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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # A retailer orders u units of an item for which he pays d dol  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 09 Feb 2013 Posts: 114 A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags Updated on: 12 Mar 2013, 00:55 1 5 00:00 Difficulty: 5% (low) Question Stats: 85% (01:57) correct 15% (02:21) wrong based on 151 sessions ### HideShow timer Statistics A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u? A. 3d - u B. 3du - 9 C. (3d)/u D. (u−d)/3 E. (du)/3 _________________ Kudos will encourage many others, like me. Good Questions also deserve few KUDOS. Originally posted by emmak on 11 Mar 2013, 22:38. Last edited by Bunuel on 12 Mar 2013, 00:55, edited 1 time in total. Edited the question. Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 12 Mar 2013, 01:01 1 emmak wrote: A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u? A. 3d - u B. 3du - 9 C. (3d)/u D. (u−d)/3 E. (du)/3 Say the retailer ordered u = 4 items for d = 4$ (1$per item). Thus: He received 4 - 3 = 1 unit for 4$, which is 3$more than the item actually costs. Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3. Answer: C. Hope it's clear. _________________ Intern Joined: 16 Jan 2012 Posts: 21 Location: India Concentration: Strategy, International Business WE: Analyst (Consulting) Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 14 Mar 2013, 00:55 Bunuel wrote: emmak wrote: A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u? A. 3d - u B. 3du - 9 C. (3d)/u D. (u−d)/3 E. (du)/3 Say the retailer ordered u = 4 items for d = 4$ (1$per item). Thus: He received 4 - 3 = 1 unit for 4$, which is 3$more than the item actually costs. Now, plug u = 4 and d = 4 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*4)/4 = 3. Answer: C. Hope it's clear. Please help me understand where am i going wrong .. Amount per items actually recieved = d/u-3 Amount per items to be recieved = d/u Overcharged amount = d/u-3 - d/u = 3d/u(u-3) Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 14 Mar 2013, 01:07 1 akshaychandna wrote: Bunuel wrote: emmak wrote: A retailer orders u units of an item for which he pays d dollars. However, he mistakenly receives u - 3 items. How much was he overcharged, in terms of d and u? A. 3d - u B. 3du - 9 C. (3d)/u D. (u−d)/3 E. (du)/3 Say the retailer ordered u = 4 items for d = 4$ (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. _________________ Manager Status: Breaking my head!! Joined: 27 Jan 2013 Posts: 65 Location: India Concentration: General Management, Operations GMAT 1: 740 Q50 V40 GPA: 3.51 WE: Other (Transportation) Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 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 SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1825 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 02 Oct 2014, 01:05 1 Price ............. Quantity ............ Total $$\frac{d}{u}$$ .................... u .................... d $$\frac{d}{u}$$ ...................... (u-3) ............... $$d - \frac{3d}{u}$$ (Three pieces less received) $$Overcharge = d - d + \frac{3d}{u} = \frac{3d}{u}$$ Answer = C _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 17 Jan 2017 Posts: 48 Location: India Concentration: General Management, Entrepreneurship GPA: 4 Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 11 Jan 2018, 09:54 Bunuel I am making a silly mistake! can't put my finger on it! can you please tell me? I plugged in 10 for u and 10 for d. 10u=10d so 1u= 1d 10-3=7 7u = 10d so 1u=10/7d 1d- 10-7d= -3/7 which is wrong! i cant figure out what am i doing wrong! Thanks VP Joined: 09 Mar 2016 Posts: 1234 A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 11 Jan 2018, 12:31 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)[/quote] 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.[/quote] Hi Bunuel can you explain how from this d - d/u*(u -3) you got this (du - du +3d)/u and this 3d/u ? btw any nice link to know better how to simplify such algebraic expressions ? I always experience such technical issues with algebra I know this time you gonna reply thanks! Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: A retailer orders u units of an item for which he pays d dol [#permalink] ### Show Tags 11 Jan 2018, 19:39 srishti201996 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 Bunuel I am making a silly mistake! can't put my finger on it! can you please tell me? I plugged in 10 for u and 10 for d. 10u=10d so 1u= 1d 10-3=7 7u = 10d so 1u=10/7d 1d- 10-7d= -3/7 which is wrong! i cant figure out what am i doing wrong! Thanks The retailer ordered u = 10 items for d = 10$ (1$per item). Thus: He received 10 - 3 = 7 unit for 10$, which is 3\$ more than the items actually costs.

Now, plug u = 10 and d = 10 into the answer choices to see which one yields 3. Only C fits: (3d)/u = (3*10)/10 = 3.

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

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11 Jan 2018, 19:42
dave13 wrote:

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.[/quote]

Hi Bunuel can you explain how from this d - d/u*(u -3) you got this (du - du +3d)/u and this 3d/u ?

btw any nice link to know better how to simplify such algebraic expressions ? I always experience such technical issues with algebra

I know this time you gonna reply thanks!
[/quote]

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

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12 Jan 2018, 07:52
Bunuel wrote:
dave13 wrote:

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.

Hi Bunuel can you explain how from this d - d/u*(u -3) you got this (du - du +3d)/u and this 3d/u ?

btw any nice link to know better how to simplify such algebraic expressions ? :) I always experience such technical issues with algebra :)

I know this time you gonna reply :) thanks!
[/quote]

Hello Bunuel ! Hope you have an amazing day! :)

Thank you for the link, i reviewed the information provided in the website but I still do have doubts.

Ok So we have this: $$d$$ - $$\frac{d}{u}$$*$$(u -3)$$

First step: multiply $$\frac{d}{u}$$ by $$(u -3)$$ ---> -d + d3 <--- so here when we multiply $$\frac{d}{u}$$ by $$U$$ --- U cancel out

Now we have d- d + d3

So where am i wrong Bunuel ?

Many thanks for your methodical explanation !
VP
Joined: 09 Mar 2016
Posts: 1234
Re: A retailer orders u units of an item for which he pays d dol  [#permalink]

### Show Tags

12 Jan 2018, 08:03
dave13 wrote:
Bunuel wrote:
dave13 wrote:

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.

Hi Bunuel can you explain how from this d - d/u*(u -3) you got this (du - du +3d)/u and this 3d/u ?

btw any nice link to know better how to simplify such algebraic expressions ? I always experience such technical issues with algebra

I know this time you gonna reply thanks!

Hello Bunuel ! Hope you have an amazing day!

Thank you for the link, i reviewed the information provided in the website but I still do have doubts.

Ok So we have this: $$d$$ - $$\frac{d}{u}$$*$$(u -3)$$

First step: multiply $$\frac{d}{u}$$ by $$(u -3)$$ ---> -d + d3 <--- so here when we multiply $$\frac{d}{u}$$ by $$U$$ --- U cancel out

Now we have d- d + d3

UPDATE: I got i forgot to multiplt d/u 3!!! i multiplied jusd D thinking that U canceled out! I am getting smarter lol

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

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10 Aug 2018, 17:46
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

Since the price per unit is d/u, the cost of u - 3 units is d/u x (u - 3) = (ud - 3d)/u, so the retailer was overcharged by:

d - (ud - 3d)/u

ud/u - (ud - 3d)/u

(ud - (ud - 3d))/u

(ud - ud + 3d)/u

(3d)/u

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

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11 Aug 2018, 05:29
1
Top Contributor
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

A retailer orders u units of an item for which he pays d dollars.
So, EACH unit costs d/u dollars

However, he mistakenly receives u - 3 items.
In other words, he received 3 fewer units than he wanted
So, he paid for 3 units that he never received (i.e., he was overcharged for 3 units)

How much was he overcharged, in terms of d and u?
He was overcharged for 3 units, and EACH unit costs d/u dollars
TOTAL overcharge = (3)(d/u)
= 3d/u

Cheers,
Brent
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Re: A retailer orders u units of an item for which he pays d dol &nbs [#permalink] 11 Aug 2018, 05:29
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