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555-605 (Medium)|   Algebra|      
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Bunuel
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 11 Jun 2015, 04:01
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C
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25% (medium)

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77% (01:33) correct 23% (01:56) wrong based on 292 sessions

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If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^5}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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C
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 11 Jun 2015, 04:33
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If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^7}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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Bunuel: Answer Options seem to be incorrect. Please check them again
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 11 Jun 2015, 04:37
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If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^7}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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Bunuel: Answer Options seem to be incorrect. Please check them again
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Should have been \(q =\frac{9^5}{7^3}\) instead of \(q =\frac{9^7}{7^3}\). Edited. Thank you for spotting the typo.
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 11 Jun 2015, 04:53
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If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^5}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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\(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\)

i.e. \(p = \frac{9^5(9^2 - 1)}{7^3(7^2 + 1)}\)

and, \(q =\frac{9^5}{7^3}\)

Now take the ratio of q and p

\(\frac{q}{p}\) = \(\frac{9^5}{7^3}\) / \(\frac{9^5(9^2 - 1)}{7^3(7^2 + 1)}\)

i.e. \(\frac{q}{p}\) = \(\frac{9^5*7^3*(7^2 + 1)}{7^3*9^5*(9^2 - 1)}\)

i.e. \(\frac{q}{p}\) = \(\frac{(7^2 + 1)}{(9^2 - 1)}\)

i.e. \(\frac{q}{p}\) = \(\frac{(50)}{(80)}\)

i.e. i.e. \(\frac{q}{p}\) = \(\frac{(5)}{(8)}\)

Answer: option
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C
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 11 Jun 2015, 05:01
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If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^5}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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\(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\)..
\(p = \frac{9^5(9^2 -1)}{7^3(7^2 +1)}\)...
\(p = \frac{9^5(80)}{7^3(50)}\)...
\(p = \frac{q(80)}{(50)}\)...
so \(\frac{p}{q}\)=\(\frac{8}{5}\) or \(\frac{q}{p}\)=\(\frac{5}{8}\)
ans C
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q Updated on: 11 Jun 2015, 05:25
Originally posted by BuggerinOn on 11 Jun 2015, 05:20.
Last edited by BuggerinOn on 11 Jun 2015, 05:25, edited 1 time in total.
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I factored out \(\frac{9^{5}}{7^{3}\) which equals Q to end up with:
\(\frac{9^{2}-1 }{7^{2}+1}\) = Q*\(\frac{80}{50}\) =P
P=Q\(\frac{80}{50}\)
\(\frac{Q}{P}=\frac{5}{8}\)
Answer C

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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 11 Jun 2015, 05:23
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Bunuel
If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^5}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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I factored out \(\frac{9^{5}}{7^{3}\) which equals Q to end up with:
\(\frac{9^{2}-1 }{7^{2}+1}\) = Q*\(\frac{80}{50}\) =P
P=Q\(\frac{80}{50}\)
\(\frac{Q}{P}=\frac{5}{8}\)
Answer C
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 15 Jun 2015, 01:59
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If \(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}\) and \(q =\frac{9^5}{7^3}\), what is the value of \(\frac{q}{p}\)?

(A) 2/5
(B) 1/2
(C) 5/8
(D) 8/5
(E) 5/2

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MANHATTAN GMAT OFFICIAL SOLUTION:

Not only does \(q =\frac{9^5}{7^3}\), but we can also factor out \(\frac{9^5}{7^3}\) of p:

\(p = \frac{(9^7 - 9^5)}{(7^5 + 7^3)}=\frac{9^5}{7^3}*\frac{(9^2 - 1)}{(7^2 + 1)}=\frac{9^5}{7^3}*\frac{8}{5}\).

Thus, \(p=q*\frac{8}{5}\) and \(\frac{p}{q}=\frac{8}{5}\) Watch out! This is one of the incorrect answers.

The question asks for \(\frac{q}{p}\), which is 5/8.

The correct answer is C.
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If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q 12 Dec 2018, 18:57
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