At least how many grams of pure bronze must be...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

At least how many grams of pure bronze must be...

by swerve » Fri Feb 23, 2018 7:50 am

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At least how many grams of pure bronze must be alloyed with 387 grams of pure copper to create an alloy that is no more than 90% copper?

A. 13
B. 43
C. 103
D. 348
E. 430

The OA is B.

Please, can any expert explain this PS question for me? I tried the following,

Can I say that
387 + x grams = y grams,
and
387 = 0.9y then y = 430.

Finally,
387 + x = 430
x = 430 - 387 = 43.

I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Feb 23, 2018 7:50 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

by DavidG@VeritasPrep » Fri Feb 23, 2018 9:21 am

swerve wrote:At least how many grams of pure bronze must be alloyed with 387 grams of pure copper to create an alloy that is no more than 90% copper?

A. 13
B. 43
C. 103
D. 348
E. 430

The OA is B.

Please, can any expert explain this PS question for me? I tried the following,

Can I say that
387 + x grams = y grams,
and
387 = 0.9y then y = 430.

Finally,
387 + x = 430
x = 430 - 387 = 43.

I need your help. Thanks.

A bit of logic eliminates most of the answer choices. Clearly, D and E would yield a mixture with much less than 90% copper. And if we estimate, we can see the same is true of C - if a mixture were 400 grams copper and you added 100 grams of bronze, the total mixture of 500 grams would be only 80% copper. C is out.

Now you only have to test one of the two remaining options. Say you tried A. If you added 13 grams of bronze, the total mixture would be 387 + 13 = 400 grams. If it were 90% copper, it would have had .9 * 400 = 360 grams copper. If there's actually 387 grams, there's clearly more than 90% copper. A is out.

You're left with B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 14, 2019 2:51 pm

swerve wrote:At least how many grams of pure bronze must be alloyed with 387 grams of pure copper to create an alloy that is no more than 90% copper?

A. 13
B. 43
C. 103
D. 348
E. 430

We can let n = the number of grams of pure bronze needed and create the equation:

387/(387 + n) = 9/10

3870 = 9(387 + n)

430 = 387 + n

43 = n

Alternate Solution:

We can let x = the total minimum weight of the alloy and create the equation:

0.9x = 387

9x = 3870

x = 3870/9

x = 430

Since the total minimum weight of the alloy must be 430 grams, we see that the minimum amount of bronze must be 430 - 387 = 43 grams.

Answer: B

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