Last Updated on May 11, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that the positive integer n is added to each of the integers 69, 94, and 121, and need to determine the value of n.
Statement One Alone:
69 + n and 94 + n are the squares of two consecutive integers.
From statement one, we can say that for some positive integer x, 69 + n = x^2 and 94 + n = (x + 1)^2. Let’s subtract the first equation from the second equation:
(94 + n) – (69 + n) = (x + 1)^2 – x^2
25 = x^2 + 2x + 1 – x^2
25 = 2x + 1
24 = 2x
12 = x
Since we know x = 12, we can substitute this into the first equation to determine the value of n:
69 + n = 12^2
69 + n = 144
n = 75
Statement one alone is sufficient to answer the question. Eliminate answer choices B, C and E.
Statement Two Alone:
94 + n and 121 + n are the squares of two consecutive integers.
We can use the same method that we used in statement one to solve for n. Therefore, without performing the actual calculations, we can conclude that we can find a unique value for n. Statement two alone is also sufficient to answer the question.
Answer: D
