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Quantitative (Math)Free

Patterns, sequences, and series — SSAT Upper practice questions

On the SSAT Upper Quantitative (Math) section, Patterns, sequences, and series covers repeating last-digit cycles, arithmetic growth, and finding a missing or next term. A student has to extend a sequence, total several days of practice that increase by a fixed amount each day, or find the units digit of a large power without computing the full value. Items are multiple-choice word problems or short next-term questions. Common traps include miscounting days, adding only the last amount, and confusing additive change with a multiplicative pattern. Answer choices are nearby integers that match those mistakes.

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

Sample questions

Question 1

What is the units digit of 347+7463^{47}+7^{46}?

  1. A0
  2. B2
  3. C4
  4. D6
  5. E8
Show answer

Answer: D — 6

Powers of 3 have units digits 3,9,7,1, repeating every 4 powers, so 3473^{47} has units digit 7. Powers of 7 have units digits 7,9,3,1, repeating every 4 powers, so 7467^{46} has units digit 9. The sum has units digit 6.

Question 2

2,6,18,54,…2, 6, 18, 54, \ldots

What is the next term in the sequence?

  1. A108
  2. B144
  3. C156
  4. D162
  5. E216
Show answer

Answer: D — 162

Each term is 3 times the preceding term, so the next term is 54×3=16254 \times 3 = 162.

Question 3

Leah practices the cello for 13 minutes on Monday. On each of the next four days, she practices 2 minutes longer than on the preceding day. How many minutes does she practice during the five days altogether?

  1. A75
  2. B80
  3. C85
  4. D90
  5. E95
Show answer

Answer: C — 85

The five practice times are 13,15,17,19,13,15,17,19, and 21 minutes. Their sum is 85 minutes.

Practice 103 Patterns, sequences, and series questions in the app

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