Number concepts and operations — SSAT Upper practice questions

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Practice 299 Number concepts and operations questions in the app

What this topic is

Number concepts and operations is the part of SSAT Upper math that tests how well you understand numbers rather than any single formula: factors and divisors, primes, absolute value, signs, and how fractions between zero and one behave.

A frequent mistake is assuming that squaring or multiplying always makes a number larger. For a value between zero and one, squaring makes it smaller, so one-half squared is one-quarter. Questions are multiple choice and often ask which expression is greatest, how many divisors meet a condition, or what an absolute value equals once a variable's sign is known.

Testing a simple value such as one-half usually settles the comparison questions quickly.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Harder

How many positive divisors of $2^{4} \cdot 3^{3} \cdot 5^{2}$ are divisible by 18 but not by 45?

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Answer: C — 8

A divisor has the form $2^{a} 3^{b} 5^{c}$ , where $0 \leq a \leq 4$ , $0 \leq b \leq 3$ , and $0 \leq c \leq 2$ . Divisibility by $18 = 2 \cdot 3^{2}$ requires $a \geq 1$ and $b \geq 2$ , giving $4 \cdot 2 \cdot 3 = 24$ divisors. Of these, the divisors also divisible by $45 = 3^{2} \cdot 5$ have $c \geq 1$ , giving $4 \cdot 2 \cdot 2 = 16$ 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 — $\frac{q}{p}$

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

Question 3Harder

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

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Answer: B — 7

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 299 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)