If a and b are positive integers, and a*10^5 = b*10^n what is the valu

Question

If a and b are positive integers, and  a*10^5 = b*10^n  what is the value of n?

(1) a = 100b
(2) a + b = 5,050

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GMATinsight · Answer

a*10^5 = b*10^n  
i.e.  a = b*10^{n-5}

Question: n = ?

Statement 1 : a = 100b

i.e.  a = 10^2*b  Also, we know that  a = b*10^{n-5}

i.e.  10^2*b = b*10^{n-5}

i.e. 2 = n-5
i.e. n = 7

SUFFICIENT

Statement 2 : a + b = 5,050 
we know that  a = b*10^{n-5}

i.e.  b*10^{n-5} + b = 5,050

i.e.  b*  = 5,050

i.e.  b*  = 50*101

i.e.  b*  = 50*

Because b is an Integer therefore, i.e. b = 50 and n = 7

SUFFICIENT

Answer: Option D

sambitspm · Answer

Kindly see the attachment.
 TIME: 2 min. 
It should take less than 1:40.

IMO D

hacorus · Answer

I'll go against the grain here, maybe I'm silly

a and b positive integers,
a*10^5=b*10^n

Statement 1
 a=100*b =b*10^2
a*10^5=b*10^(5+2)
so n=7
Statement one is sufficient, A or D

Statement 2,
 a+b=5050
if a=5000 and b=50, then 5000*10^5=5*10^8=50*10^7 so n=7

However, if a=50 and b=5,000, we have a*10^5=50*10^5=5*10^6=5*10^3*10^3=5000*10^3=b*10^3, so n=3
If we use the other methodology, I think we should also consider the case of: b =5000(1+10^-2) which would give n-5=-2 and n=3
So insufficient

IMO: A

bumpbot · Answer

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If a and b are positive integers, and a10^5 = b10^n what is the valu

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