DSQ: Understanding exponents

Practice Questions

GMAT Quantitative Reasoning › DSQ: Understanding exponents

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1

is an integer. Is there a real number such that $x^{A}=B$ ?

Statement 1: is negative

Statement 2: is even

2

Does $\log_{2} \left ( MN \right )$ exist?

Statement 1: and are both negative.

Statement 2: divided by 2 yields an integer.

3

Johnny was assigned to write a number in scientific notation by filling the circle and the square in the pattern below with two numbers.

$\bigcirc \times 10 ^{\square }$

Johnny filled in both shapes with numbers. Did he succeed?

Statement 1: He filled in the circle with the number "10".

Statement 2: He filled in the square with a negative integer.

4

Solve the following rational expression:

$\frac{x^{m-n}10^{n-1}}{10^{(\frac{m}{2}-2)}x^{n}}$

(1)

(2)

5

is a number not in the set $\left{-1, 0, 1 \right}$ .

Of the elements $\left { x^{2}, x^{3}, x^{4}\right }$ , which is the greatest?

Statement 1: is a negative number.

Statement 2: $\left | x\right |>\frac{1}{2}$

6

Is $x^{2} < x$ ?

(1)

(2)

7

is a number not in the set $\left{-1, 0, 1 \right}$ .

Of the elements $\left { x^{4}, x^{5}, x^{6}\right }$ , which is the greatest?

Statement 1: is a negative number.

Statement 2: $\left | x\right | > 1$

8

Myoshi has been assigned to write one number in the circle and one number in the square in the diagram below in order to produce a number in scientifc notation.

$\bigcirc \times 10^{\square }$ .

Did Myoshi succeed?

Statement 1: Myoshi wrote in the circle.

Statement 2: Myoshi wrote in the square.

9

Philip has been assigned to write one number in the circle and one number in the square in the diagram below in order to produce a number in scientifc notation.

$\bigcirc \times 10^{\square }$ .

Did Philip succeed?

Statement 1: Philip wrote in the circle.

Statement 2: Philip wrote in the square.

10

Chord

Note: Figure NOT drawn to scale.

Examine the above diagram. True or false: $\overline{AB} \cong \overline{YZ}$ .

Statement 1: $\Delta ACB \sim \Delta ZXY$

Statement 2: $\Delta ACB$ and $\Delta ZXY$ have the same perimeter.

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