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505-555 (Easy)|   Exponents|      
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Bunuel
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(4^8 - 3^8)/(4^4 + 3^4)= 14 Feb 2022, 09:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

85% (01:22) correct 15% (02:05) wrong based on 99 sessions

History

Date
Time
Result
Not Attempted Yet
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216
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D
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(4^8 - 3^8)/(4^4 + 3^4)= Updated on: 14 Feb 2022, 10:54
Originally posted by BrentGMATPrepNow on 14 Feb 2022, 10:37.
Last edited by BrentGMATPrepNow on 14 Feb 2022, 10:54, edited 1 time in total.
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Bunuel
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216
Show more

Key property (difference of squares): \(x^2 - y^2 = (x+y)(x-y)\)

We can quickly answer the question if we first recognize that \(4^8 - 3^8\) is a difference of squares that can be factored to get:

\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\frac{{(4^4 + 3^4)(4^4 - 3^4)}}{{4^4 + 3^4}}\)

\(=4^4 - 3^4\)

Note: At this point, we can either evaluate \(4^4 - 3^4\) by calculating the individual values of \(4^4\) and \(3^4\), or we can apply one more factorization.
I'm going to apply one more factorization
\(4^4 - 3^4 = (4^2 + 3^2)(4^2 - 3^2)\)
\( = (16 + 9)(16 - 9)\)
\( = (25)(7)\)
\( = 175\)

Answer: D
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(4^8 - 3^8)/(4^4 + 3^4)= 14 Feb 2022, 10:45
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BrentGMATPrepNow
Bunuel
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216

Key property (difference of squares): \(x^2 - y^2 = (x+y)(x-y)\)

We can quickly answer the question if we first recognize that \(4^8 - 3^8\) is a difference of squares that can be factored to get:

\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\frac{{(4^4 + 3^4)(4^4 - 3^4)}}{{4^4 + 3^4}}\)

\(=4^4 - 3^4\)

Note: At this point, we can either evaluate \(4^4 - 3^4\) by calculating the individual values of \(4^4\) and \(3^4\), or we can apply one more factorization.
I'm going to apply one more factorization
\(4^4 - 3^4 = (4^2 + 3^2)(4^2 - 3^2)\)
\( = (16 + 9)(16 - 9)\)
\( = (25)(7)\)
\( = 225\)
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175, but agree up until then

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(4^8 - 3^8)/(4^4 + 3^4)= 14 Feb 2022, 10:56
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Regor60


175, but agree up until then

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Thanks for the heads up.
Turns out that multiplying 25 by 7 is the trickiest part of the question!
I've edited my response.

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(4^8 - 3^8)/(4^4 + 3^4)= 14 Feb 2022, 14:07
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Bunuel
\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}=\)

A. 7
B. 25
C. 156
D. 175
E. 216
Show more

\(\frac{{4^8 - 3^8}}{{4^4 + 3^4}}\) = \(\frac{{(4^4 + 3^4)}*{(4^4 - 3^4)}}{{4^4 + 3^4}}\)

= \(4^4 - 3^4\)
= \(256 - 81\)
= \(175\)

Hence, our answer is option D, 175.
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