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Math Expert V
Joined: 02 Sep 2009
Posts: 58374
Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (01:48) correct 37% (02:10) wrong based on 156 sessions

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Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

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Math Expert V
Joined: 02 Sep 2009
Posts: 58374
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

MANHATTAN GMAT OFFICIAL SOLUTION:

Fractions that have only factors of 2 and 5 in the denominator equate to terminating decimals. Since x/y = r.sss, a non-terminating decimal, y must have some other prime factors besides just 2 and/or 5.

(A) y = 12, 120, 1,200, etc. Prime factors of 12: (2)(2)(3)
(B) y = 15, 150, 1,500, etc. Prime factors of 15: (3)(5)
(C) y = 18, 180, 1,800, etc. Prime factors of 18: (2)(3)(3)
(D) y = 25, 250, 2,500, etc. Prime factors of 25: (5)(5). CANNOT be true—only has 5's and 2's.
(E) y = 27, 270, 2,700, etc. Prime factors of 27: (3)(3)(3)

The correct answer is D.
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CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
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Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

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Intern  Joined: 12 Oct 2014
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GMAT Date: 07-15-2015
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option D is correct answer?

Cheers,
Sri
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Status: GMATINSIGHT Tutor
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Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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2
Sri22 wrote:
Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option D is correct answer?

Cheers,
Sri

Hi Sri,

I would say YES, you can conclude it but only in grave situations when you have already given up on question and have to move on with one of the answer choices as selection.  _________________
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e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
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Intern  Joined: 12 Feb 2013
Posts: 20
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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2
1
For such questions... generally one rule works most of the time
if there is only 2 or 5 or combination of 2 and 5 in denominator, it will always give u a fixed output rather than a never ending one.
You can try few examples

33/5 = 6.6
3333333333/5 = 666666.6 something

1111/2 = 555.5

in all options except D, there is a factor of 3 involved... where as in D only 5 is there (5*5 = 25)
in GMAT you dont need to solve every expression... there might be possibility of other options as correct but first skim through options and then use logic.
I have solved numerous questions of gmat but never felt the need to solve anything for such questions..

yes, if still you want to use logic, then a perfect algebric solution is provided by GMATINSIGHT
Non-Human User Joined: 09 Sep 2013
Posts: 13161
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

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_________________ Re: Let x and y be positive integers, and r and s be single-digit positive   [#permalink] 19 Mar 2018, 06:42
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