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Math Expert V
Joined: 02 Sep 2009
Posts: 56244
If a, b, c, d, and e are positive integers such that  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 65% (01:58) correct 35% (02:11) wrong based on 223 sessions

### HideShow timer Statistics 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.

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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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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
##### General Discussion
Manager  Joined: 27 Dec 2013
Posts: 222
Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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1
Yes It has to be D.

10^0 =1 an Integer

10^ any number= integer.

Bunuel wrote:
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.

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Kudos to you, for helping me with some KUDOS.
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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1
2
Bunuel wrote:
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.

MANHATTAN GMAT OFFICIAL SOLUTION:
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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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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
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Senior Manager  S
Joined: 08 Dec 2015
Posts: 287
GMAT 1: 600 Q44 V27 If a, b, c, d, and e are positive integers such that  [#permalink]

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1
1
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.

Senior Manager  Joined: 02 Mar 2012
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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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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
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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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_________________ Re: If a, b, c, d, and e are positive integers such that   [#permalink] 09 Apr 2019, 10:28
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