Proportions and Unknown multiplier problem

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Thu Jul 05, 2012 11:03 pm

Hello,

This is from MGMAT Guide 1 (5th edition):

Alexandra needs to mix cleaning solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Alexandra makes a mistake and mixes in half as much bleach as she ought to have. The total solution consists of 27 ml. How much bleach did Alexandra put into the solution?

Answer given is 3 ml

Any suggestions on how to solve this problem? Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Problem Solving | Thu Jul 05, 2012 11:03 pm

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Fri Jul 06, 2012 3:16 am

For the proper ratio, we need:

1 part bleach: 4 parts water = 1:4
If only half of bleach is put in, the ratio becomes
1/2 : 4 = 1:8

Let amount of bleach that Alexandra put in the solution is x. Then amount of water = 8x.
Now total amount = x+8x = 9x.
We are given that 9x=27 => x=3.

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Bill@VeritasPrep: GMAT Instructor; Posts: 1248; Joined: Thu Mar 29, 2012 2:57 pmFollowed by: 192 members; Location: Everywhere; Thanked: 503 times; GMAT Score:780

by Bill@VeritasPrep » Fri Jul 06, 2012 5:40 pm

eagleeye wrote:For the proper ratio, we need:

1 part bleach: 4 parts water = 1:4
If only half of bleach is put in, the ratio becomes
1/2 : 4 = 1:8

Let amount of bleach that Alexandra put in the solution is x. Then amount of water = 8x.
Now total amount = x+8x = 9x.
We are given that 9x=27 => x=3.

This is the best approach. Take the original ratio, apply the change given (half as much bleach), and then incorporate the actual amount (27 mL).

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windchaser: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sat Jun 16, 2012 10:28 pm

by windchaser » Mon Jul 09, 2012 12:15 am

This is my approach:
original ratio is 1:4
half as much as she ought to have, means it is now 0.5 : 4
27/4.5= 6
6*0.5 = 3mL

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