GRE Math

The sum of 2 numbers, x and y, equals twice their product. If x=3, what is the value of y?

create formula: x + y = 2(xy) if x=3 ...then... 3 + y = 2(3y) solve for y 3+y = 6y 3 = 6y−y 3 = 5y *y = 3/5*

If x is an integer and x²<37, what is the greatest possible value of x minus the least possible value of x?

greatest possible = 6² = 36 least possible = (-6)² = 36 6 - (-6) = 12

What is the number of squares of perimeter 36 into which a rectangle with width 36 and length 72 can be partitioned?

32

Exponents

(-#) raised to an even power = positive number (-#) raised to an odd power = negative number (−3)² = (−3)(−3) = 9 (−3)⁵ = (−3)(−3)(−3)(−3)(−3) = −243 x⁰=1 x⁻¹ = 1/x x⁻³ = 1/(x³) (x)(x⁻¹) = x(1/x) = 1

The average (arithmetic mean) of five numbers is 25. After one of the numbers is removed, the average of the remaining numbers is 31. What number has been removed?

1

Sally is making sun tea. Every hour, the concentration of the tea doubles. If it takes 6 hours for the tea to be ready, how long would it take for the tea to reach half of the final concentration?

1 hour = C(2) 2 hour = 2(2) = 4 3 hour = 4(2) = 8 4 hour = 8(2) = 16 5 hour = 16(2) = 32 6 hour = 32(2) = 64 how long would it take the tea to reach HALF of the final concentration of 64? 64/2 = 32... 32 is on the 5th hour *5* hours

To the nearest 10 percent, the decline in farm population in Country X between 1950 and 1960 represented what percent of the 1950 farm population? (see graph)

1950 = 23 1960 = 16 (23-16) = 7 7/23 = 0.30 = 30%

A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?

2¼

What is the units digit of the product (3)(2⁹⁹)

4

City Y has installed 30 parking meters at 15-foot intervals along a straight street. What is the number of feet between the first meter and the last meter?

435 -If there are 30 parking meters at 15-foot intervals, the total number of 15-foot intervals is 29. - 15(29) = 435.

If the radius of a circle is decreased by 30 percent, by what percent will the area of the circular region be decreased?

51% -Area of a circle = πr²

When a certain number is divided by 7, the remainder is 0. If the remainder is not 0 when the number is divided by 14, then the remainder must be

7 Consider the number 21, which is divisible by 7 but not divisible by 14. When 21 is divided by 14, 14 goes into 21 one time with a remainder of 7.

How many positive whole numbers less than 81 are not equal to squares of whole numbers?

72

A farmer has two rectangular fields. The larger field has twice the length and 4 times the width of the smaller field. If the smaller field has area K, then the area of the larger field is greater than the area of the smaller field by what amount?

7K

If 3ⁿ=243, what is the value of n?

n = 5

A=(πd²)/x If the formula above gives the area A of a circular region in terms of its diameter d, then x=

x = 4

Jerry received both the 15th highest and the 15th lowest mark in the class. How many students are in the class?

number up to 15 being the midway point. That puts 14 numbers behind, 14 numbers ahead, plus the one middle number of 15. (14)+(14)+(1) = 29 kids