A survey was taken among 100 brainiacs . Of those surveyed , twice as many…

2025

A survey was taken among 100 brainiacs . Of those surveyed , twice as many brainiacs like rebus teasers as math teasers . If 18 brainiacs like both rebus teasers and math teasers and 4 like neither kind of teaser . How many brainiacs like math teasers but not rebus teasers ?

  1. A.

    20

  2. B.

    38

  3. C.

    58

  4. D.

    76

Attempted by 51 students.

Show answer & explanation

Correct answer: A

Answer: 20

  1. Let x be the number of brainiacs who like math teasers.

  2. Then the number who like rebus teasers is 2x (twice as many).

  3. Those who like only math = x − 18. Those who like only rebus = 2x − 18. Both = 18. Neither = 4.

  4. All groups together sum to 100, so (x − 18) + (2x − 18) + 18 + 4 = 100.

  5. Simplify: 3x − 14 = 100, so 3x = 114 and x = 38.

  6. The number who like math teasers but not rebus teasers = x − 18 = 38 − 18 = 20.

Check: only-math 20 + only-rebus (2×38 − 18 = 58) + both 18 + neither 4 = 20 + 58 + 18 + 4 = 100, so the answer is consistent.

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