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# An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur

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Math Expert
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An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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26 Nov 2014, 06:46
1
14
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Difficulty:

25% (medium)

Question Stats:

77% (02:03) correct 23% (02:27) wrong based on 459 sessions

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Tough and Tricky questions: Mixture Problems.

An alloy weighing 24 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?

A) 6
B) 9
C) 12
D) 24
E) 48

Kudos for a correct solution.

Source: Chili Hot GMAT

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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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28 Nov 2014, 00:39
10
8
Just want show the solution of such problems without unknown variables in three operations:) The main hint is to focus on the part that doesn't change!

Operation 1: Find the weight of part of alloy that doesn't change
30% of 24=0.3*24=7.2 ounces

Operation 2: Find the new weight of alloy. Since the weight of not gold part of alloy doesn't change after adding pure gold, 7.2 in new alloy is 10% of total weight.

7.2*10=72 ounces

Operation 3: Find what we add: 72-24=48 ounces of pure gold.

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##### General Discussion
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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26 Nov 2014, 09:42
2
An alloy of 24oz which is 70% gold means we have 16.8 oz of gold. To get to something that is 90% gold, let's use this expression: (16.8 + x)/(24 + x) = 0.9 with x representing the amount of pure gold that must be added to get to 90%. The expression thus represents the new weight of gold over the total new weight of the alloy and this fraction should represent 90%. I was just surprised the answer was quite high--48oz... That's gonna get expensive. But that's the price you pay to have nice things, eh?

Choose E
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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26 Nov 2014, 20:22
3
In 24 ounces, gold is 24 * (70/100) = 16.8 ounces. Now we add x ounces of pure gold to make it 90% gold.
So 16.8 + x = (24 + x)* 90/100 => x =48.
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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26 Nov 2014, 22:54
7

Gold .......................... Not Gold ................. Total

16.8 .............................. 7.2 ........................ 24 (70% is gold. 30% is NOTGOLD)

16.8+x ............................ 7.2 ...................... 24+x (Say "x" gold is added to make it 90% gold. Means NOTGOLD will decrease to 10%)

Setting up the equation

$$\frac{10}{100}(24+x) = 7.2$$

x = 72-24 = 48
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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05 Jan 2016, 05:59
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.

An alloy weighing 24 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?

A) 6
B) 9
C) 12
D) 24
E) 48

Initial: 24 ounces, 70 %gold or, 0.7*24 = 16.8 ounces gold and rest 7.2 other material.
Setp 1: Only gold is added.
Let x ounces gold is added.
Gold: 16.8 + x, Other material = x

Final: We need 90% gold in the alloy.
Total weight = 24 + x

16.8 + x should be 90% of 24 + x
Hence, 16.8 + x = 0.9*(24 + x)
0.1*x = 4.8
x = 48

Option E
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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05 Jan 2016, 21:29
2
1
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.

An alloy weighing 24 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?

A) 6
B) 9
C) 12
D) 24
E) 48

Kudos for a correct solution.

Source: Chili Hot GMAT

Back to weighted averages discussed here: http://www.veritasprep.com/blog/2011/04 ... -mixtures/

w1/w2 = (100 - 90)/(90 - 70) = 1/2

Since 70% gold weighs 24 ounces, pure gold added should weigh twice of that so 48 ounces.

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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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24 Nov 2016, 14:37
Bunuel wrote:

Tough and Tricky questions: Mixture Problems.

An alloy weighing 24 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?

A) 6
B) 9
C) 12
D) 24
E) 48

Kudos for a correct solution.

Source: Chili Hot GMAT

.7*24+x=.9(24+x)
x=48
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An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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05 May 2017, 23:36
We can use a direct formula for such questions:

Formula = $$\frac{Solution * (Required Value - Present Value)}{(100 - Required Value)}$$

therefore,$$\frac{24*(90 - 70)}{(100 - 90)}$$

=> $$\frac{24 * 20}{10}$$
=> 24 * 2
=> 48

Ans: E
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur  [#permalink]

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02 Aug 2018, 01:37
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Re: An alloy weighing 24 ounces is 70 percent gold. How many ounces of pur &nbs [#permalink] 02 Aug 2018, 01:37
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