don't understand ratio question

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allenkt: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Sat Apr 14, 2007 8:06 am

by allenkt » Sat Apr 21, 2007 2:26 pm

Even after seeing the answer, this one has me stumped. Question 97 from OG11 PS questions:

Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2 : 16. Approximately how many grams of oxygen are there in 144 grams of water?

So I see this as 2 / 16 with 2 grams of hydrogen for every 16 grams of oxygen. But taking 144 times 2/16 doesn't produce the answer.

In the answer guide they say, From this, the ratio of oxygen to water's hydrogen and oxygen combination is known to be 16 / (2 + 16) then they set that equal to x / 144 and solve for x.

Where did they come up with 16 / (2 + 16) ?? I'm just not seeing it.

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Source: Beat The GMAT — Problem Solving | Sat Apr 21, 2007 2:26 pm

rajeshvellanki: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Mon Apr 09, 2007 6:20 am; Thanked: 2 times

by rajeshvellanki » Sat Apr 21, 2007 3:12 pm

lets say H-->x and O--y

H/0=2/16=1/8==> y=8x

x+y=144

9x=144

x=144/9=16

==> H=16grams and O=8x=8(16)=128

==>0=128

What are the answer choices?

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allenkt: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Sat Apr 14, 2007 8:06 am

by allenkt » Sat Apr 21, 2007 3:39 pm

The answer choices are:

a. 16
b. 72
c. 112
d. 128
e. 142

And the correct answer, as you might have guessed is d. I can follow your method much easier than the books. I still don't know where they came up with their method. The book is much more confusing to me. That answer reads as such:

From this, the ratio of oxygen to water's hydrogen and oxygen combination is known to be 16 / (2 + 16). Letting x be the number of grams of oxygen in 144 grams of water, the proportion comparing oxygen to water's hydrogen and oxygen combination can be expressed as

16 / (2 + 16) = x / 144 and solved as follows:

16 / 18 = x / 144

8 / 9 = x / 144

9x = 1152

x = 128

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sun Apr 22, 2007 4:21 am

Hey this one is pretty simple...Ratio of H:O = 2:16 which means 18 parts (or 16+2) of water consists of 2 parts of hydrogen and 16 parts of oxygen. Hence the correct approach is the one mentioned in the guide i.e. 144*(16/18)

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