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What is the value of (2^8 + 2^9 + 2^{10} + 2^{11}) / 32?

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by Max@Math Revolution » Sun Jan 27, 2019 11:47 pm

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[GMAT math practice question]

What is the value of (2^8 + 2^9 + 2^{10} + 2^{11}) / 32?

A. 80
B. 96
C. 100
D. 120
E. 160
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by fskilnik@GMATH » Mon Jan 28, 2019 4:11 am
Max@Math Revolution wrote:[GMAT math practice question]

What is the value of (2^8 + 2^9 + 2^{10} + 2^{11}) / 32?

A. 80
B. 96
C. 100
D. 120
E. 160
$$? = \frac{{{2^8} + {2^9} + {2^{10}} + {2^{11}}}}{{{2^5}}} = \frac{{{2^8}\left( {1 + 2 + {2^2} + {2^3}} \right)}}{{{2^5}}} = \underleftrightarrow {{2^3} \cdot 15 = 8\left( {10 + 5} \right)} = 120$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Wed Jan 30, 2019 1:06 am
=>
$$\frac{\left(2^8+2^9+2^{10}+2^{11}\right)}{32}$$
$$=\frac{\left(2^8+2^82^1+2^82^2+2^82^3\right)}{2^5}$$
$$=\frac{2^8\left(1+2^1+2^2+2^3\right)}{2^5}$$
$$=2^3\left(1+2+4+8\right)$$
$$=8\cdot15$$
$$=120$$

Therefore, the answer is D.
Answer: D
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by Scott@TargetTestPrep » Wed Jan 30, 2019 6:02 pm
Max@Math Revolution wrote:[GMAT math practice question]

What is the value of (2^8 + 2^9 + 2^{10} + 2^{11}) / 32?

A. 80
B. 96
C. 100
D. 120
E. 160
We can factor out 2^8 from each term in the numerator. Simplifying, we have:

[2^8(1 + 2^1 + 2^2 + 2^3)]/2^5

2^3(1 + 2 + 4 + 8) = 8 x 15 = 120

Answer: D

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