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18 Feb 2023, 11:46
Kudos
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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:
95%
(hard)
Question Stats:
34% (02:04) correct
66%
(01:38)
wrong
based on 121
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are non-negative integers, is \(4x^4 + 3y \) even?
1. \(x^3\) is odd
2. \(y^{2x} + 3\) is even
1. \(x^3\) is odd
2. \(y^{2x} + 3\) is even
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
25 Feb 2023, 08:13
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gmatophobia
1. \(x^3\) is odd
So \(x\) is odd and the LHS of the eqn. in the stem is even but we do not know anything abou \(y.\)
Status will change depending upon whether \(y\) is even or odd.
INSUFF
2. \(y^{2x} + 3\) is even
Although this looks suff, this is not. Note that \(x \) can be zero
We know \(y^{2x}\) is odd
\(y = 2 \) and \(x=0 \) yes to the stem
\(y =1\) and \(x=1\) No the stem
INSUFF.
1+2
From (1) we know \(x\) is odd
From (2) we get \(y\) is odd
Hence we can answer a definite NO to the stem.
SUFF.
Ans C
Hope it helps.
07 Mar 2023, 01:54
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gmatophobia
Solution:
Pre Analysis:
- x and y are non-negative integers
- We are asked if \(4x^4 + 3y \) is even or odd. This is a YES-NO question
- We can be sure that \(4x^4\) will always be even no matter the value of x
- So, the even odd nature of \(4x^4 + 3y \) depends only on the even odd nature of y
Statement 1: \(x^3\) is odd
- No info of y
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(y^{2x} + 3\) is even
- \(y^{2x} + 3=even\)
- This doesn't mean that y has to be odd
- If x = 0, then y can be odd or even and \(y^{2x}\) will be 1 which is odd
- Thus, statement 2 alone is also not sufficient and we can eliminate option B
\(⇒y^{2x}=even-3\)
\(⇒y^{2x}=even-odd\)
\(⇒y^{2x}=odd\)
TRAP!!
Combining:
- From statement 1, we can be sure that \(x≠0\)
- Now when we analyze statement 2 and \(y^{2x}=odd\), we can be sure that y is odd
Hence the right answer is Option C
