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27 Nov 2022, 09:15
Kudos
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D
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Difficulty:
75%
(hard)
Question Stats:
38% (02:18) correct
62%
(01:48)
wrong
based on 29
sessions
History
Date
Time
Result
Not Attempted Yet
If \(\frac{1}{pq} = \frac{4}{15}\) and \(p > q\), what is the value of \(\frac{1}{q }− \frac{1}{p}\) ?
(1) \(p + q = 4\)
(2) \(\frac{1}{p} = \frac{2}{5}\)
(1) \(p + q = 4\)
(2) \(\frac{1}{p} = \frac{2}{5}\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
27 Nov 2022, 13:31
Kudos
Bookmarks
Bunuel
Given
- \(\frac{1}{pq} = \frac{4}{15}\)
- \(p > q\)
\(pq = \frac{15}{4}\) ---- (1)
Statement 1
\(p + q = 4\)
Substituting the value of p from equation (1)
\( \frac{15}{4q} + q = 4\)
\( 15 + 4q^2 = 16q\)
\( 4q^2 - 16q + 15 = 0\)
\( (2q-3)(2q-5) = 0\)
\(q = \frac{3}{2 } \) or \( q = \frac{5}{2}\)
If q = \(\frac{3}{2}\) ; p = \(\frac{5}{2}\) | Valid
If q = \(\frac{5}{2}\); p = \(\frac{3}{2}\) | Invalid as p < q
This statement is sufficient. Hence we can eliminate B, C and E.
Statement 2
\(\frac{1}{p} = \frac{2}{5}\)
As the value of p is given, we can find the value of q from equation 1.
Sufficient.
Option D
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