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Algebra

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by GMATGuruNY » Mon Oct 28, 2013 3:04 am
The problem should read as follows:
The value of (2ˉ¹� + 2ˉ¹� + 2ˉ¹� + 2ˉ¹�)/5 is how times the value of 2ˉ¹�?

A. 3/2

B. 5/2

C. 3

D. 4

E. 5
Factor out the MOST NEGATIVE EXPONENT:

(2ˉ¹� + 2ˉ¹� + 2ˉ¹� + 2ˉ¹�)/5

= [2ˉ¹� * (2³ + 2² + 2¹ + 1)] / 5

= (2ˉ¹� * 15) / 5

= 2ˉ¹� * 3.

Thus, the given expression is 3 times the value of 2ˉ¹�.

The correct answer is C.
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by Brent@GMATPrepNow » Mon Oct 28, 2013 6:19 am
The value of (2ˉ¹� + 2ˉ¹� + 2ˉ¹� + 2ˉ¹�)/5 is how many times the value of 2ˉ¹�?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5
Mitch solved the question the same way that I'd solve it. Having said that, here's another option:

First, asking "The value of x is how many times the value of y?" is the same as asking, "What is the value of x/y?"

So, this question is asking us to evaluate: [(2ˉ¹� + 2ˉ¹� + 2ˉ¹� + 2ˉ¹�)/5]/(2ˉ¹�)
This equals (1/5)[(2ˉ¹� + 2ˉ¹� + 2ˉ¹� + 2ˉ¹�)/(2ˉ¹�)]

Second, (a + b + c)/d = a/d + b/d + c/d
So, (1/5)[(2ˉ¹� + 2ˉ¹� + 2ˉ¹� + 2ˉ¹�)/(2ˉ¹�)] = (1/5)[(2ˉ¹�)/(2ˉ¹�) + (2ˉ¹�)/(2ˉ¹�) + (2ˉ¹�)/(2ˉ¹�) + (2ˉ¹�)/(2ˉ¹�)]
= (1/5)[2³ + 2² + 2¹ + 2^0]
= (1/5)[8 + 4 + 2 + 1]
= (1/5)[15]
= 3
= C

Cheers,
Brent
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by Brent@GMATPrepNow » Mon Oct 28, 2013 10:33 am
Here's a similar question to practice with: https://www.beatthegmat.com/power-of-3-t268940.html

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Brent
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