GRE® Quant Practice | Numeric Entry Q3

The GRE quant sample question given below is a Numeric Entry question in Set Theory. This question also touches upon framing some elementary Linear Equations. A GRE hard math question.

Question 3: Last summer vacation John played with Sam either in the evening or in the morning, never once playing both in the morning and the evening on the same day. On a few days, John did not play with Sam. If they did not play in the mornings for 18 days and did not play in the evenings on 21 days and played together 27 days, how long was the summer vacation?

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Video Explanation

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Explanatory Answer | GRE Set Theory Questionbank Q3

Objective: Compute Total length of the Summer Vacation

Let the number of days in the summer vacation be n.
Let us decode the information and frame equations:
They did not play in the mornings for 18 days. So, they played together in the mornings on (n - 18) days.
They did not play in the evenings on 21 days. So, they played together in the evenings on (n - 21) days.
They played together for 27 days.
So, the sum of number of days they played together in the mornings and the number of days they played together in the evenings should be 27.

i.e., (n - 18) + (n - 21) = 27
2n - 39 = 27
2n = 66 → n = 33

The summer vacation lasted for 33 days.