If p = (9^7 - 9^5)/(7^5 + 7^3) and q = 9^7/7^3, what is the value of q

Question

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

Kudos for a correct  solution .

GMATinsight · Answer

Bunuel : Answer Options seem to be incorrect. Please check them again

Bunuel · Answer

Should have been  q =\frac{9^5}{7^3}  instead of  q =\frac{9^7}{7^3} . Edited. Thank you for spotting the typo.

GMATinsight · Answer

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  C

chetan2u · Answer

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

BuggerinOn · Answer

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

I can't find the delete button, please remove this post as I entered an updated version below. Sorry for the hassle.

BuggerinOn · Answer

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

Bunuel · Answer

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.

bumpbot · Answer

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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

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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

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