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A certain industrial machine requires 15 quarts (Grockit)

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A certain industrial machine requires 15 quarts (Grockit)

by clawhammer » Tue Nov 09, 2010 5:14 am
A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 8% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?

a 260

b 280

c 290

d 300

e 320

PLEASE EXPLAIN....
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by Geva@EconomistGMAT » Tue Nov 09, 2010 6:08 am
two equations, two unknowns:

You know that A+B=480
form an equation for the actual number of ounces of special additive, which should sum up to 30 ounces
5%A + 8%B = 30

5A/100 + 8b/100 = 30
multiply by 100
5A+8B = 30*100
Divide by 8 to Isolate B

5/8A + B = 30*100/8

Now subtract this equation from the top equation (A+B=480) to get
A-5/8A + B-B = 480 - 30*100/8
3/8A = 480 - 30*100/8
Multiply times 8
3A = 480*8 - 30*100
divide by 3
A = 160*8 - 10*100 = 1280-1000 =280.
Answer should be B.

You could reverse Plug in the answer choices here as well:
If we assume that answer choice B is correct, i.e. that A=280, then we have 5%*280 = 14 ounces additive from A
The remaining 200 ounces are B at 8% additive, or 8/100*200 = 8*2 = 16 ounce additive from B, which together with the 14 ounces from A brings you back to the required 30 ounces - which means that B checks out as the right answer.
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by clawhammer » Tue Nov 09, 2010 6:19 pm
Thanks. The question somehow got me all puzzled, but you seem to have made it easy.
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by saurabhmahajan » Thu Nov 11, 2010 4:08 am
well you can do it by plugging values from options.....

First take the middle value, say oil a is 290 ounces. So 5% of additives will be 14.5 (290*.05). to make it 30 ounces of additive we now require more 15.5 ounces of additives from oil B. so the remaining 190 (480-290) should give us 15.5. 190*.08=15.2....we fall short. so minimize oil A and maximize oil B
take value 280 for oil A...so additive from oil A= 280*.05= 14
additive from oil B required is 16... 200*.08 (480-280) = 16
14+16 =30

therefore answer is B.
Thanks and regards,
Saurabh Mahajan

I can understand you not winning,but i will not forgive you for not trying.
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