SSAT Upper Level Quantitative - Algebra

Evaluate: $\begin{vmatrix}; ; \left | 5- 3 \cdot 4\right |-8 \right ;\end{vmatrix}$

Explanation

$\begin{vmatrix}; ; \left | 5- 3 \cdot 4\right |-8 \right ;\end{vmatrix}=\begin{vmatrix}; ; \left | 5- 12\right |-8 \right ;\end{vmatrix}=\begin{vmatrix}; ; \left | -7\right |-8 \right ;\end{vmatrix}=| 7 - 8| = | -1| = 1$

and are both positive integers; A is odd. What can you say about the number

$(A + B + 1)^{A+B+1}$ ?

$(A + B + 1)^{A+B+1}$ is odd if is odd, and even if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and odd if is even.

$(A + B + 1)^{A+B+1}$ is odd if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is even if is even, and can be odd or even if is odd.

Explanation

If is odd, then , the sum of three odd integers, is odd; an odd number taken to any positive integer power is odd.

If is even, then , the sum of two odd integers and an even integer, is even; an even number taken to any positive integer power is even.

Therefore, $(A + B + 1)^{A+B+1}$ always assumes the same odd/even parity as .

Michael scores a 95, 87, 85, 93, and a 94 on his first 5 math tests. If he wants a 90 average, what must he score on the final math test?

Explanation

To solve for the final score:

Add the five past test scores and you get 454. Then set up an algebraic equation where you add 454 to , which is the final test score, and divide by six, because you want the average for 6 tests now. You make this equation equal to 90 because that is the average Michael wants and solve for :

$\left ( 454+x\right )\div6 = 90$

Evaluate: $\begin{vmatrix}; ; \left | 5- 3 \cdot 4\right |-8 \right ;\end{vmatrix}$

Explanation

Michael scores a 95, 87, 85, 93, and a 94 on his first 5 math tests. If he wants a 90 average, what must he score on the final math test?

Explanation

To solve for the final score:

$\left ( 454+x\right )\div6 = 90$

Evaluate: $\dpi{100} (3^{3})^{2}$

$\dpi{100} 3^{6}$

$\dpi{100} 3^{5}$

$\dpi{100} 243$

$\dpi{100} 729$

Explanation

A power raised to a power indicates that you multiply the two powers.

$\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$

and are both positive integers; A is odd. What can you say about the number

$(A + B + 1)^{A+B+1}$ ?

$(A + B + 1)^{A+B+1}$ is odd if is odd, and even if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and odd if is even.

$(A + B + 1)^{A+B+1}$ is odd if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is even if is even, and can be odd or even if is odd.

Explanation

If is odd, then , the sum of three odd integers, is odd; an odd number taken to any positive integer power is odd.

If is even, then , the sum of two odd integers and an even integer, is even; an even number taken to any positive integer power is even.

Therefore, $(A + B + 1)^{A+B+1}$ always assumes the same odd/even parity as .

Michael scores a 95, 87, 85, 93, and a 94 on his first 5 math tests. If he wants a 90 average, what must he score on the final math test?

Explanation

To solve for the final score:

$\left ( 454+x\right )\div6 = 90$

and are both positive integers; A is odd. What can you say about the number

$(A + B + 1)^{A+B+1}$ ?

$(A + B + 1)^{A+B+1}$ is odd if is odd, and even if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and odd if is even.

$(A + B + 1)^{A+B+1}$ is odd if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is even if is odd, and can be odd or even if is even.

$(A + B + 1)^{A+B+1}$ is even if is even, and can be odd or even if is odd.

Explanation

If is odd, then , the sum of three odd integers, is odd; an odd number taken to any positive integer power is odd.

If is even, then , the sum of two odd integers and an even integer, is even; an even number taken to any positive integer power is even.

Therefore, $(A + B + 1)^{A+B+1}$ always assumes the same odd/even parity as .

Evaluate: $\dpi{100} (3^{3})^{2}$

$\dpi{100} 3^{6}$

$\dpi{100} 3^{5}$

$\dpi{100} 243$

$\dpi{100} 729$

Explanation

A power raised to a power indicates that you multiply the two powers.

$\dpi{100} (3^{3})^{2}=3^{3\cdot 2}=3^{6}$

Algebra

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