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

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New post Updated on: 28 Sep 2018, 10:07
1
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A
B
C
D
E

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

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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.
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Re: Positive integers A, B, C are such that C is a multiple of B & B is a  [#permalink]

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New post 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.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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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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