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Algebra Question

Expert replies
by Spartacus2000 » Thu Aug 11, 2011 3:59 pm
Marta bought several pencils. If each pencil was either a 23-cent pencil or a 21-cent pencil, how many 23-cent pencils did Marta buy?

(1) Marta bought a total of 6 pencils

(2) The total value of the pencils Marta bought was 130 cents

Thanks,
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Source: — Data Sufficiency |

by GmatKiss » Thu Aug 11, 2011 4:43 pm
IMO:C
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by Spartacus2000 » Thu Aug 11, 2011 5:35 pm
According to the answer key the ans. is B.

Not sure how to come to that.
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by edvhou812 » Thu Aug 11, 2011 7:24 pm
This is a tricky one. They are trying to get us to quickly pass DS item #2 since there are two variables.

I came to 'B' by looking at the units digits of .23 and .21, and multiplying them till the sum of the two products was divisible by 10.

Units digit of .23 is 3. Units digit of .21 is 1. 3x2=6; 1x4=4. 6+4=10.
Now plug into the equation: .23(2)+.21(4)=.46+.84=1.30.

I admit that I used DS item #1 to speed things up, but I worked assuming that a person that is stronger in math would have found a way to get there without "cheating", so I assumed '2' must be sufficient in all cases. Maybe an expert can weigh in, but I agree that the answer is B.
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by GmatKiss » Fri Aug 12, 2011 12:53 am
I got it now,

21x + 23y = 130
=> 21.4 + 23.2 =130 (x=4 , y=2)only way possible!

So, answer is 2 alone, B
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