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pleasssseee help - how do I find m

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by gmatpup » Fri Nov 11, 2011 12:02 pm
If (1/5)^m * (1/4)^18 = 1/2(10)^35 then m = ?

A. 17

B. 18

C. 34

D. 35

E. 36

Answer is D

I am soo lost, please help!

Thanks soso much:)
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by GMATGuruNY » Fri Nov 11, 2011 12:24 pm
gmatpup wrote:If (1/5)^m * (1/4)^18 = 1/2(10)^35 then m = ?

A. 17

B. 18

C. 34

D. 35

E. 36

Answer is D

I am soo lost, please help!

Thanks soso much:)
No need to simplify the whole equation.

Every prime factor on the right side must also appear on the left side.
On the right side we have 1/10³� = 1/2³� * 1/5³�.
Thus, the left side must also include 1/5³�, implying that m=35.

The correct answer is D.
Last edited by GMATGuruNY on Thu Feb 16, 2012 7:28 pm, edited 1 time in total.
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by gmatpup » Fri Nov 11, 2011 12:35 pm
GMATGuruNY wrote:
gmatpup wrote:If (1/5)^m * (1/4)^18 = 1/2(10)^35 then m = ?

A. 17

B. 18

C. 34

D. 35

E. 36

Answer is D

I am soo lost, please help!

Thanks soso much:)
No need to simplify the whole equation.

Every factor on the right side must also appear on the left side.
On the right side we have 1/10³� = 1/2³� * 1/5³�.
Thus, the left side must also include 1/5³�, implying that m=35.

The correct answer is D.

OH! So the answer is 35 simply because this number appears on the right, thus is must also appear on the left?

I know other times when trying to find a variable you have to get like bases... how do I know when I need like bases or when it is a situation such as this?

Thanks again!!
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by GMATGuruNY » Sat Nov 12, 2011 5:22 am
gmatpup wrote:
GMATGuruNY wrote:
gmatpup wrote:If (1/5)^m * (1/4)^18 = 1/2(10)^35 then m = ?

A. 17

B. 18

C. 34

D. 35

E. 36

Answer is D

I am soo lost, please help!

Thanks soso much:)
No need to simplify the whole equation.

Every factor on the right side must also appear on the left side.
On the right side we have 1/10³� = 1/2³� * 1/5³�.
Thus, the left side must also include 1/5³�, implying that m=35.

The correct answer is D.

OH! So the answer is 35 simply because this number appears on the right, thus is must also appear on the left?

I know other times when trying to find a variable you have to get like bases... how do I know when I need like bases or when it is a situation such as this?

Thanks again!!
Each side of the equation is a series of factors.
Thus, if one side has a prime number raised to a power, the other side must have the same prime number raised to the same power.
In the problem above, m appears only once -- as part of 1/(5^m) -- so this is the only factor that concerns us.
Once we recognize that the right hand side includes 1/(5³�), we know that the left hand side must also include 1/(5³�).
Thus, m=35. No need to do any more math.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by chetane » Fri Nov 18, 2011 3:02 pm
While the answer above is the fastest way to find the solution, here's the full explanation (for understanding purposes):

(a * b) ^ c = a^c + b^c

So:

1/(2 * 10^35)
= 1 / (2 * (2*5)^35)
= 1 / (2 * 2^35 * 5^35)
= 1 / (2^36 * 5^35)
= 1 / (4^18 * 5^35) // Note that 2*2 = 4, so 2^36 = 4^18
= (1 / 4^18) * (1/5^35) // Note that 1 = 1^18 = 1^35
= (1/4)^18 * (1/5)^35
= (1/4)^15 * (1/5)^m

so m = 35
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