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# Gmat club tests M22 Q12

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Senior Manager
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Gmat club tests M22 Q12 [#permalink]  17 Jan 2010, 17:34
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?$27
$31$35
$39$41

Could someone elaborate on this, I could not understand explanation provided by GMAT club
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Re: Gmat club tests M22 Q12 [#permalink]  17 Jan 2010, 18:27
mirzohidjon 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?$27
$31$35
$39$41

Could someone elaborate on this, I could not understand explanation provided by GMAT club

I am sure there is a shorter way but:

15N + 10U = 125 where N = new books sold and U = used books sold
5N + 2U = x where x = total profit

subtract both equations
4U = 125 - 3x

You can substitute each number above and 125-3x must be a multiple of 4
a 125 - 3(27) = 44
b 125 - 3(31) = 32
c 125 - 3(35) = 20
d 8

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Re: Gmat club tests M22 Q12 [#permalink]  19 Jan 2010, 03:57
mirzohidjon 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?$27
$31$35
$39$41

Could someone elaborate on this, I could not understand explanation provided by GMAT club

Try this approach:
Since Total Sales is $125 (odd), no of new books sold should be odd So following are the four possible scenario 1. 1 New + 11 Old => profit (1*5)+(11*2)=$27
2. 3 New + 8 Old => profit (3*5)+(8*2)=$31 3. 5 New + 5 Old => profit (5*5)+(5*2)=$35
4. 7 New + 2 Old => profit (7*5)+(2*2)=$39 hence (E). Hope this helps Senior Manager Joined: 18 Aug 2009 Posts: 437 Schools: UT at Austin, Indiana State University, UC at Berkeley WE 1: 5.5 WE 2: 5.5 WE 3: 6.0 Followers: 6 Kudos [?]: 66 [0], given: 16 Re: Gmat club tests M22 Q12 [#permalink] 21 Jan 2010, 07:59 Now, I got it. Thank you _________________ Never give up,,, Manager Joined: 16 Feb 2011 Posts: 197 Schools: ABCD Followers: 1 Kudos [?]: 70 [0], given: 78 Re: Gmat club tests M22 Q12 [#permalink] 30 Jul 2012, 04:29 Bunuel, How can I solve this method in two minutes? Any tips? THE OE says "The maximum number of new books that could have been sold is 7. In this case the profit would have been highest: USD. 41 USD is an impossible profit." If 125 = 15*1 + 11*10=> Maximum number of books = 12 and not 7. I wrote two equations : 15X + 10y =125; 5X+2Y = (substitute answer choice). However, this took me over 4 minutes. Thanks Math Expert Joined: 02 Sep 2009 Posts: 27123 Followers: 4199 Kudos [?]: 40541 [1] , given: 5540 Re: Gmat club tests M22 Q12 [#permalink] 30 Jul 2012, 04:52 1 This post received KUDOS Expert's post voodoochild wrote: Bunuel, How can I solve this method in two minutes? Any tips? THE OE says "The maximum number of new books that could have been sold is 7. In this case the profit would have been highest: USD. 41 USD is an impossible profit." If 125 = 15*1 + 11*10=> Maximum number of books = 12 and not 7. I wrote two equations : 15X + 10y =125; 5X+2Y = (substitute answer choice). However, this took me over 4 minutes. Thanks OE says that "The maximum number of new books that could have been sold is 7" not total number of books. Below is new OE for this question: 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).

Hope it's clear.
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Re: Gmat club tests M22 Q12   [#permalink] 30 Jul 2012, 04:52
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# Gmat club tests M22 Q12

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