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10 Mar 2022, 02:30
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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:
5%
(low)
Question Stats:
92% (00:53) correct
8%
(00:50)
wrong
based on 73
sessions
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Not Attempted Yet
If x and y are positive integers, is x + y^2 odd?
(1) y is odd.
(2) x is odd.
(1) y is odd.
(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
10 Mar 2022, 02:53
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\(\frac{AD}{BCE}\)
Statement 1: Insufficient.
X can have any positive value (Even or Odd).
Since Y = Odd, \(Y^2\) = odd
If X = Odd, then X+\(Y^2\) = even (Odd + Odd = even)
If X = Even, then X + \(Y^2\) = odd (Even + Odd = odd)
Eliminate A & D
Statement 2: Insufficient
X = Odd
Y can have any positive value (Even or Odd).
If Y = odd, \(Y^2\) = odd, then Odd + Odd = Even
If Y = even, \(Y^2\) = even, then Odd + Even = Odd
Eliminate B
Combining 1 & 2
Y = Odd
X = Odd
X+\(Y^2\) = Odd + Odd = Even.
We get a definite No
Answer C
Statement 1: Insufficient.
X can have any positive value (Even or Odd).
Since Y = Odd, \(Y^2\) = odd
If X = Odd, then X+\(Y^2\) = even (Odd + Odd = even)
If X = Even, then X + \(Y^2\) = odd (Even + Odd = odd)
Eliminate A & D
Statement 2: Insufficient
X = Odd
Y can have any positive value (Even or Odd).
If Y = odd, \(Y^2\) = odd, then Odd + Odd = Even
If Y = even, \(Y^2\) = even, then Odd + Even = Odd
Eliminate B
Combining 1 & 2
Y = Odd
X = Odd
X+\(Y^2\) = Odd + Odd = Even.
We get a definite No
Answer C
10 Mar 2022, 09:41
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C If x and y are positive integers, Q: is x + y^2 odd?
(1) y is odd. NOT Sufficient y has no factor of 2, therefore y^2 also has no factor of 2. Without knowing x, we can’t answer the question. The data is NOT Sufficient.
If x is even, and we add an odd number, the outcome is odd. If x is odd and we add an odd number, the outcome is even. Without knowing x, we can’t answer the question. The data is NOT Sufficient.
(2) x is odd. If y is even (has a factor of 2) then y^2 is even. If this is so, then x + y^2 IS odd, but we do not know this. If y is odd (has no factor of 2), then this sum is even.
Without knowing y, we can’t answer the question. The data is NOT Sufficient.
NOT Sufficient
TOGETHER: y is odd (no factor of 2 in y^2) so y^2 is odd too.
x is odd.
ODD plus ODD = EVEN.
There IS enough information to answer the question. The answer happens to be “NO!”, but the data Is SUFFICIENT!!
(1) y is odd. NOT Sufficient y has no factor of 2, therefore y^2 also has no factor of 2. Without knowing x, we can’t answer the question. The data is NOT Sufficient.
If x is even, and we add an odd number, the outcome is odd. If x is odd and we add an odd number, the outcome is even. Without knowing x, we can’t answer the question. The data is NOT Sufficient.
(2) x is odd. If y is even (has a factor of 2) then y^2 is even. If this is so, then x + y^2 IS odd, but we do not know this. If y is odd (has no factor of 2), then this sum is even.
Without knowing y, we can’t answer the question. The data is NOT Sufficient.
NOT Sufficient
TOGETHER: y is odd (no factor of 2 in y^2) so y^2 is odd too.
x is odd.
ODD plus ODD = EVEN.
There IS enough information to answer the question. The answer happens to be “NO!”, but the data Is SUFFICIENT!!
