If a, b, c, d, and e are positive integers such that

Question

If a, b, c, d, and e are positive integers such that  \frac{a*10^d}{b*10^e}=c*10^4  is bc/a an integer?

(1) d – e ≥ 4
(2) d – e > 4

Kudos for a correct  solution .

ManojReddy · Answer

If a, b, c, d, and e are positive integers such that  \frac{a∗10^d}{b∗10^e} = c∗10^4  is bc/a an integer?

\frac{a∗10^d}{b∗10^e} = c∗10^4 
bc/a =  \frac{10^d}{10^e*10^4}

bc/a =  10^{d-e-4}

for bc/a to be integer, {d-e-4} should be an integer greater than 0

(1) d – e ≥ 4

{d-e} can take any value greater than or equal to 4
so d-e-4 will be ≥ 0

Ex: d-e =4 then bc/a = 10^0 = 1
 d-e =5 then bc/a = 10^1 = 10

so bc/a is integer

Sufficient.

(2) d – e > 4

{d-e} can take any value greater than 4
so d-e-4 will be ≥ 1

so bc/a is integer
 Sufficient

Ans: D

shriramvelamuri · Answer

Yes It has to be D.

10^0 =1 an Integer

10^ any number= integer.

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION: 2015-06-22_1708.png

OptimusPrepJanielle · Answer

If a, b, c, d, and e are positive integers such that (a∗10^d)/(b∗10^e)=c∗10^4 is bc/a an integer?

(1) d – e ≥ 4  sufficient 
(2) d – e > 4  sufficient

iliavko · Answer

Strange question, why do even need the statements to answer?

It says that A/B=C and I don't see how the powers of 10 are relevant. We are told from the stem that a,b,c are positive integers, so A is a multiple of B and B is a multiple of C (A is a multiple of C) so obviously if we "reverse" the operation and multiple C*B we get A and BC/A will yield 1. Given the stem, there is no way A/B=C is not an integer! Even if we consider that C could be a fraction, but then again we are told that c is * 10^4  so it's a not a fraction, it's an integer.

Then the statements say that d-e = 4 or 4+?.. Well it's already in the question stem, it says there that d-e is 4 (same base 10 we subtract d-e to get base 10 power 4). No new information.

So what is being asked?...

hsbinfy · Answer

D

strange choices but both say same leaving =4

1)if you reduce the expression it will come as bc/a =10^d-e-4.So if d-e>=4 the output will always be an integer.

2) also says the same d-e>4 always an intergerv

Ashish632 · Answer

well a quick doubt here , here it says d-3 greater than or equal to 4 , well lets say d-3 is 4.5 so it leads to the equation being 10^0.5 , which may not be an integer isnt it ...

Can someone clarify ????

Ashish632 · Answer

oh sorry , my bad , i just realised , that its given that all are integers , well lets just say that its not given that they are integers , in that case , is my assumption correct , will the answer be E then ?

bumpbot · Answer

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If a, b, c, d, and e are positive integers such that

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