Number concepts and operations — SSAT Upper practice questions

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Practice 289 Number concepts and operations questions in the app

What this topic is

On the SSAT Upper Quantitative (Math) exam, Number concepts and operations covers how integers, fractions, and rationals are factored, combined, and compared, including exponents, divisors, absolute value, and signed numbers.

A student has to count special divisors of a prime-power product, solve an absolute-value equation when a variable is negative, and identify which algebraic expression is largest when two rationals lie between zero and one. Items are multiple choice.

Common traps include dropping a divisibility constraint, ignoring a sign restriction, or ranking expressions in the wrong order. Answer choices tend to be nearby integers or look-alike expressions that follow from a single missed step.

Sample questions

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Question 1Harder

How many positive divisors of $2^4\cdot3^3\cdot5^2$ are divisible by 18 but not by 45?

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Answer: C — 8

A divisor has the form $2^a3^b5^c$ , where $0\le a\le4$ , $0\le b\le3$ , and $0\le c\le2$ . Divisibility by $18=2\cdot3^2$ requires $a\ge1$ and $b\ge2$ , giving $4\cdot2\cdot3=24$ divisors. Of these, the divisors also divisible by $45=3^2\cdot5$ have $c\ge1$ , giving $4\cdot2\cdot2=16$ divisors. Therefore $24-16=8$ divisors meet the condition.

Question 2Mid

Let $p$ and $q$ be rational numbers such that $0<p<q<1$ . Which expression has the greatest value?

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Answer: E — $\dfrac{q}{p}$

Since $q>p>0$ , $\dfrac{q}{p}>1$ . Each other expression is less than 1, so $\dfrac{q}{p}$ is greatest.

Question 3Harder

If $x$ is negative and $|2x - 4| = |x + 5|$ , what is $|6x - 5|$ ?

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Answer: B — 7

Equal absolute values imply $2x-4=x+5$ or $2x-4=-(x+5)$ , giving $x=9$ or $x=-1/3$ . Since $x$ is negative, $x=-1/3$ . Thus $|6x-5|=|-2-5|=7$ .

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Practice 289 Number concepts and operations questions in the app

Number concepts and operations — SSAT Upper practice questions

What this topic is

Sample questions

More SSAT Upper topics

Quantitative (Math)