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 ?
- A.
20
- B.
38
- C.
58
- D.
76
Attempted by 51 students.
Show answer & explanation
Correct answer: A
Answer: 20
Let x be the number of brainiacs who like math teasers.
Then the number who like rebus teasers is 2x (twice as many).
Those who like only math = x − 18. Those who like only rebus = 2x − 18. Both = 18. Neither = 4.
All groups together sum to 100, so (x − 18) + (2x − 18) + 18 + 4 = 100.
Simplify: 3x − 14 = 100, so 3x = 114 and x = 38.
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.