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A bookstore sells new books for $15 each and used books for [#permalink] ### Show Tags 21 Aug 2010, 21:52 2 This post was BOOKMARKED 00:00 Difficulty: 75% (hard) Question Stats: 58% (03:25) correct 42% (01:45) wrong based on 96 sessions ### HideShow timer Statistics A bookstore sells new books for$15 each and used books for $10 each. On every new book, the store makes a profit of$5 while on every used book it makes a profit of $2. If on a given day the bookstore's sales amounted to$125, which of the following cannot be the profit made on that day?

A. $27 B.$31
C. $35 D.$39
E. $41 m22 q12 [Reveal] Spoiler: OA Last edited by Bunuel on 22 Apr 2014, 12:58, edited 2 times in total. Edited the question. GMAT Tutor Joined: 24 Jun 2008 Posts: 1183 Followers: 423 Kudos [?]: 1530 [1] , given: 4 Re: 700 level question [#permalink] ### Show Tags 21 Aug 2010, 22:42 1 This post received KUDOS Expert's post shekar123 wrote: A bookstore sells new books for$15 each and used books for $10 each. On every new book, the store makes a profit of$5 while on every used book it makes a profit of $2. If on a given day the bookstore's sales amounted to$125, which of the following cannot be the profit made on that day?

A.27

B.31

C.35

D.29

E.41

I can suggest a couple of systematic ways to look at this, though I think it's practical to get the answer within two minutes by guessing-and-checking. First you might notice that the number of new books sold must be odd; otherwise the total sales in dollars would end in 0. You could then take an algebraic approach. If n is the number of new books and u the number of used books, we know that 15n+10u = 125, or dividing by 5, we have:

3n + 2u = 25

We want to know the value of 5n + 2u, which is the profit in dollars. Notice how similar this is to the left side of the equation above:

5n + 2u = 2n + (3n + 2u) = 2n + 25

So we just want to find what values are possible for 2n + 25. Remembering that n must be odd, it's easy enough just to plug in n=1, 3, 5 and 7 to see that every answer choice is possible except for 41.

Or, if you know that n is odd, you can replace it with 2k + 1, for some integer k. Then the quantity we're trying to find becomes

2u + 25 = 2(2k+1) + 25 = 4k + 27 = 4k + 24 + 3 = 4(k+6) + 3

So our profit is 3 greater than a multiple of 4, and thus has a remainder of 3 when divided by 4. Thus 41 is impossible (you might, when looking at the answers, see that 41 is a bit suspicious - all of the answer choices give a remainder of 3 when divided by 4 with one exception - 41). That's probably more work than the first approach, though it's perhaps interesting to see why each answer has the same remainder by 4.

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22 Apr 2014, 11:58
My way

OK so we have that:

15N + 10U = 125
3N + 2U = 25 (1)

Now we are trying to find 5N+2U

Therefore, we will have 25 + 2N, which one CANNOT be expressed in this form?

Well if 25 + 2N = 41 then 2N=16, N=8

Therefore replacing in (1) , 3N = 24 and 2U = 1, U=1/2 which CAN'T be correct because we can't sell 1/2 a book

Thus E stands

Hope this helps
Cheers!
J
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Re: A bookstore sells new books for $15 each and used books for [#permalink] ### Show Tags 22 Apr 2014, 12:57 shekar123 wrote: A bookstore sells new books for$15 each and used books for $10 each. On every new book, the store makes a profit of$5 while on every used book it makes a profit of $2. If on a given day the bookstore's sales amounted to$125, which of the following cannot be the profit made on that day?

A. $27 B.$31
C. $35 D.$39
E. $41 Given: $$15n+10u=125$$, where $$n$$ is the number of new books sold and $$u$$ is the number of used books sold. Question: taking into account above equation which value is not possible for $$5n+2u$$? Reduce $$15n+10u=125$$ by 5: $$3n+2u=25$$. Notice that this equation to hold true $$n$$ must be odd, since if $$n=even$$ then $$3n+2u=even+even=even$$ so, it cannot equal to odd number 25. Next, $$5n+2u=2n+(3n+2u)=2n+25$$. Now, you can notice that if $$n$$ is 1, 3, 5, or 7 then options A, B, C and D are possible (else notice that E to be possible $$n$$ must be 8, so even and we know that $$n$$ is odd). Answer: E. _________________ Manager Joined: 04 Jan 2014 Posts: 129 Followers: 1 Kudos [?]: 10 [0], given: 24 Re: A bookstore sells new books for$15 each and used books for [#permalink]

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05 May 2014, 04:47
Bunuel wrote:
Next, $$5n+2u=2n+(3n+2u)=2n+25$$. Now, you can notice that if $$n$$ is 1, 3, 5, or 7 then options A, B, C and D are possible (else notice that E to be possible $$n$$ must be 8, so even and we know that $$n$$ is odd).

Hi Bunnel, why do we have 2n + (3n+2u)?
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05 May 2014, 21:34
shekar123 wrote:
A bookstore sells new books for $15 each and used books for$10 each. On every new book, the store makes a profit of $5 while on every used book it makes a profit of$2. If on a given day the bookstore's sales amounted to $125, which of the following cannot be the profit made on that day? A.$27
B. $31 C.$35
D. $39 E.$41

m22 q12

Cost of new books is $15 and old is$10. Total sale price is $125. This tells me that number of new books sold was definitely odd since the total sale price ends with a 5. Had number of new books sold been even, the total sale price would have been a multiple of 10. So there must have been 1, 3, 5 or 7 new books and rest old books. So profit would have been an odd multiple of 5 + a multiple of 2. Number of new and old books could be 1 and 11 (total revenue of 125). Profit 5 + 2*11 = 27 Number of new and old books could be 3 and 8. Profit 15 + 2*8 = 31 Number of new and old books could be 5 and 5. Profit 25 + 5*2 = 35 Number of new and old books could be 7 and 2. Profit 35 + 2*2 = 39 A profit of 41 is not possible. Answer (E) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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