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

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Joined: 04 Jan 2015
Posts: 2577
Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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Updated on: 30 Apr 2017, 10:56
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5
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Difficulty:

75% (hard)

Question Stats:

48% (01:47) correct 52% (01:21) wrong based on 116 sessions

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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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24 Apr 2017, 22:12
Reserving this space to post the official solution.
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Re: Anna wants to distribute chocolates among her four children in the rat  [#permalink]

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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

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

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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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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

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

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

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

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

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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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