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

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Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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New post Updated on: 30 Apr 2017, 10:56
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Q. 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


Thanks,
Saquib
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Originally posted by EgmatQuantExpert on 24 Apr 2017, 22:11.
Last edited by EgmatQuantExpert on 30 Apr 2017, 10:56, edited 1 time in total.
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Re: Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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Re: Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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New post 24 Apr 2017, 22:43
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
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Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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New post Updated on: 13 Aug 2017, 03:24
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The LCM of 2,5,6 and 12 is 60. If we distribute 60 with the given ratios, it will give
\(\frac{60}{2}+\frac{60}{5}+\frac{60}{6}+\frac{60}{12}=57\)

Originally posted by deucebigalow on 12 Aug 2017, 05:29.
Last edited by deucebigalow on 13 Aug 2017, 03:24, edited 2 times in total.
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Re: Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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New post 12 Aug 2017, 07:07
EgmatQuantExpert wrote:
Q. 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


Thanks,
Saquib
Quant Expert
e-GMAT

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

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

Answer must be (C)
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Re: Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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New post 27 Sep 2018, 14:29
EgmatQuantExpert wrote:
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


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

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

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

\(\left( * \right)\,\,\,\,\left\{ \matrix{
5k\,\, = {\mathop{\rm int}} \hfill \cr
2k = 12k - 10k\,\, = \,\,{\mathop{\rm int}} - {\mathop{\rm int}} = {\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,k = 5k - 2 \cdot \left( {2k} \right) = {\mathop{\rm int}} - 2 \cdot {\mathop{\rm int}} = {\mathop{\rm int}}\)


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

Regards,
Fabio.
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Re: Anna wants to distribute chocolates among her four children in the rat   [#permalink] 27 Sep 2018, 14:29
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