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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:
28% (03:06) correct
72%
(02:23)
wrong
based on 36
sessions
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Not Attempted Yet
If p, q, and r are positive integers and \(p^4 + q^5 = r^4\), is \(p^4 + q^5\) odd?
1) \(p^8 * q^9 = r^7\)
2) \(p^3 + 2q^3\) is not divisible by 3
1) \(p^8 * q^9 = r^7\)
2) \(p^3 + 2q^3\) is not divisible by 3
14 Apr 2023, 02:11
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gmatophobia
From the stem we know :
If \(p\) and \(q\) are both even then \(r\) is even ...(i)
If \(p\) and \(q\) are both odd then \(r\) is even ...(ii)
If \(p\) is even and \(q\) is odd then \(r\) is odd...(iii)
If \(p\) is odd and \(q\) is even then \(r\) is odd...(iv)
1) \(p^8 * q^9 = r^7\)
This statement in combination with the pre-analysis tells us the \(p\) and \(q\) are both even.
Hence we can answer a definite NO to the question.
Just to further clarify.
If \(p\) and \(q\) are both odd then according to stem, \(r\) should be even , but according to statement 1 , we would get \(r\) as odd. Hence \(p\) and \(q\) both cannot be odd.
Similarly if \(p\) is even and \(q\) is odd then according to stem \(r\) should be odd well as according to statement 1, \(r\) becomes even. Hence this case also can be rejected.
Hence the only possibility is that both \(p\) and \(q\) are even and we can answer a definite NO.
SUFF.
2) \(p^3 + 2q^3\) is not divisible by 3
\(p=1\) and \(q=3\) : No to the stem
\(p=2\) and \(q=1 \): yes to the stem
INSUFF.
Ans A
Hope it's clear.
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