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word problem

by jzw » Wed Feb 29, 2012 8:37 pm
I was able to solve it algebraically, but when I plug in the answers I can't seem to get it to match. What am I missing?

The price of X and Y was $1,500. If X had been purchased with Z, whose price was $2,000 more than that of X, then the price of Y would have been 1/8 of the total. What was the price of X?

A. $900
B. $1,000
C. $1,100
D. $1,200
E. $1,300

Ok; so...

8Y = X + X + 2000
X + Y = 1,500 or X = -Y + 2000

so...

8Y = -2Y + 5,000
10Y = 5000
Y = 500

So then if Y = $500 then X must be $1,000 because $1,500 - $500 = $1,000 and B is in fact, the correct answer.

My problem, and maybe it's late @ night so my brain is malfunctioning, is that X + Y + Z = $4,500 (had they been purchased all together like the question stem said) and Y is 1/9 of $4,500. What am I doing wrong here?
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by GMATGuruNY » Thu Mar 01, 2012 4:50 am
jzw wrote:
The price of X and Y was $1,500. If X had been purchased with Z, whose price was $2,000 more than that of X, then the price of Y would have been 1/8 of the total. What was the price of X?

A. $900
B. $1,000
C. $1,100
D. $1,200
E. $1,300
We can plug in the answers, which represent the value of X.

Answer choice C: X=1100
Since Z costs 2000 more, Z = 1100+2000 = 3100.
X+Z = 1100+3100 = 4200.
Since Y is 1/8 of X and Z, Y = (1/8)4200 = 525.
X+Y = 1100+525 = 1625.
Too big: the sum of X and Y must be 1500.
Eliminate C, D and E.

Answer choice D: X=1000
Since Z costs 2000 more, Z = 1000+2000 = 3000.
X+Z = 1000+3000 = 4000.
Since Y is 1/8 of X and Z, Y = (1/8)4000 = 500.
X+Y = 1000+500 = 1500.
Success!

The correct answer is B.
My problem, and maybe it's late @ night so my brain is malfunctioning, is that X + Y + Z = $4,500 (had they been purchased all together like the question stem said) and Y is 1/9 of $4,500. What am I doing wrong here?
From the problem: if X had been purchased with Z...
Here, all three are NOT being purchased together: X is being purchased with Z INSTEAD OF with Y.
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by jzw » Thu Mar 01, 2012 9:19 am
Thanks. Was this just a poorly worded question by whoever wrote it (who, not whom, right?) or can I expect real GMAT questions to sound like this?
GMATGuruNY wrote:
jzw wrote:
The price of X and Y was $1,500. If X had been purchased with Z, whose price was $2,000 more than that of X, then the price of Y would have been 1/8 of the total. What was the price of X?

A. $900
B. $1,000
C. $1,100
D. $1,200
E. $1,300
We can plug in the answers, which represent the value of X.

Answer choice C: X=1100
Since Z costs 2000 more, Z = 1100+2000 = 3100.
X+Z = 1100+3100 = 4200.
Since Y is 1/8 of X and Z, Y = (1/8)4200 = 525.
X+Y = 1100+525 = 1625.
Too big: the sum of X and Y must be 1500.
Eliminate C, D and E.

Answer choice D: X=1000
Since Z costs 2000 more, Z = 1000+2000 = 3000.
X+Z = 1000+3000 = 4000.
Since Y is 1/8 of X and Z, Y = (1/8)4000 = 500.
X+Y = 1000+500 = 1500.
Success!

The correct answer is B.
My problem, and maybe it's late @ night so my brain is malfunctioning, is that X + Y + Z = $4,500 (had they been purchased all together like the question stem said) and Y is 1/9 of $4,500. What am I doing wrong here?
From the problem: if X had been purchased with Z...
Here, all three are NOT being purchased together: X is being purchased with Z INSTEAD OF with Y.
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