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01 Feb 2023, 12:15
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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:
45%
(medium)
Question Stats:
55% (01:36) correct
45%
(01:52)
wrong
based on 22
sessions
History
Date
Time
Result
Not Attempted Yet
If \(X = P*N^K + 12\) where N and K are positive integers, is X divisible by 2?
(1) Half of N is 456.5
(2) \(P^{35} + 33\) is Even
(1) Half of N is 456.5
(2) \(P^{35} + 33\) is Even
06 Feb 2023, 06:15
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Bunuel
(1) Half of N is 456.5
So N is 913 , however we know nothing about P.
If P is even , Yes to the stem
If P is odd , No to the stem.
INSUFF.
(2) \(P^{35} + 33\) is even
So \( p^{35}\) is odd
However P could be an odd integer or something like \(5^{\frac{1}{35}}\)
Also we know nothing about N.
INSUFF.
1+ 2
We know N is odd
If P is odd we have NO to the stem
if P is something like \(6^{\frac{1}{35}}\) it is still NO.
Hence we can definitely say NO to the stem.
SUFF.
Ans C
Hope it's clear.
07 Feb 2023, 04:02
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Bunuel
Solution:
Pre Analysis:
- N and K are positive integers whereas P is a real number
- We are asked if \(X = P*N^K + 12\) is divisible by 2 or not or if it even or not
- We know that 12 is even
- So, for \(X = P*N^K + 12\) to be even, the first term i.e., \(P*N^K\) has to even
Statement 1: Half of N is 456.5
- According to this statement, \(\frac{N}{2}=456.5\) or \(N=913\)
- So, \(N=913=odd\) and \(N^K=913^K\) will also be odd
- The nature of \(P*N^K\) will then depend on the value of P
- Thus, statement 1 alone is not sufficient and we can eliminate opinions A and D
Statement 2: \(P^{35} + 33\) is Even
- We know 33 is odd
- Which means \(P^{35}\) is also odd or \(P\) is also odd
- The nature of \(P*N^K\) will then depend on the value of N
- Thus, statement 2 alone is also not sufficient
Combining:
- From statement 1, we get \(N=913\) and \(N^K=odd\)
- From statement 2, we get \(P=odd\)
- The value of \(P*N^K\) will be odd
Hence the right answer is Option C
