is 0.05% of 8

.004

What is n^0?

1

What are the multiples of 1 less than 4?

1, 2, 3, 4

k is a digit in the decimal 1.3k5, and 1.3k5 is less than 1.33. What is greater k or 1?

1.30 < 1.3k5 < 1.33; k<=2 so could be 0,1,2 - don't know

a^-1

1/a

If 5/12 of class is boys, what is ratio of girls to boys?

12 total, 7 girls; 7:5 ratio 7/5

What percent of the normal distribution is less than a standard deviation of 1? Where does 15th percentile fall?

14% + 2% = 16% are less than 1 standard deviation. 15% is less than 16% so it is below -1.

What are the divisors of 17?

17, 1

The company at which Mark is employed has 80 employees, each of whom has a different salary. Mark's salary of $43,700 is the second-highest salary in the first quartile of the 80 salaries. If the company were to hire 8 new employees at salaries that are less than the lowest of the 80 salaries, what would Mark's salary be with respect to the quartiles of the 88 salaries at the company, assuming no other changes in the salaries?

1st quartile is 0-25%; 4th quartile is 76%-100%

If 20 is diameter of a circle and shaded area is 80TT, what is area of non-shaded region?

20/2=10, a=TTr^2; a=100TT-80TT=20TT

Aisha's income in 2004 was 20 percent greater than her income in 2003. What is the ratio of Aisha's income in 2004 to her income in 2003 ?

2004=120; 2003=100 - 120/10=1.2; 6/5=1.2

What are the divisors of 21?

21, 7, 3, 1

What is the least positive integer that is not a factor of 25! and is not a prime number?

25! is equal to the product of all positive integers from 1 to 25, inclusive. Thus, every positive integer less than or equal to 25 is a factor of 25!. Also, any integer greater than 25 that can be expressed as the product of different positive integers less than 25 is a factor of 25!

Each integer 1-50 w/ units digit 3 available. 2 picks made, what is probability that both are prime?

3, 13, 23, 33, 43; 4/5 prime; 4/5x3/4=3/5

What is the tens digit in 345

4

What is the units digit in 1,254

4

If four boys shovel driveway in 4 hours, how many min long it take 6 boys

4 boys x 240 min = 960 boy-min; 960/6= 160 min

What are the multiples of 5 less than 16?

5, 10, 15

Y has a mean of 200 and a standard dev of 10. What is greater - probability that Y is >220 or 1/6?

95% of outcomes are within 2 std devs so <5% (1/20) chance it is 220+

If (x+2)/17=x/16, what is (x+6)/19

Cross multiply, 17x=16(x+2), solve for x and plug

Compare: 2^x; 3^x+1 given that: x is a negative integer

Plug and solve, examine relationship each time. Start with -1, then -2 and -3. Cannot be determined.

Eight points are equally spaced on a circle. If 4 of the 8 points are to be chosen at random, what is the probability that a quadrilateral having the 4 points chosen as vertices will be a square?

Ask yourself / draw: HOW MANY SQUARES CAN BE DRAWN? # of squares that can be drawn / # of quadrilaterals that can be drawn

If the total enrollment is 12 percent greater than it was five years ago, what was the total enrollment five years ago?

Cannot use 1400- it is not 12% less than it currently is. It is 12% greater than it was FIVE YEARS AGO. Backsolve using the answers.

m=10^32+2; when m is divided by 11, the remainder is r. Compare: r, 3

Compute the remainders of 10^1, 10^2, 10^3 and check for a pattern

What is the probability that a three digit number chosen at random is a palindrome

Counting principle, 3 jobs, 9x10x1=90/900

Theoperation⊗isdefinedforallintegersxandyasx⊗y=xy−y.Ifxand y are positive integers, which of the following CANNOT be zero?

For each option, set the equation equal to zero and try to find integers that make it zero. If you can't find integers that work that is the correct equation.

Of the people in a certain survey, 58 percent were at most 40 years old and 70 percent were at most 60 years old. If 252 of the people in the survey were more than 40 years old and at most 60 years old, what was the total number of people in the survey?

Given the information, 70% - 58% of people (12%) were 40<12%<=60; We are told that 252 are in the 12% so 252/.12=2,100

In the xy-plane, the equation of line k is 3x − 2y = 0 - what is greater - x or y intercept?

Intercepts are when the value of x or y when the other = 0

The length of each side of rectangle R is an integer, and the area of R is 36. Compare: The number of possible values of the perimeter R; 6

Length of each side of rectangle is a factor of the area. (1x36) (2x18) (3x12) (4x9) (6x6) 5 rectangles

Two people buy TV. Cashier 1 adds tax then applies discount. Cashier 2 applies discount then adds tax. Who pays more?

Pay the same - increase of x, decrease of y=decrease of y, increase of x

In 1950 Rob was 4x as old as Juan. In 1955, Rob was 3x as old as Juan. How old Rob when Juan born?

Make table. 4x+5=3(x+5)=3x+15; x=10

If the area of rectangle is 40, which of the following could be perimeter?

Perimeter is smallest when rectangle is a square; must be at least 4root(40)

The circles shown are tangent at point B. Point A is the center of the larger circle, and line segment AB is a diameter of the smaller circle. The area of the smaller circle is what fraction of the area of the larger circle?

Plug in a random number for line segment AB. Find area of larger circle using line AB (radius). Divide line AB by 2 to get the radius of smaller circle and calc the area using that.

if 1/(k^2)+1/(k^2)=1/(x^2) then x expressed in terms of k is

Plug in for K, narrow answer choices down. If multiple answers work, plug in a different number until only one answer choice remains.

If p is a negative number and 0<s<|p| which of the following must also be a negative number?

Plug in numbers - For all the choices - if any term is squared, even if the result inside the ( ) is negative - IT WILL RESULT IN A POSITIVE, so immediately take those out.

The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00.

Price=x; 7<1.04x<10; divide by 1.04; 6.73<x<9.62

In a single line of people waiting to purchase tickets for a movie, there are CURRENTLY 10 people behind Sarah. If 3 of the people who are CURRENTLY in line ahead of Sarah purchase tickets and leave the line, there will be 8 people ahead of Sarah in line. How many people are in the line CURRENTLY?

READ - "IF" 3 of the people leave. THEY DIDNT LEAVE. IT SAYS IF THEY LEAVE. READ

Compare: (3^(-1))/(4^(-1)); 4/3

REMEMBER that a^(-1)/1=1/a AND 1/a^(-1)=a

Compare area of 45 triangle vs. 30/60 triangle w/ same hypotenuse

Root(2) and Root(3); 2

The integer v is greater than 1. If v is the square of an integer, which of the following numbers must also be the square of an integer?

Set v=square of an integer (ie. 4) and then plug in for all values of v for the options

Which of the following is an equation of a line that is perp to line 2x+3y=4

Slope intercept-> y=-2/3x+4/3; slope=-2/3; perp line has slope that is negative reciprocal

Compare the length of the hypotenuse of a triangle enclosed in a circle if you know the length of the legs and that the angle of middle of triangle is greater than 90.

Solve for hypotenuse as if it was a right triangle. Since you know it is greater than 90, you know that the hyp you solved for is the MINIMUM it could be.

x, y and z are sides of triangle. Compare: x+y+z; 2z

Subtract z from both sides. x+y=z. Ina all triangle the length of each side must be less than the sum of the length of the two other sides.

Compare: sum of odd integers from 1 to 199; sum of even integers from 2 to 198

Subtract, divide by two and add 1 and that is the number of integers you are summing. Compare and if one is greater than that is the choice

Alice earns d dollars and has t percent of what she earns deducted for taxes. How much of what she earns does Alice have left after taxes?

T percent can be expressed as t/100 or .01t so it is d(1-.01t)

Twelve numbers are given. They are 10, 10, 10, 10, 8, 8, 8, 8, 12, 12, 11, and y. The twelve numbers shown represent the age, in years, of the twelve houses on a certain city block. What is the median age, in years, of the twelve houses on the block?

Take whatever number is in the middle. Add "y" one above and one below and then see if it would make a difference.

Compare: 950^2,000; 10^6,000

Them both in the same base. You know 10^3 = 1,000; (10^3)^2,000=10^6,000 but since 10^3 is > 950; 10^6K is greater

How do you calculate the median from a frequency distribution graph?

The median is the average of the two middle numbers

For how many positive integers m<=100 is (m-5)(m-45) positive?

The numbers must either both be POSITIVE or NEGATIVE; so find out what #s would work for the expressions to either BOTH be positive or BOTH be negative.

Compare: # of subsets of S that consist of 1 object vs. # of subsets of S that consist of 4 objects given that: set S consists of 5 objects

There is ONE subset with 1 object and ONE subset with 4 objects (they are EQUAL)

If an investment of P dollars is made today and the value of the investment doubles every 7 years, what will be the value of the investment, in dollars, 28 years from today?

Today = P 7 Years = 2P 14 Years = 4P 21 years = 8P 28 Years = 16P

What length is greater - average of two chords or diameter

Two chords are both less than diameter in length so average of two chords would also be less

In the figure above, O and P are the centers of the two circles. If each circle has radius r, what is the area of the shaded region?

Use area of equilateral triangle: (s^2root(3))/4; s=r

In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence?

WORK BACKWARDS. (19+3) / 2 etc.

If 1/(2^11)(5^17) is expressed as a terminating decimal, how many nonzero digits will the decimal have?

Write the fraction in powers of 10 using rules of exponents

Compare x, y: 1/x=1+1/y

Y-x=xy

Compare: u & v given that: 2u+v=14; uv=0

You know one or the other is 0. Plug 0 in for each and you'll see either could be greater, not enough info to determine

Compare: xy; -12 given that: (x+3)(y-4)=0

You know that at least on of the terms is 0 but maybe not both. If x=-3 the equation is satisfied but y could equal 1 which would make xy>-12 so you don't have enough info.

1/a^-1

a

Which of the following expresses area of circle in terms of circumference?

plug and solve for radius; c^2/4TT

xy=8; x=y-2. Compare: y, 0

plug in for x to get y^2-2y-8=0 REMEMBER YOU CAN BRING THE 8 OVER AND GET ZERO. Factor and get (y-4)(y+2) - can either be -2 or +4 so we dont know if it is greater than or less than zero

(x+y)^2

x^2 + 2xy + y^2

(x-y)^2

x^2 - 2xy + y^2

(x+y)(x-y)

x²-y²