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

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

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New post 19 Jun 2015, 02:07
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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?

(1) d – e ≥ 4
(2) d – e > 4


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

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New post 19 Jun 2015, 02:24
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1
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
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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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New post 19 Jun 2015, 02:49
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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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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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New post 22 Jun 2015, 06:09
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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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2015-06-22_1708.png
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 22 Jun 2015, 13:35
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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If a, b, c, d, and e are positive integers such that  [#permalink]

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New post 25 Jun 2016, 02:10
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?...
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Re: If a, b, c, d, and e are positive integers such that  [#permalink]

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New post 25 Jun 2016, 04:52
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 &nbs [#permalink] 21 Mar 2018, 10:25
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