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2^5+2^5+3^5+3^5+3^5=?

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by Brent@GMATPrepNow » Fri Mar 15, 2013 2:51 pm
paresh_patil wrote:2^5+2^5+3^5+3^5+3^5=?

A) 5^6
B) 13^5
C) 2^6+3^6
D) 2^7+3^8
E) 4^5+9^5
What we really have here is an algebra question involving the combining of like terms.

First, notice that K + K = 2K
Using the same logic, 2^5 + 2^5 = 2(2^5) = (2^1)(2^5) = 2^6

Similarly, notice that M + M + M = 3M
Using the same logic, 3^5 + 3^5 + 3^5 = 3(3^5) = (3^1)(3^5) = 3^6

So, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^6 + 3^6

Answer: C

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by paresh_patil » Fri Mar 15, 2013 3:31 pm
Brent-

then how do I tackle this one: 2^x-2^(x-2)=3(2^13) x=?
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by Zarrolou » Fri Mar 15, 2013 3:41 pm
2^x-2^(x-2)=3(2^13) x=?

I can take this:

2^x(1-2^(-2))=3*(2^13)
2^x(1-1/4))=3*(2^13)
2^x(3/4)=3*(2^13)

The first part:
2^x(3/4) = 2^x(3/(2^2)) = 3*(2^x/2^2) = 3*2^(x-2)
I hope the last passage is clear...

3*2^(x-2)=3*(2^13) divide by 3
2^(x-2)=(2^13)

x=15
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by Brent@GMATPrepNow » Fri Mar 15, 2013 3:47 pm
paresh_patil wrote:Brent-

then how do I tackle this one: 2^x-2^(x-2)=3(2^13) x=?
This requires some factoring.
2^x - 2^(x-2) = 3(2^13)
2^(x-2)[2^2 - 1] = 3(2^13)
2^(x-2)[3] = 3(2^13)
So, 2^(x-2)= 2^13
x-2 = 13
[spoiler]x = 15[/spoiler]

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by GMATGuruNY » Sat Mar 16, 2013 3:05 am
When you post a problem, please include the answer choices.
2^5+2^5+3^5+3^5+3^5=?

A) 5^6
B) 13^5
C) 2^6+3^6
D) 2^7+3^8
E) 4^5+9^5
An alternate approach is to BALLPARK.

2� = 32.
3� = 3(3�) = 3*81 ≈ 250.

Thus:
2� + 2� + 3� + 3� + 3� = 2(32) + 3(250) ≈ 60+750 ≈ 800.

Since 3� ≈ 250, 3� ≈ 750.
Thus, the only viable answer choice is C.
Last edited by GMATGuruNY on Thu Mar 31, 2016 5:55 am, edited 1 time in total.
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by GMATGuruNY » Sat Mar 16, 2013 3:08 am
paresh_patil wrote: then how do I tackle this one: 2^x-2^(x-2)=3(2^13) x=?
When you post a question, please include the answer choices.
If 2^X - 2^(X-2) = 3 x 2^17, What is the value of X?

A. 16
B. 17
C. 18
D. 19
E. 20
We can plug in the answers, which represent the value of X.

Answer choice C: 18.
2^18 - 2^(18-2) = 3 * 2^17
2^18 - 2^16 = 3 * 2^17
2*16(2^2 - 1) = 3 * 2^17
2^16 * 3 = 3 * 2^17.
Doesn't work. Eliminate C.

To match 2^17 on the right side of the equation, the exponent on the left side of the equation needs to be increased by 1.

The correct answer is D.

Answer choice D: 19.
2^19 - 2^(19-2) = 3 * 2^17
2^19 - 2^17 = 3 * 2^17
2*17(2^2 - 1) = 3 * 2^17
2^17 * 3 = 3 * 2^17.
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