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If p and q are prime numbers such that p<q
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12 Aug 2026, 01:36
12 Aug 2026, 01:36
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Question Stats:
83% (02:00) correct
16% (01:40) wrong based on 6 sessions
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If p and q are prime numbers such that p<q , which of the following expressions must be an odd integer?
A. \(p^q+q \)
B. \(p(q-1)\)
C. \(q^2-p^2\)
D. \(2^p+q \)
E. \(p^{q-1}+q \)
A. \(p^q+q \)
B. \(p(q-1)\)
C. \(q^2-p^2\)
D. \(2^p+q \)
E. \(p^{q-1}+q \)
- Part of the project: GRE Daily Quant Challenge ALL 4 CORE QUANT AREAS
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If p and q are prime numbers such that p<q
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18 Aug 2026, 09:29
18 Aug 2026, 09:29
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Expert Reply
Explanation
We need to find the expression that is always odd.
Since p and q are primes and \(p<q,\) consider the possibilities involving 2.
Because there is only one even prime, if \(p=2,\) then \(q\) is odd. If \(p>2,\) both \(p,q\) are odd.
Check the choices
\(A. p^q+q\)
If p,q are both odd: odd + odd = even.
Not always odd.
\(B. p(q−1)\)
If p,q are odd: odd * even = even.
Not always odd.
C. \(q^2-p^2\)
If both primes are odd, odd2 − odd2 = even.
\(D. 2^p+q\)
2p is even, and q is odd (whether p=2 or p,q are both odd). Therefore:
\(even+odd=odd\)
So this must be odd.
\(E. p^{q-1}+q\)
If p,q are both odd, odd + odd = even.
Answer: D
We need to find the expression that is always odd.
Since p and q are primes and \(p<q,\) consider the possibilities involving 2.
Because there is only one even prime, if \(p=2,\) then \(q\) is odd. If \(p>2,\) both \(p,q\) are odd.
Check the choices
\(A. p^q+q\)
If p,q are both odd: odd + odd = even.
Not always odd.
\(B. p(q−1)\)
If p,q are odd: odd * even = even.
Not always odd.
C. \(q^2-p^2\)
If both primes are odd, odd2 − odd2 = even.
\(D. 2^p+q\)
2p is even, and q is odd (whether p=2 or p,q are both odd). Therefore:
\(even+odd=odd\)
So this must be odd.
\(E. p^{q-1}+q\)
If p,q are both odd, odd + odd = even.
Answer: D
gmatclubot
If p and q are prime numbers such that p<q [#permalink]
18 Aug 2026, 09:29
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