GRE Quantitative Reasoning

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GRE Quantitative Reasoning › GRE Quantitative Reasoning

Questions 1 - 10

Which statement is true assuming that a represents the range, b represents the mean, c represents the median, and d represents the mode.

Which sequence is correct for the number set: 51, 8, 51, 17, 102, 31, 20

c < b < d < a

b < d < c < a

c < a < d < b

a < b < d < c

d < c < a < b

Explanation

The answer is c < b < d < a.

When we arrange the number set we see: 8, 17, 20, 31, 51, 51, 102

a = range = 94

b = mean = 40

c = median = 31

d = mode = 51

median < mean < mode < range so c < b < d < a

Choose the answer which best solves the following equation:

$-7 \cdot -18 =$

Explanation

When multiplying integers, if both of the signs of the integers are the same (positive, or negative) then your result will be positive:

First multiply the ones digit of both numbers together. If the product is greater than ten remember to carry the one to the tens place.

$7\cdot 8=56$

Next multiply the ones digit of the smaller number with the tens digit of the larger number and add the number that was carried over.

$(7\cdot 1) +5=12$

Combine these two together to get:

$-7 \cdot -18 = 126$

A square is inscribed in a circle. The diameter of the circle is 10 feet. What is the area of the square?

$\dpi{100} \small 50ft^{2}$

$\dpi{100} \small 100ft^{2}$

$\dpi{100} \small 25ft^{2}$

$\dpi{100} \small 36ft^{2}$

It cannot be determined from the information provided.

Explanation

Since the diameter of the circle is 10, we know the radius of the circle is 5 feet. We can then draw radii that go from the center to two consecutive corners of the square. These radii are both 5 feet, and form a 90 degree angle (since they are diagonals of a square). Thus, with the enclosed side of the square they form a 45-45-90 triangle. Thus, the side of the square must be $\dpi{100} \small 5\sqrt{2}$ (this can also be found with the Pythagorean theorem). Then, the area of the square is

$\dpi{100} \small 5\sqrt{2}\times 5\sqrt{2}=50ft^{2}$

If 5 + x is 5 more than 5,what is the value of 2_x_?

Explanation

5 more than 5 = 10

5 + x = 10

Subtract 5 from each side of the equation: x = 5 → 2_x_ = 10

Quantity A: $\frac{15}{x}+\frac{12}{y}$

Quantity B: $\frac{15y+12x}{xy}$

Which of the following is true?

The two quantities are equal.

The relationship between the two quantities cannot be determined.

Quantity A is larger.

Quantity B is larger.

Explanation

Start by looking at Quantity A. The common denominator for this expression is . To calculate this, you perform the following multiplications:

$\frac{15}{x}*\frac{y}{y}+\frac{12}{y}*\frac{x}{x}$

This is the same as:

$\frac{15y}{xy}+\frac{12x}{xy}$ , or $\frac{15y+12x}{xy}$

This is the same as Quantity B. They are equal!

There is a line defined by the equation below:

There is a second line that passes through the point and is parallel to the line given above. What is the equation of this second line?

$y=-\frac{3}{4}x+2.75$

$y=-\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.75$

$y=\frac{3}{4}x+1.25$

$y=\frac{3}{4}x+2.625$

Explanation

Parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope-intercept form.

3x + 4y = 12

4y = _–_3x + 12

y = –(3/4)x + 3

slope = _–_3/4

We know that the second line will also have a slope of _–_3/4, and we are given the point (1,2). We can set up an equation in slope-intercept form and use these values to solve for the y-intercept.

y = mx + b

2 = _–_3/4(1) + b

2 = _–_3/4 + b

b = 2 + 3/4 = 2.75

Plug the y-intercept back into the equation to get our final answer.

y = –(3/4)x + 2.75

If $c\neq 0$ , then $\frac{(c^3)^2}{c^2c^4}=?$

Cannot be determined

Explanation

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

What's the distance between and on a number line?

Explanation

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract from to get .

Quantity A:

(0.5)3(0.5)3

Quantity B:

(0.5)7

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Explanation

When we have two identical numbers, each raised to an exponent, and multiplied together, we add the exponents together:

xaxb = xa+b

This means that (0.5)3(0.5)3 = (0.5)3+3 = (0.5)6

Because 0.5 is between 0 and 1, we know that when it is multipled by itself, it decreases in value. Example: 0.5 * 0.5 = 0.25. 0.5 * 0.5 * 0.5 = 0.125. Etc.

Thus, (0.5)6 > (0.5)7

For $\$15$ , Chelsea can get either a $16\ in$ diameter pizza or two $8\ in$ diameter pizzas. Which is the better deal?