A ten-gram piece of a certain alloy contains only gold and

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Aug 12, 2019 2:30 pm

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Source: Manhattan Prep

A ten-gram piece of a certain alloy contains only gold and silver. If the piece currently contains exactly 3 grams of silver, how many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?

A. 30
B. 27
C. 25
D. 20
E. 17

The OA is D

Source: Beat The GMAT — Problem Solving | Mon Aug 12, 2019 2:30 pm

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

silver

by GMATGuruNY » Mon Aug 12, 2019 2:36 pm

BTGmoderatorLU wrote:Source: Manhattan Prep

A ten-gram piece of a certain alloy contains only gold and silver. If the piece currently contains exactly 3 grams of silver, how many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?

A. 30
B. 27
C. 25
D. 20
E. 17

Since the resulting piece must be 10 percent silver, the 3 grams of silver in the current piece must constitute 1/10 of the new total weight:
3 = (1/10)t
t = 30 grams
Thus, the weight of the added gold = (weight of the resulting piece) - (weight of the current piece) = 30 - 10 = 20 grams.

The correct answer is D.

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by Scott@TargetTestPrep » Sat Aug 24, 2019 4:18 am

BTGmoderatorLU wrote:Source: Manhattan Prep

A ten-gram piece of a certain alloy contains only gold and silver. If the piece currently contains exactly 3 grams of silver, how many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?

A. 30
B. 27
C. 25
D. 20
E. 17

The OA is D

Let x = the number of grams of gold that must be added to the piece so that the resulting piece is 10 percent silver. We can create the equation:

3/(10 + x) = 1/10

10 + x = 30

x = 20

Alternate Solution:

As the number of grams of silver in the alloy after the addition of gold does not change, the resulting alloy will contain 3 grams of silver as well. If the resulting piece is 10% silver, then the resulting piece must weigh 30 grams (so that 10% of it is 3 grams). Since the original piece was 10 grams, 30 - 10 = 20 grams of gold must be added.

Answer: D

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 24, 2019 6:14 am

BTGmoderatorLU wrote:Source: Manhattan Prep

A ten-gram piece of a certain alloy contains only gold and silver. If the piece currently contains exactly 3 grams of silver, how many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?

A. 30
B. 27
C. 25
D. 20
E. 17

The OA is D

GIVEN: The piece weighs 10 grams. The piece contains 3 grams of silver, which means the remaining 7 grams are gold
Let x = the number of EXTRA grams of gold needed for the piece to be 10 percent silver.
With the addition of x grams of gold, the NEW weight of the piece = 10 + x

How many more grams of gold must be added to the piece so that the resulting piece is 10 percent silver?
We want: (grams of silver)/(TOTAL weight of piece) = 10%
Fill in values to get: 3/(10 + x) = 1/10 (aka 10%)
Cross multiply to get: (1)(10 + x) = (3)(10)
Simplify to get: 10 + x = 30
Solve: x = 20

Answer: D

Cheers,
Brent

10 + x = 30

x = 20

Brent Hanneson - Creator of GMATPrepNow.com

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