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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Help me solve this GMAT Quant Question (GMATPrep) #4
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EricImasogie
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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.
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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Brent@GMATPrepNow
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(1/5)^m * (1/4)^18 = 1/(2(10)^35). Find the value of M.
17
18
34
35
36
Thank you!
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(2^35)(5^35) = (2)(2)(2)(2).....(2)(5)(5)(5).....(5)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)(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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MartyMurray
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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.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.
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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GMATGuruNY
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No need to simplify the whole equation.If (1/5)^m * (1/4)^18 = 1/2(10)^35 then m = ?
A. 17
B. 18
C. 34
D. 35
E. 36
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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Mathsbuddy
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(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
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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Mathsbuddy
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Or put more simply, the only exponent of 5 is 35.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
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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!
This gives us 2*10³� = 5� * 4¹�, or
2*2³�*5³� = 5� * 2³�
Hence m = 35, and we're done!
