Anna wants to distribute chocolates among her four children

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu Sep 27, 2018 10:19 am

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Anna wants to distribute chocolates among her four children in the ratio 1/2 : 1/5 : 1/6 : 1/12. How many minimum chocolates should she buy, so that she can distribute the chocolates in the given ratio?

A. 30
B. 45
C. 57
D. 90
E. 120

The OA is C.

Source: e-GMAT

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Sep 27, 2018 1:25 pm

swerve wrote:Anna wants to distribute chocolates among her four children in the ratio 1/2 : 1/5 : 1/6 : 1/12. How many minimum chocolates should she buy, so that she can distribute the chocolates in the given ratio?

A. 30
B. 45
C. 57
D. 90
E. 120

Let the total number of chocolates = the LCM of the four denominators 2, 5, 6 and 12 = 60.
Number of chocolates given to the four children:
(1/2)(60) = 30
(1/5)(60) = 12
(1/6)(60) = 10
(1/12)(60) = 5
Total number of chocolates = 30+12+10+5 = 57.

The correct answer is C.

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Sep 27, 2018 2:22 pm

swerve wrote:Anna wants to distribute chocolates among her four children in the ratio 1/2 : 1/5 : 1/6 : 1/12. How many minimum chocolates should she buy, so that she can distribute the chocolates in the given ratio?

A. 30
B. 45
C. 57
D. 90
E. 120
Source: e-GMAT

\[? = \min \left( {{\text{Total}}} \right)\]
\[\frac{1}{2}\,\,:\,\,\frac{1}{5}\,\,:\,\,\frac{1}{6}\,\,:\,\,\frac{1}{{12}}\,\,\,\,\mathop \Leftrightarrow \limits_{:\,\,60}^{ \cdot \,\,60} \,\,\,\,30:12:10:5\]
\[\left\{ \begin{gathered}
{\text{Child}}\,1 = 30k \hfill \\
{\text{Child}}\,2 = 12k \hfill \\
{\text{Child}}\,3 = 10k \hfill \\
{\text{Child}}\,4 = 5k \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,Total = 57k\,\,\,\,\,\,\mathop \Rightarrow \limits^{k\,\,\operatorname{int} \,\,\left( * \right)} \,\,\,\,\,\,? = \min \,\,\left( {{\text{Total}}} \right)\,\,\, = \,\,57 \cdot 1 = 57\]
$$\left( * \right)\,\,\,\,\left\{ \matrix{
5k\,\, = {\mathop{\rm int}} \hfill \cr
2k = 12k - 10k\,\, = \,\,{\mathop{\rm int}} - {\mathop{\rm int}} = {\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,k = 5k - 2 \cdot \left( {2k} \right) = {\mathop{\rm int}} - 2 \cdot {\mathop{\rm int}} = {\mathop{\rm int}} $$

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Oct 02, 2018 6:56 pm

swerve wrote:Anna wants to distribute chocolates among her four children in the ratio 1/2 : 1/5 : 1/6 : 1/12. How many minimum chocolates should she buy, so that she can distribute the chocolates in the given ratio?

A. 30
B. 45
C. 57
D. 90
E. 120

Since the LCM of 2, 5, 6, and 12 is 5 x 12 = 60; we can multiply each fraction by 60 so that each fraction becomes a whole number: 1/2 x 60 = 30, 1/5 x 60 = 12, 1/6 x 60 = 10 and 1/12 x 60 = 5. Therefore, the ratio can be written as 30 : 12 : 10 : 5 and, hence, the minimum number of chocolates she should buy is 30 + 12 + 10 + 5 = 57.

Answer: C

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