Grandmother's Punch hangover cure is a mix of two

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AAPL: Moderator; Posts: 2695; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Mon Sep 17, 2018 8:03 am

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Economist GMAT

Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

OA B.

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Source: Beat The GMAT — Problem Solving | Mon Sep 17, 2018 8:03 am

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

by fskilnik@GMATH » Mon Sep 17, 2018 11:26 am

AAPL wrote:Economist GMAT

Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

Excellent occasion for the alligation :

\[? = x\,\,\,\left[ {{\text{ml}}} \right]\]
\[\frac{x}{{750}} = \frac{{20 - \frac{{58}}{5}}}{{20 - 5}}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,750} \,\,\,\,\,\,\,? = x = \frac{{750\left( {100 - 58} \right)}}{{5 \cdot 15}} = \frac{{150 \cdot 42}}{{15}} = 420\,\,\,\left[ {{\text{ml}}} \right]\]

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

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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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 » Mon Sep 17, 2018 12:18 pm

AAPL wrote:Economist GMAT

Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

We can PLUG IN THE ANSWERS, which represent the amount of cider.
When the correct answer is plugged in, the amount of alcohol in the 750 ml bottle = 87 ml.
Since the alcohol percentage in the cider = 5% = 1/20, the correct answer is almost
certain to be a multiple of 20.
Of the five answer choices, only B is a multiple of 20.

B: 420 ml cider, implying that the extraction = 750-420 = 330 ml
Total alcohol = (5% of 420 ml of cider) + (20% of 330 ml of extraction) = 21 + 66 = 87,
Success!

The correct answer is B.

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by [email protected] » Mon Sep 17, 2018 3:07 pm

Hi All,

We're told that Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. We're asked if a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contain. This question can be solved in a variety of different ways, including Algebraically:

H = number of milliliters of herbal extract
A = number of milliliters of apricot cider

With 750 total milliliters and 87 milliliters of alcohol, we can create the following equations:

H + A = 750
(.2H + .05A) = 87

We can multiply the second equation by 20...
4H + A = 1740

and then substitute in H = (750 - A) ....

4(750 - A) + A = 1740
3000 - 4A + A = 1740
1260 - 3A = 0
1260 = 3A
420 = A

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Tue Sep 18, 2018 5:44 pm

AAPL wrote:Economist GMAT

Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

Let's let H = the number of milliliters of the herbal extraction and A = the number of milliliters of the apricot cider. We can create the equations:

0.2H + 0.05A = 87

20H + 5A = 8700

4H + A = 1,740

A = 1,740 - 4H

And

A + H = 750

So H = 750 - A. Substituting 750 - A for H in A = 1,740 - 4H, we have:

A = 1,740 - 4(750 - A)

A = 1,740 - 3,000 + 4A

-3A = -1,260

A = 420

Alternate Solution:

We have x milliliters of herbal extraction that has 20% alcohol. We add (750 - x) milliliters of apricot cider that has 5% alcohol. The result is a solution of Grandma's Punch that contains 87 milliliters of alcohol. We can express this as:

0.20x + (750 - x)(0.05) = 87

0.20 x + 37.5 - 0.05x = 87

0.15x = 49. 5

x = 330

Since we have 330 milliliters of herbal extraction, then we have (750 - 330) = 420 milliliters of apricot cider.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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