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21 Mar 2023, 09:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
49% (02:01) correct
51%
(02:12)
wrong
based on 78
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are positive integers, is x^2 + y^2 + 2 divisible by 6?
(1) xy is even
(2) x is odd
(1) xy is even
(2) x is odd
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
31 Mar 2023, 14:16
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Bunuel
For x^2 + y^2 + 2 to be divisible by 6, x^2 + y^2 + 2 should be even.
Statement 1
(1) xy is even
Case 1: x = 6, y = 4
x^2 + y^2 + 2 = 36 + 16 + 2 = 54
Is 54 divisible by 6 - Yes!
Case 2: x = 1, y = 4
x^2 + y^2 + 2 = 1 + 16 + 2 = 19
Is 19 divisible by 6 - No!
As we are getting multiple answers to the question, the statement alone is not sufficient.
We can eliminate A and D.
Statement 2
(2) x is odd
Case 1: x = 1, y = 3
x^2 + y^2 + 2 = 1 + 9 + 2 = 12
Is 12 divisible by 6 - Yes!
Case 2: x = 1, y = 4
x^2 + y^2 + 2 = 1 + 16 + 2 = 19
Is 19 divisible by 6 - No!
As we are getting multiple answers to the question, the statement alone is not sufficient.
We can eliminate B.
Combined
Combined, x is odd and y is even.
In that case, x^2 + y^2 + 2 = odd.
Is x^2 + y^2 + 2 divisible by 6? - No !
We have a definite answer to the question. Hence, we can answer the question when the statements are taken combined.
Option C
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