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Problem Solving (PS) | Numbers p, q, r and s have 7, 16, 20 and 22 factors. Which of these co

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Mahmud6 wrote:

Numbers p, q, r and s have 7, 16, 20 and 22 factors. Which of these could be a perfect cube?

A. p and q
B. q and r
C. r and s
D. p, q and r
E. p, q and s


any cube is of the form\(a^{3k}\) , and hence the number of factors for this number will be\(3k+1\)

This implies that the number of factors when divided by\(3\) will leave\(1\) as remainder.

so for our question\(7\) ,\(16\) &\(22\) will leave a remainder of\(1\) when divided by\(3\) . Hence\(p\) ,\(q\) &\(s\) can be a perfect cube

OptionE

for the sake of explanation,
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