Anna wants to distribute chocolates among her four children in the rat

Question

Anna wants to distribute chocolates among her four children in the ratio \(\frac{1}{2} : \frac{1}{5} : \frac{1}{6} : \frac{1}{12}\). 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

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Official Answer

C

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deucebigalow · Accepted Answer

The LCM of 2,5,6 and 12 is 60. If we distribute 60 with the given ratios, it will give 
 \frac{60}{2}+\frac{60}{5}+\frac{60}{6}+\frac{60}{12}=57

skothaka · Answer

from the give options choose the lowest numer which is a multiple of LCM of 2, 5, 6, 12. This is because when all the fractions are multiplied by the number of chocolates you need to get an integer.
LCM = 60

Hence answer is C

Abhishek009 · Answer

\frac{1}{2} : \frac{1}{5} : \frac{1}{6} : \frac{1}{12}  =  30 : 12 : 10 : 5

So, The minimum number of chocolates she should have bought is  30 + 12 + 10 + 5 = 57

Answer must be (C)

fskilnik · Answer

? = \min \left( {{\rm{Total}}} \right)

{1 \over 2}\,\,:\,\,{1 \over 5}\,\,:\,\,{1 \over 6}\,\,:\,\,{1 \over {12}}\,\,\,\,\mathop \Leftrightarrow \limits_{:\,\,60}^{ \cdot \,\,60} \,\,\,\,30:12:10:5

\left\{ \matrix{
 {\rm{Child}}\,1 = 30k \hfill \cr 
 {\rm{Child}}\,2 = 12k \hfill \cr 
 {\rm{Child}}\,3 = 10k \hfill \cr 
 {\rm{Child}}\,4 = 5k \hfill \cr} \right.\,\,\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,Total = 57k\,\,\,\,\,\,\mathop \Rightarrow \limits^{k\,\,{\mathop{\rm int}} \,\,\left( * \right)} \,\,\,\,\,\,? = \min \,\,\left( {{\rm{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.

Kinshook · Answer

Given: Anna wants to distribute chocolates among her four children in the ratio  \frac{1}{2} : \frac{1}{5} : \frac{1}{6} : \frac{1}{12} .

Asked: How many minimum chocolates should she buy, so that she can distribute the chocolates in the given ratio?

Anna wants to distribute chocolates among her four children in the ratio 30/60: 12/60: 10/60: 5/60 
She has to purchase chocalates = 30k + 12k + 10k + 5k = 57k

Minimum chocholates she should buy = 57

IMO C

adityaprateek15 · Answer

Bunuel   Krunaal  Does this question really belong to 655-705 level? Marking it for your review.

Bunuel · Answer

The difficulty level of a question on the site, after sufficient attempts, is determined  automatically  based on various parameters collected from users' attempts via timer, such as the percentage of correct answers and the time taken to answer the question. So, this is an easy 655-705 level question based on our statistics.

Anna wants to distribute chocolates among her four children in the rat

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