A difficult math, pls help to explain

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tracyyahoo: Master | Next Rank: 500 Posts; Posts: 147; Joined: Tue Jun 14, 2011 7:03 am; Thanked: 3 times

by tracyyahoo » Sat Sep 03, 2011 3:50 am

if 2^x+2^x+2^x+2^x=2^n, what is x in terms of n?

a)n/4
b)4n
c)2n
d)n-2
e)n+2

pls explain

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Source: Beat The GMAT — Problem Solving | Sat Sep 03, 2011 3:50 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Sep 03, 2011 3:57 am

tracyyahoo wrote:if 2^x+2^x+2^x+2^x=2^n, what is x in terms of n?

--> 2^x+2^x+2^x+2^x = 2^n
--> 4*(2^x) = 2^n
--> (2^2)*(2^x) = 2^n
--> 2^(x+2) = 2^n

Hence, x = n - 2

The correct answer is D.

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sat Sep 03, 2011 6:33 am

tracyyahoo wrote:if 2^x+2^x+2^x+2^x=2^n, what is x in terms of n?

a)n/4
b)4n
c)2n
d)n-2
e)n+2

pls explain

Plug in some values of x to find the value of n and get the pattern....

Let x be 0

Then ,

2^x+2^x+2^x+2^x = 2^n

2^0+2^0+2^0+2^0 = 2^2

So n = 2 ; when x = 0

Let x be 1

Then ,

2^x+2^x+2^x+2^x = 2^n

2^1+2^1+2^1+2^1 = 2^3

So n = 3 ; when x is 1

Now U can easily derive the pattern ,

n = x + 2

or x = n - 2.

Abhishek

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