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# If a carton containing a dozen mirrors is dropped, which of the follow

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
If a carton containing a dozen mirrors is dropped, which of the follow  [#permalink]

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01 Nov 2018, 03:04
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Difficulty:

15% (low)

Question Stats:

77% (00:54) correct 23% (00:59) wrong based on 58 sessions

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If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?

(A) 2:1
(B) 3:1
(C) 3:2
(D) 1:1
(E) 7:5

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Re: If a carton containing a dozen mirrors is dropped, which of the follow  [#permalink]

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01 Nov 2018, 03:49
1
Because we have a dozen mirrors, we would have to find a ratio that corresponds with 12.

A) 2:1 --> 2+1 = 3 and 12 can be divided by 3
B) 3:1 --> 3+1 = 4 and 12 can be divided by 4
C) 3:2 --> 3+2 = 5 and 12 can not be divided by 5 --> answer C cannot be the ratio of broken mirrors to unbroken mirrors.
D) 1:1 --> 1+1 = 2 and 12 can be divided by 2
E) 7:5 ---> 7+5 = 12 and 12 can be divided by 12.
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Re: If a carton containing a dozen mirrors is dropped, which of the follow  [#permalink]

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01 Nov 2018, 04:02
Bunuel wrote:
If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?

(A) 2:1
(B) 3:1
(C) 3:2
(D) 1:1
(E) 7:5

$$12\,\,{\rm{mirrors}}\,\,\,\left\{ \matrix{ {\rm{broken}}\,\,{\rm{:}}\,\,b \hfill \cr {\rm{unbroken}}\,\,{\rm{:}}\,\,u \hfill \cr} \right.$$

$$?:\,\,\,b:u\,\,\,\underline {{\rm{impossible}}}$$

The k technique is very useful here!

$$\left( {\rm{A}} \right)\,\,\,\left\{ \matrix{ \,b = 2k \hfill \cr u = k \hfill \cr} \right.\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\,\, \Rightarrow \,\,\,3k = 12\,\,\, \Rightarrow \,\,\,{\rm{viable}}$$

$$\left( {\rm{B}} \right)\,\,\,\left\{ \matrix{ \,b = 3k \hfill \cr u = k \hfill \cr} \right.\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\,\, \Rightarrow \,\,\,4k = 12\,\,\, \Rightarrow \,\,\,{\rm{viable}}$$

$$\left( {\rm{C}} \right)\,\,\,\left\{ \matrix{ \,b = 3k \hfill \cr u = 2k \hfill \cr} \right.\,\,\,\left( {k = 3k - 2k \ge 1\,\,\underline {{\mathop{\rm int}} } } \right)\,\,\,\,\,\, \Rightarrow \,\,\,5k = 12\,\,\, \Rightarrow \,\,\,\underline {{\rm{not}}} \,\,{\rm{viable}}$$

The correct answer is therefore (C).

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)
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Re: If a carton containing a dozen mirrors is dropped, which of the follow  [#permalink]

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01 Nov 2018, 04:09

Solution

Given:
• Total number of mirrors in the carton, which is dropped = 12

To find:
• Which among the given answer choices cannot be the ratio of broken to unbroken mirrors

Approach and Working:
• Let us assume that the ratio of broken to unbroken mirrors is m : n
• Then (m + n) * p must be equal to 12, where p is a positive integer
o Implies, (m + n) must be a factor of 12

• Now, if we see the answer choices, only (3 + 2) is not a factor of 12

Therefore, the ratio of broken to unbroken mirrors cannot be 3 : 2

Hence, the correct answer is Option C

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Re: If a carton containing a dozen mirrors is dropped, which of the follow   [#permalink] 01 Nov 2018, 04:09
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