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If a, b, c, d, and e are positive integers such that
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19 Jun 2015, 02:07
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65% (01:58) correct 35% (02:11) wrong based on 223 sessions
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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 Kudos for a correct solution.
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Re: If a, b, c, d, and e are positive integers such that
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19 Jun 2015, 02:24
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 = \(10^{de4}\)
for bc/a to be integer, {de4} should be an integer greater than 0
(1) d – e ≥ 4
{de} can take any value greater than or equal to 4 so de4 will be ≥ 0
Ex: de =4 then bc/a = 10^0 = 1 de =5 then bc/a = 10^1 = 10
so bc/a is integer
Sufficient.
(2) d – e > 4
{de} can take any value greater than 4 so de4 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
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19 Jun 2015, 02:49
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
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22 Jun 2015, 06:09
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:Attachment:
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Re: If a, b, c, d, and e are positive integers such that
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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
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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 de = 4 or 4+?.. Well it's already in the question stem, it says there that de is 4 (same base 10 we subtract de 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
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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^de4.So if de>=4 the output will always be an integer.
2) also says the same de>4 always an intergerv



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