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How much was he overcharged, in terms of d and u?

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by himu » Mon Apr 08, 2013 8:03 pm
A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

3d - u
3du - 9
(3d)u
(u−d)3
(du)3
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by Brent@GMATPrepNow » Mon Apr 08, 2013 9:07 pm
himu wrote:A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

3d - u
3du - 9
(3d)u
(u−d)3
(du)3
I'm assuming that the retailer paid a total of d dollars for all u units.

If so, then the items cost d/u dollars each.
Since the retailer received 3 units fewer than what he wanted, we can say that he paid for 3 items that he didn't receive.
If each item costs d/u dollars each, the total cost of these 3 missing items is 3(d/u) dollars.
We can also write this as [spoiler]3d/u[/spoiler] dollars.

I don't see this as one of the answer choices, but perhaps you made a mistake in rewriting them??

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by Anju@Gurome » Mon Apr 08, 2013 9:11 pm
himu wrote:A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u?

3d - u
3du - 9
(3d)/u
(u−d)3
(du)/3
Plugging number is a good choice for this method.
Let's plug u = 4 and d = 4.
So, he ordered 4 items and each item costs $1.
Now, he received (4 - 1) = 3 items for $4.
Hence, he was overcharged by $(4 - 1) = $3

Now, plug these values of u and d in the answer choices,
  • A. 3d - u = 3*4 - 4 = 8 --> NO
    B. 3du - 9 = 3*4*4 - 9 = 39 --> NO
    C. (3d)/u = 3*4/4 = 3 --> YES
    D. (u-d)3 = (4 - 4)/3 = 0 --> NO
    E. (du)/3 = 4*4/3 --> NO
The correct answer is C.

Note : While plugging numbers for PS problems always remember to check all the options as it may be possible that for the particular numbers you have chosen, more than one options will work.
Anju Agarwal
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by himu » Mon Apr 08, 2013 11:18 pm
Thanks Anju & Brent.

Yes Brent, the thing which caused the confusion was -->paid a total of d dollars...I assumed paid D dollars for each.
Hence I wasn't getting the correct ans ! The Q seems to have some issue.
Thanks for your help :)
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