Number Concepts and Operations

Help Questions

SSAT Upper Level Quantitative › Number Concepts and Operations

Questions 1 - 10

Solve,

$\frac{2}{13}+\frac{4}{13}=?$

$\frac{6}{13}$

$\frac{6}{26}$

$\frac{3}{13}$

$\frac{2}{13}$

Explanation

Since the denominators for the fractions are the same, keep the denominator and add the numerators.

$\frac{2}{13}+\frac{4}{13}=\frac{2+4}{13}=\frac{6}{13}$

Define a function as follows:

$f(x) = 10 - \sqrt[3]{x} - \sqrt[5]{x}$

Evaluate .

The expression is undefined.

The correct answer is not among the other responses.

Explanation

$f(x) = 10 - \sqrt[3]{x} - \sqrt[5]{x}$

$f(-1) = 10 - \sqrt[3]{-1} - \sqrt[5]{-1} = 10 - (-1)- (-1)= 10+1+1 = 12$

Simplify:

$\frac{1+\frac{1}{x}}{3+\frac{3}{x}}$

$\frac{1}{3}$

$\frac{X+1}{X+3}$

Explanation

Simplify into a complex fraction for the numerator and denominator.

For the numerator, we need to multiply $1\cdot \left(\frac{x}{x}\right)$ then the top should read $\frac{x+1}{x}$ .

For the bottom, we need to multiply $3 \cdot \left(\frac{x}{x} \right )$ in order to add the components. Thus the bottom should read $\frac{3x+3}{x}$ .

Dividing fractions is the same as multiplying the numerator by the reciprocal of the denominator.

Therefore, multiply top and bottom by $\frac{x}{3x+3}$ and then you should see that if you factor a on the bottom, the cancels along with the .

$\frac{x+1}{x}\cdot \frac{x}{3x+3}\rightarrow \frac{x+1}{x}\cdot \frac{x}{3(x+1)}=\frac{1}{3}$

The answer then should be $\frac{1}{3}$ .

and are prime integers. and .

How many possible values of are there?

Five

Six

Four

Seven

Eight

Explanation

The prime integers between 65 and 75 are 67, 71, and 73, so assumes one of those values; the prime integers between 45 and 55 are 47 and 53, so assumes one of those values. Therefore, one of the following holds true: