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

Question

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

alexanderstudent · Answer

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.

fskilnik · Answer

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.

EgmatQuantExpert · Answer

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

Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

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

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

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