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

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

83% (02:19) correct 17% (00:42) wrong based on 35 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.
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Re: A retailer orders u units of an item for which he pays d dol [#permalink] New post 12 Mar 2013, 01:01
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.

Answer: C.

Hope it's clear.

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Re: A retailer orders u units of an item for which he pays d dol [#permalink] New post 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.

Answer: C.

Hope it's clear.




Please help me understand where am i going wrong ..

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)
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Re: A retailer orders u units of an item for which he pays d dol [#permalink] New post 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.

Answer: C.

Hope it's clear.




Please help me understand where am i going wrong ..

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.

Answer: C.

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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