Got this question in GMAT but was not able to solve then, found some inconsistency in answers given, thus sharing the same.If 20/2^5 = (1/2^m) + (1/2^n), what is value of mn ? Please ignore answer choices if you believe they are wrong. Have tried to recall the question and options that were in exam.
a. 4
b. 3
c. 6
d. 5
e. 2
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GMAT exam question
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theCEO
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ans = [spoiler]3 = b[/spoiler]
20/2^5 = (1/2^m) + (1/2^n)
20 = (2^5/2^m) + (2^5/2^n)
20 = 2^(5-m) + 2^(5-n)
both terms are less than 20, therefore each term equates to one of the following:
1,2,4,8,16
Of these numbers only 4 + 16 can be added to get 20
therefore
20 = 2^(5-m) + 2^(5-n)
20 = 2^(5-1) + 2^(5-3) = 16 + 4
m=1 and n=3 , mn = 3
value of m could be 3 and n could be 1. It doesn't matter because the product gives the same answer of 3
20/2^5 = (1/2^m) + (1/2^n)
20 = (2^5/2^m) + (2^5/2^n)
20 = 2^(5-m) + 2^(5-n)
both terms are less than 20, therefore each term equates to one of the following:
1,2,4,8,16
Of these numbers only 4 + 16 can be added to get 20
therefore
20 = 2^(5-m) + 2^(5-n)
20 = 2^(5-1) + 2^(5-3) = 16 + 4
m=1 and n=3 , mn = 3
value of m could be 3 and n could be 1. It doesn't matter because the product gives the same answer of 3
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anks17
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Thanks CEO.
20/2^5 = (1/2^m)+ (1/2^n)= [(2^n) + (2^m)]/2^(m+n) ]
Thus, m+n = 5 by comparing denominator-----1
but by comparing numerators, we get n= 4 and m = 2 as 2^4 + 2^2 = 20 i.e. numerator------2
Value of m+n doesn't match from 1 and 2. What is wrong here. Tried this way in exam and got stuck there.
20/2^5 = (1/2^m)+ (1/2^n)= [(2^n) + (2^m)]/2^(m+n) ]
Thus, m+n = 5 by comparing denominator-----1
but by comparing numerators, we get n= 4 and m = 2 as 2^4 + 2^2 = 20 i.e. numerator------2
Value of m+n doesn't match from 1 and 2. What is wrong here. Tried this way in exam and got stuck there.
"doesn't matter ver u r...ur destiny depends upon vho u choose 2 b!!!!"
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theCEO
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Hi anks17,anks17 wrote:Thanks CEO.
20/2^5 = (1/2^m)+ (1/2^n)= [(2^n) + (2^m)]/2^(m+n) ]
Thus, m+n = 5 by comparing denominator-----1
but by comparing numerators, we get n= 4 and m = 2 as 2^4 + 2^2 = 20 i.e. numerator------2
Value of m+n doesn't match from 1 and 2. What is wrong here. Tried this way in exam and got stuck there.
The mistake is to say 2^(m+n) = 2^5 by comparing the denominator !
take a look at this example:
2/8 = 1/4
2/2^3 = 1/2^2
based on what you did you would be saying 3 = 2
If this is still not clear let me know
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everything's eventual
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Why can't you do it this way :
20/2^5 = 1/2^m + 1/2^n
Take the left side of the equation : (2^2 * 5^1)/2^5 = 5^1/2^3
Right Side = (2^m + 2^n) / 2^ m+n
Comparing the numerator of both sides, 5 = 2^m + 2^n. . This can be solved only for m = 2 and n=1 ( or m =1 and n=2)
Therefore mn = 2.
Let me put m = 2 and n=1 back in the original equation, then both side equal = 5/8
20/2^5 = 1/2^m + 1/2^n
Take the left side of the equation : (2^2 * 5^1)/2^5 = 5^1/2^3
Right Side = (2^m + 2^n) / 2^ m+n
Comparing the numerator of both sides, 5 = 2^m + 2^n. . This can be solved only for m = 2 and n=1 ( or m =1 and n=2)
Therefore mn = 2.
Let me put m = 2 and n=1 back in the original equation, then both side equal = 5/8
