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Help me solve this GMAT Quant Question (GMATPrep) #4

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by EricImasogie » Wed Dec 17, 2014 8:30 pm
Hey guys, I need your help in understanding this one.

for the right side of the equation I read online that essentially you can pull out (2^35)*(5^35) which equates to 10^35 . I am having trouble conceptualizing this because I always thought that (2)(5^35) was equal to 10^35.


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by Brent@GMATPrepNow » Wed Dec 17, 2014 9:13 pm
(1/5)^m * (1/4)^18 = 1/(2(10)^35). Find the value of M.

17
18
34
35
36

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by Brent@GMATPrepNow » Wed Dec 17, 2014 9:19 pm
EricImasogie wrote:Hey guys, I need your help in understanding this one.

....essentially you can pull out (2^35)*(5^35) which equates to 10^35 .
I am having trouble conceptualizing this because I always thought that (2)(5^35) was equal to 10^35.
(2^35)(5^35) = (2)(2)(2)(2).....(2)(5)(5)(5).....(5)
= (2)(5)x(2)(5)x(2)(5)x(2)(5)x........x(2)(5)
= (10)(10)(10)(10)(10).....(10)
= 10^35


Whereas...
(2)(5^35)=(2)(5)(5)(5)....(5)
= (2)(5)x(5)(5)....(5)
= 10x(5)(5)....(5)
= 10x(5^34)

Cheers,
Brent
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by MartyMurray » Wed Dec 17, 2014 9:31 pm
EricImasogie wrote:Hey guys, I need your help in understanding this one.

for the right side of the equation I read online that essentially you can pull out (2^35)*(5^35) which equates to 10^35 . I am having trouble conceptualizing this because I always thought that (2)(5^35) was equal to 10^35.


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(ab)^35 = a^35 * b^35. Think about what you said Eric. How could 2^1 * 5^35 possibly equal 10^35? That's not logical. You can't just double 5^35 and get 10^35.

Check this out. 10^5 = (5 * 2)^5. So we need five 5's and five 2's to get 10^5.

10^5 = 10 * 10 * 10 * 10 * 10 = (5 * 2) * (5 * 2) * (5 * 2) * (5 * 2) * (5 * 2) = 5 * 5 * 5 * 5 * 5 * 2 * 2 * 2 * 2 * 2.

In the problem, the denominator in the right side of the equation has 35 5's and 35 + 1 = 36 2's.

In the denominator on the left side, 4^18 = (2 * 2)^18 = 2^36. So we are all set with enough 2's. Now to get enough 5's we need m to equal 35.

Choose D.
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by GMATGuruNY » Thu Dec 18, 2014 3:04 am
If (1/5)^m * (1/4)^18 = 1/2(10)^35 then m = ?

A. 17

B. 18

C. 34

D. 35

E. 36
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.
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by Mathsbuddy » Fri Dec 19, 2014 4:09 am
(1/5)^m * (1/4)^18 = 1/(2(10)^35)
Find the reciprocal:
5^m * 4^18 =2(10)^35
5^m * 4^18 =2 x 2^35 x 5^35)
5^m * 4^18 =2 x 2^17 x 2^18 x 5^35
5^m * 4^18 =2^36 x 5^35
5^m * 4^18 =4^18 x 5^35
m = 35
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by Mathsbuddy » Fri Dec 19, 2014 4:11 am
Mathsbuddy wrote:(1/5)^m * (1/4)^18 = 1/(2(10)^35)
Find the reciprocal:
5^m * 4^18 =2(10)^35
5^m * 4^18 =2 x 2^35 x 5^35)
5^m * 4^18 =2 x 2^17 x 2^18 x 5^35
5^m * 4^18 =2^36 x 5^35
5^m * 4^18 =4^18 x 5^35
m = 35
Or put more simply, the only exponent of 5 is 35.
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by Matt@VeritasPrep » Mon Dec 22, 2014 1:01 pm
Let's cross multiply to get rid of the denominators.

This gives us 2*10³� = 5� * 4¹�, or

2*2³�*5³� = 5� * 2³�

Hence m = 35, and we're done!
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