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07 Jun 2022, 13:11
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Difficulty:
95%
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Question Stats:
23% (02:11) correct
77%
(02:27)
wrong
based on 97
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p, q and r are positive integers such that p < q < r .
When p is expressed as a percent of (p + q), it is equal to when q is expressed as a percent of (q + r). What is the value of p?
(1) q has exactly two factors.
(2) r = 4
When p is expressed as a percent of (p + q), it is equal to when q is expressed as a percent of (q + r). What is the value of p?
(1) q has exactly two factors.
(2) r = 4
08 Jun 2022, 06:50
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AbhiroopGhosh
Let us simplify the statement - When p is expressed as a percent of (p + q), it is equal to when q is expressed as a percent of (q + r).
\(\frac{p}{p+q}*100=\frac{q}{q+r}*100...........p(q+r)=q(p+q)........pq+pr=pq+q^2.........q^2=pr\)
(1) q has exactly two factors.
This means q is a prime number.
Surely \(q^2\) will have only 3 factors 1, q and \(q^2\). Now, p<q<r, which means p=1, and r=q^2.
Sufficient
(2) r = 4
\(q^2=pr=4p\), so q is surely a multiple of 2.
Since r is the greatest, p has to be either 1 or 2, and q either 2 or 3. But q is a multiple of 2, so q=2, and p<q will make p as 1.
Sufficient
D
28 Nov 2024, 17:28
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