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# What percent of juice bottles are labeled correctly; that is, Guava Ju

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What percent of juice bottles are labeled correctly; that is, Guava Ju  [#permalink]

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11 Oct 2018, 03:11
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Difficulty:

25% (medium)

Question Stats:

78% (01:34) correct 22% (01:23) wrong based on 44 sessions

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What percent of juice bottles are labeled correctly; that is, Guava Juice label on the bottles that have guava juice in them and Orange Juice label on the bottles that have orange juice in them.

(1) Of those which are labeled guava juice, 20 percent have orange juice in them.
(2) 80 percent of the bottles are labeled orange Juice.

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Re: What percent of juice bottles are labeled correctly; that is, Guava Ju  [#permalink]

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11 Oct 2018, 05:09

(1) gives us the breakdown of correct/incorrect among bottles labeled guava, but we don't know how many there are in general, or what the breakdown is among bottles labeled orange.Insufficient!

(2) gives us the general breakdown of which bottles are labeled what, but no data on whether these labels are correct. Insufficient!

combined, we have enough information to find the amount of guava bottles there are which are labelled correctly (gave bottles labeled guava - 0.2*0.2=0.044). But we have no information about the bottles labeled orange juice - how many are labeled correctly, how many aren't. Insufficient!
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Re: What percent of juice bottles are labeled correctly; that is, Guava Ju  [#permalink]

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11 Oct 2018, 07:16
Bunuel wrote:
What percent of juice bottles are labeled correctly; that is, Guava Juice label on the bottles that have guava juice in them and Orange Juice label on the bottles that have orange juice in them.

(1) Of those which are labeled guava juice, 20 percent have orange juice in them.
(2) 80 percent of the bottles are labeled orange Juice.

$$?\,\, = \,\,\frac{{\# \,\,{\text{correct}}\,\,{\text{match}}\,\,{\text{label - content}}}}{{\# \,\,{\text{total}}}}$$

Let´s go straight to (1+2): there is a viable bifurcation, hence this bifurcation is valid for (1) and (2) considered separately.

Suppose there are exactly 100 bottles, 80 labelled Orange and 20 labelled Guava (statement (2)).

Besides that, the 20 labelled Guava are such that 4 have Orange juice inside, 16 have Guava juice inside (statement (1)).

(At least) Two situations are possible, all restrictions above respected:

> All 80 labelled Orange have Orange juice inside. In this case,

$$? = \frac{{16 + 80}}{{100}} = 96\%$$

> All 80 labelled Orange have Guava juice inside. In this case,

$$? = \frac{{16 + 0}}{{100}} = 16\%$$

The correct answer is therefore (E).

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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: What percent of juice bottles are labeled correctly; that is, Guava Ju   [#permalink] 11 Oct 2018, 07:16
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