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# A retailer orders u units of an item for which he pays d dol

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Manager
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A retailer orders u units of an item for which he pays d dol [#permalink]  11 Mar 2013, 22:38
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Difficulty:

5% (low)

Question Stats:

82% (02:21) correct 18% (01:19) wrong based on 55 sessions
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?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Mar 2013, 00:55, edited 1 time in total.
Edited the question.
Math Expert
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Kudos [?]: 27290 [1] , given: 2732

Re: A retailer orders u units of an item for which he pays d dol [#permalink]  12 Mar 2013, 01:01
1
KUDOS
Expert's post
emmak 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?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Say the retailer ordered u = 4 items for d = 4$(1$ per item). Thus:

He received 4 - 3 = 1 unit for 4$, which is 3$ more than the item actually costs.

Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3.

Hope it's clear.
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Posts: 22
Location: India
Schools: Duke '17, ISB '16
WE: Analyst (Consulting)
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Kudos [?]: 7 [0], given: 6

Re: A retailer orders u units of an item for which he pays d dol [#permalink]  14 Mar 2013, 00:55
Bunuel wrote:
emmak 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?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Say the retailer ordered u = 4 items for d = 4$(1$ per item). Thus:

He received 4 - 3 = 1 unit for 4$, which is 3$ more than the item actually costs.

Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3.

Hope it's clear.

Amount per items actually recieved = d/u-3

Amount per items to be recieved = d/u

Overcharged amount = d/u-3 - d/u = 3d/u(u-3)
Math Expert
Joined: 02 Sep 2009
Posts: 23064
Followers: 3540

Kudos [?]: 27290 [0], given: 2732

Re: A retailer orders u units of an item for which he pays d dol [#permalink]  14 Mar 2013, 01:07
Expert's post
akshaychandna wrote:
Bunuel wrote:
emmak 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?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Say the retailer ordered u = 4 items for d = 4$(1$ per item). Thus:

He received 4 - 3 = 1 unit for 4$, which is 3$ more than the item actually costs.

Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3.

Hope it's clear.

Amount per items actually recieved = d/u-3

Amount per items to be recieved = d/u

Overcharged amount = d/u-3 - d/u = 3d/u(u-3)

The retailer received u - 3 items for the price of u items .

The price of u items is d dollars (so, the price of an items d/u dollars);
The price of u - 3 items is d/u*(u -3) dollars;

The difference is d - d/u*(u -3) = (du - du +3d)/u = 3d/u.

Hope it helps.
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Manager
Joined: 27 Jan 2013
Posts: 59
Location: India
Concentration: General Management, Operations
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 2

Kudos [?]: 18 [0], given: 33

Re: A retailer orders u units of an item for which he pays d dol [#permalink]  14 Mar 2013, 02:17
emmak 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?

A. 3d - u
B. 3du - 9
C. (3d)/u
D. (u−d)/3
E. (du)/3

Algebraic Solution
Amount overcharged = Amount paid by him - Amount he should have paid
Amount he should have paid=
original price of items*total items purchased
\frac{d}{u}*(u-3)
Amount paid by him was d dollars
Thus amount overcharged = d-d*\frac{(u-3)}{u}
On solving we get 3d/u
Thus C
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Re: A retailer orders u units of an item for which he pays d dol [#permalink]  19 Sep 2014, 01:26
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Re: A retailer orders u units of an item for which he pays d dol   [#permalink] 19 Sep 2014, 01:26
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