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It costs x dollars each to make the first 1,000 copies of

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It costs x dollars each to make the first 1,000 copies of

by VJesus12 » Wed Jun 20, 2018 2:36 am

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It costs x dollars each to make the first 1,000 copies of a compact disc and y dollars to make each subsequent copy. If z is greater than 1,000, how many dollars will it cost to make z copies of the compact disc?

(A) 1,000x + yz
(B) zx - zy
(C) 1,000 (z - x) + xy
(D) 1,000 (z - y) + xz
(E) 1,000 (x - y) + yz

The OA is the option E.

How can I get the last expression? Could someone help me? Please. I'd be thankful.
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by Vincen » Wed Jun 20, 2018 3:42 am
Hello Vjesus12.

Let's take a look at your question.

We know the following:

- It costs x dollars to make each of the first 1,000 copies.
- It costs y dollars to make each subsequent copy.
- z is greater than 1,000.

Now, the cost for the first 1,000 copies is equal to 1,000*x.

The number of copies over 1,000 is given by z-1,000. Since the cost for the rest of the copies is y dollars, then the cost to make the excess of copies (over 1,000) is given by
$$\left(z-1,000\right)\cdot y.$$ Therefore, the total cost is given by $$1,000\cdot x+\left(z-1,000\right)\cdot y=1,000\cdot x+z\cdot y-1,000\cdot y=1,000\left(x-y\right)+yz.$$ This implies that the correct answer is the option E.

I hope it helps you. <i class="em em-smiley"></i>
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by [email protected] » Wed Jun 20, 2018 9:17 pm
Hi VJesus12,

We're told that it costs X dollars each for the first 1,000 copies of a compact disc and Y dollars to make each subsequent copy. If Z is greater than 1,000, how many dollars will it cost to make Z copies of the compact disc. This question can be solved by TESTing VALUES.

IF...
X = 1, Y = 2 and Z = 1,001
Then the total cost would be (1000)($1) + (1)($2) = $1,002

Thus, we're looking for an answer that equals 1,002 when we plug X=1, Y=2 and Z=1,001 into it. There's only one answer that matches....

Final Answer: E

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Rich
Contact Rich at [email protected]
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by Jeff@TargetTestPrep » Thu Jun 21, 2018 4:12 pm
VJesus12 wrote:It costs x dollars each to make the first 1,000 copies of a compact disc and y dollars to make each subsequent copy. If z is greater than 1,000, how many dollars will it cost to make z copies of the compact disc?

(A) 1,000x + yz
(B) zx - zy
(C) 1,000 (z - x) + xy
(D) 1,000 (z - y) + xz
(E) 1,000 (x - y) + yz
The cost is:

1000x + y(z - 1000)

1000x + yz - 1000y

1000(x - y) + yz

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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