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26 Apr 2026, 04:17
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
67% (02:35) correct
33%
(02:59)
wrong
based on 6
sessions
History
Date
Time
Result
Not Attempted Yet
Esther and Florian have a son named Diego. The average of their three ages is 16 greater than Diego’s age and 11 less than Florian’s age. If Esther is 37, how old is Diego?
(A) 2
(B) 3
(C) 6
(D) 11
(E) 16
(A) 2
(B) 3
(C) 6
(D) 11
(E) 16
26 Apr 2026, 05:20
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Answer is (E) 16.
This is a Word Problems question testing your ability to set up a system of equations. The wording is designed to trip you up, and honestly, I read it twice the first time I saw a question like this.
Let me call Diego's age D, Florian's age F, and the average of all three ages A.
1. We're told the average is 16 greater than Diego's age: A = D + 16
2. We're told the average is 11 less than Florian's age: A = F - 11
3. From (1) and (2): F - 11 = D + 16, so F = D + 27
4. The average formula: A = (37 + F + D) / 3
5. Substituting A = D + 16: (37 + F + D) / 3 = D + 16, which gives 37 + F + D = 3D + 48
6. Plug in F = D + 27: 37 + (D + 27) + D = 3D + 48
7. 64 + 2D = 3D + 48
8. D = 16
The trap here is (D) 11. A lot of people see "11 less than Florian" and somehow write Diego = 11 instead of using it as a relationship between the average and Florian's age. The question is testing whether you can keep track of what "11 less than" belongs to.
Quick check: D = 16, F = 43, A = (37 + 43 + 16)/3 = 96/3 = 32. Is 32 equal to D + 16? 16 + 16 = 32. Yes. Is 32 equal to F - 11? 43 - 11 = 32. Yes.
Always back-substitute in these word problems. Takes 10 seconds and saves you from a wrong answer.
This is a Word Problems question testing your ability to set up a system of equations. The wording is designed to trip you up, and honestly, I read it twice the first time I saw a question like this.
Let me call Diego's age D, Florian's age F, and the average of all three ages A.
1. We're told the average is 16 greater than Diego's age: A = D + 16
2. We're told the average is 11 less than Florian's age: A = F - 11
3. From (1) and (2): F - 11 = D + 16, so F = D + 27
4. The average formula: A = (37 + F + D) / 3
5. Substituting A = D + 16: (37 + F + D) / 3 = D + 16, which gives 37 + F + D = 3D + 48
6. Plug in F = D + 27: 37 + (D + 27) + D = 3D + 48
7. 64 + 2D = 3D + 48
8. D = 16
The trap here is (D) 11. A lot of people see "11 less than Florian" and somehow write Diego = 11 instead of using it as a relationship between the average and Florian's age. The question is testing whether you can keep track of what "11 less than" belongs to.
Quick check: D = 16, F = 43, A = (37 + 43 + 16)/3 = 96/3 = 32. Is 32 equal to D + 16? 16 + 16 = 32. Yes. Is 32 equal to F - 11? 43 - 11 = 32. Yes.
Always back-substitute in these word problems. Takes 10 seconds and saves you from a wrong answer.
