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# Positive integers A, B, C are such that C is a multiple of B & B is a

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Senior Manager
Joined: 15 Feb 2017
Posts: 299
Positive integers A, B, C are such that C is a multiple of B & B is a  [#permalink]

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Updated on: 28 Sep 2018, 10:07
1
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:53) correct 40% (01:22) wrong based on 34 sessions

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Positive integers A, B, C are such that C is a multiple of B & B is a multiple of A. Is A multiple of 5?

(1) B x C is a multiple of 5
(2) A x B is a multiple of 5

_________________
IMPOSSIBLE IS JUST AN OPINION

Originally posted by sonusaini1 on 28 Sep 2018, 10:02.
Last edited by Bunuel on 28 Sep 2018, 10:07, edited 1 time in total.
Renamed the topic and edited the question.
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: Positive integers A, B, C are such that C is a multiple of B & B is a  [#permalink]

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28 Sep 2018, 10:21
sonusaini1 wrote:
Positive integers A, B, C are such that C is a multiple of B & B is a multiple of A. Is A multiple of 5?

(1) B x C is a multiple of 5
(2) A x B is a multiple of 5

$$A,B,C\,\,\, \geqslant 1\,\,\,{\text{ints}}$$

$$\frac{C}{B} = \operatorname{int} \,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\frac{B}{A} = \operatorname{int}$$

$$\frac{A}{5}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int}$$

$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ {{BC} \over 5} = {\mathop{\rm int}} \hfill \cr {{AB} \over 5} = {\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,$$

$$\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {A,B,C} \right) = \left( {1,5,5} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \,{\text{Take}}\,\,\left( {A,B,C} \right) = \left( {5,5,5} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.$$

The correct answer is therefore (E).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: Positive integers A, B, C are such that C is a multiple of B & B is a   [#permalink] 28 Sep 2018, 10:21
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