GRE MATH EXAM QUESTIONS

What is the side length of an equilateral triangle with altitude 6?

4sqrt3 [The triangle can be divided into two equal 30-60-90 triangles with side 6 as the side in which 6 = xsqrt3. So x =2sqrt3...]

5 bakeries sell an average of 300 muffins per bakery per day. If 2 stop making muffins but the total muffins sold stays the same, what is the average of muffins per bakery sold among the remaining?

500

If Madagascar exports totaled 1.3 billion in 2009, and 4% came from China, what was the value in millions of the country exports to China?

52

What is the area of a regular hexagon with side 6?

54sqrt3. [divide the hexagon into 6 congruent equilateral triangles.]

Reduce: 4.8 : 0.8 : 1.6

6 : 1 : 2

What are the smallest three prime numbers greater than 65?

67, 71, 73

What is the third quartile of the following data set: 44, 58, 63, 63, 68, 70, 82

70

What number between 70 and 75, inclusive, has the greatest number of factors?

72

What is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2, 4, and 6?

75:11

The four angles around a point measure y, 2y, 35 and 55 respectively. What is the value of y?

90

Find the surface area of a cylinder with radius 3 and height 12.

90pi

Ratio of ages of Anna and Emma is 3:5 and of Emma and Nicolas is 3:5. What is the ratio of Anna to Nicholas?

9:25

What transformation occurs if point C is reflected over the x-axis and then the y-axis?

A reflection of the axis (going from x to y)

Employee X is paid 19.50 per hour no matter how many a week. Employee Y earns 18 for the first 40 and 1.5 the hourly wage for every hour after that. If both earned the same amount and worked the same in one week, how many did each work?

48

In similar hexagons, the ratio of the areas is 16:25. What is the ratio of their corresponding sides?

4:5

For similar triangles, the ratio of their corresponding sides is 2:3. What is the ratio of their areas?

4:9. The ratio of the areas of two similar triangles equals the square of the ratio of the corresponding sides.

Simplify (a^2 + b)^2 - (a^2 - b)^2

4a^2(b)

For what values should the domain be restricted for the function f(x) = sqrt(x + 8)

-8

If 4500 is invested at a simple interest rate of 6%, what is the value of the investment after 10 months?

4725

How many digits are there between the decimal point and the first even digit in the decimal equivalent of 1/[(2^8)(5^3)]

0

A cylinder has a surface area of 22pi. If the cylinder has a height of 10, what is the radius?

1

A cylinder has surface area 22pi. If the cylinder has a height of 10, what is its radius?

1

If r, t, s & u are distinct, consecutive prime numbers, less than 31, which of the following could be an average of them (4, 4.25, 6, 9, 24, 22, 24)?

4.25, 6, 22

If 10800 is invested at a simple interest rate of 4%, what is the value of the investment after 18 months?

$11,448

Hector invested $6000. Part was invested in account with 9% simple annual interest, and the rest in account with 7% simple annual interest. If he earned $490 in the first year of these investments, how much did he invest in each account?

$3,500 in the 9% and $2,500 in the 7%.

Simplify the expression [(b^2 - c^2) / (b - c)]

(b + c)

Simplify the expression (p^2 - q^2)/ -5(q - p)

(p + q)/5

What is the maximum value for the function g(x) = (-2x^2) -1?

-1

A company places a 6-symbol code on each product. The code consists of the letter T, followed by 3 numerical digits, and then 2 consonants (Y is a conson). How many codes are possible?

441000 = 1 10 10 10 21 * 21

6w^2 - w - 15 = 0. What is the value of x?

-3/2 , 5/3

(a^-1)/a^5

1/a^6

There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. In how many ways can the judges award the 3 prizes?

10! / (10-3)! = 720

There are 10 finalists for the school spelling bee. A first, second, and third place trophy will be awarded. How many different people can get the three prizes?

10! / 3!(10-3)! = 120

From a box of 12 candles, you are to remove 5. How many different sets of 5 candles could you remove?

12! / 5!7! = 792

The perimeter of a square is 48 inches. The length of its diagonal is:

12sqrt2

What is the surface area of a cylinder with radius 5 and height 8?

130pi

A triangle is inscribed in a semi-circle with legs 5 and 12. What is the circumference of the semicircle?

13pi/2

If the 80th percentile of the measurements is 72 degrees, about how many measurements are between 69 degrees and 72 degrees? Round your answer to the nearest tenth

18

What is the coefficient of the x^2 term in the product of (x + 1)(x + 2)(x -1)?

2

In a triangle where the two legs are 4 and 3, what is the value of a line directly intersecting the middle coming from the meeting point of the two legs?

2.4 [We calculate the area (6) and then turn the triangle on its side and use x as the height to calculate again. (5x)/2=6]

A brick with dimensions 10. 15 and 25 weighs 1.5 kg. A second brick (same density) has dimensions 12, 18, and 30. What is the weight of the second brick?

2.592kg

If 8 schools are in a conference, how many games are played if each team plays each other exactly once?

28. n = 8, k = 2. n! / k!(n-k)!

How many 3-digit positive integers are even and do not contain the digit 4?

288 (8 9 4)

Nine coins are tossed simultaneously. In how many of the outcomes will the fourth coin tossed show heads?

2^9 / 2 = 256

Simplify 4sqrt21 X 5sqrt2 / 10sqrt7

2sqrt6

Simplify 9^(1/2) X 4^3 X 2^(-6)?

3

200 < x < 300. How many values of x are divisible by 5 & 8?

3 (240, 215 ,280)

P and r are factors of 100. What is greater, pr or 100?

Indeterminable

Which is greater? 200x^295 or 10x^294?

Relationship cannot be determined [what if x is negative?]

Describe the relationship between 3x^2 and 3(x - 1)^2

The graph of 3(x - 1)^2 is a translation (shift) of the graph one unit or space to the right.

Describe the relationship between the graphs of x^2 and (1/2)x^2

The second graph is less steep.

What are the roots of the quadrinomial x^2 + 2x + 1?

The two x's after factoring.

T or F? Given d,e & f =/ 0, [(d^3)e(f^5)] / 2d(e^3) / [3(d^2)(e^3)(f^7)] / [6(e^5)(f^2)]?

True

5x^2 - 35x -55 = 0. What is the value of x?

[(7+ sqrt93) /2], [(7 - sqrt93) / 2]

What is the common monomial factor in the expression 4(c^3)d - (c^2)(d^2) + 2cd?

cd

Suppose you have a set of n objects, and you want to select k of them, but the order doesn't matter. What formula do you use to determine the number of combinations of n objects taken k at a time?

n! / (k!)(n-k)!

If you have a set of n objects, but you only want to order k of them, what formula do you use to determine the number of permutations?

n! / (n-k)!

Factor x^2 - xy + x.

x(x - y + 1)

Suppose that the graph of f(x) is the result of stretching y=x + 5 away from the x-axis by a factor of 2. What is the new equation for the graph f(x)?

y = (x + 5)/2

Suppose that the graph of f(x) is the result of sliding the graph of y=2x^2 down 3 units of spaces. What is the new equation?

y = 2x^2 - 3