Discussion

If \(52272 = p^{2} \times q^{3} \times r^{4}\), where p, q and r are prime numbers, then the value of (2p + q - r) is

Answer: C

The value of 2p + q - r is 23.

Factorise 52272:

\[ \begin{aligned} 52272 &= 16 \times 3267 \\ &= 2^{4} \times 27 \times 121 \\ &= 11^{2} \times 3^{3} \times 2^{4} \end{aligned} \]

Matching with \(p^{2} \times q^{3} \times r^{4}\) gives p = 11, q = 3 and r = 2. Then

\[ 2p + q - r = 22 + 3 - 2 = 23 \]

21 comes from subtracting q and adding r the wrong way, and 22 is just 2p. 29 would need different primes in the factorisation.

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