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Number concepts and operations — SSAT Upper practice questions

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.

  • Section: Quantitative (Math) 50 questions on the paper
  • 263 practice questions in the app

Sample questions

Question 1

How many positive divisors of 24⋅33⋅522^4\cdot3^3\cdot5^2 are divisible by 18 but not by 45?

  1. A4
  2. B6
  3. C8
  4. D12
  5. E16
Show answer

Answer: C — 8

A divisor has the form 2a3b5c2^a3^b5^c, where 0≤a≤40\le a\le4, 0≤b≤30\le b\le3, and 0≤c≤20\le c\le2. Divisibility by 18=2⋅3218=2\cdot3^2 requires a≥1a\ge1 and b≥2b\ge2, giving 4⋅2⋅3=244\cdot2\cdot3=24 divisors. Of these, the divisors also divisible by 45=32⋅545=3^2\cdot5 have c≥1c\ge1, giving 4⋅2⋅2=164\cdot2\cdot2=16 divisors. Therefore 24−16=824-16=8 divisors meet the condition.

Question 2

Let pp and qq be rational numbers such that 0<p<q<10<p<q<1. Which expression has the greatest value?

  1. Apqpq
  2. Bpq\dfrac{p}{q}
  3. Cq−pq-p
  4. Dqq
  5. Eqp\dfrac{q}{p}
Show answer

Answer: E — qp\dfrac{q}{p}

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

Question 3

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

  1. A-7
  2. B7
  3. C3
  4. D49
  5. E−13-\dfrac{1}{3}
Show answer

Answer: B — 7

Equal absolute values imply 2x−4=x+52x-4=x+5 or 2x−4=−(x+5)2x-4=-(x+5), giving x=9x=9 or x=−1/3x=-1/3. Since xx is negative, x=−1/3x=-1/3. Thus ∣6x−5∣=∣−2−5∣=7|6x-5|=|-2-5|=7.

Practice 263 Number concepts and operations questions in the app

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Quantitative (Math)

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