pq < 70, where both P and Q are distinct odd primes. Determine PQ. Statement

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pq < 70, where both P and Q are distinct odd primes. Determine PQ.

Statement (1): PQ is one greater than a power of two.

Statement (2): The sum of the digits of PQ is a prime number.



OA C

Source: Veritas Prep

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BTGmoderatorDC wrote:
Tue Oct 26, 2021 7:30 pm
pq < 70, where both P and Q are distinct odd primes. Determine PQ.

Statement (1): PQ is one greater than a power of two.

Statement (2): The sum of the digits of PQ is a prime number.



OA C

Source: Veritas Prep
From 1
\(PQ=32+1=33=3*11\)
\(PQ=64+1=65=5*13\)
Not Sufficient. \(\Large{\color{red}\chi}\)

From 2
\(PQ=65\)
\(PQ=41\)
Not sufficient. \(\Large{\color{red}\chi}\)

1 and 2 Combined
\(PQ=65=64+1=5*13\) and \(6+5=11\) a prime. Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, C