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# M22-12

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Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135295 [0], given: 12686

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16 Sep 2014, 01:16
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Difficulty:

75% (hard)

Question Stats:

40% (02:07) correct 60% (02:48) wrong based on 15 sessions

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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
[Reveal] Spoiler: OA

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Kudos [?]: 135295 [0], given: 12686

Math Expert
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135295 [1], given: 12686

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16 Sep 2014, 01:16
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Expert's post
Official Solution:

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).

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Kudos [?]: 135295 [1], given: 12686

Intern
Joined: 17 Mar 2015
Posts: 16

Kudos [?]: 6 [0], given: 13

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02 Jul 2016, 00:00
How is one supposed to notice such stuff? Is it realistic to notice and solve this in 2 mins?

Kudos [?]: 6 [0], given: 13

Manager
Joined: 21 Sep 2015
Posts: 82

Kudos [?]: 126 [3], given: 323

Location: India
GMAT 1: 730 Q48 V42
GMAT 2: 750 Q50 V41

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28 Jul 2016, 06:29
3
KUDOS
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

Alternate solution :

Try to find the max and min profit

Min profit will happen when the store sells maximum used books i.e 11 used books and 1 new book
Min profit = 22+5 =27$Max profit will happen when the store sells maximum new books i.e 7 new books and 2 old books Max profit = 35 + 4 = 39$

Therefore it is not possible to make a profit of 41\$
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Appreciate any KUDOS given !

Kudos [?]: 126 [3], given: 323

Manager
Joined: 12 Jun 2016
Posts: 227

Kudos [?]: 46 [0], given: 149

Location: India
WE: Sales (Telecommunications)

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19 Oct 2017, 09:44
Here is a (long) Algebraic approach.

Let $$n$$ be the number of new books and $$u$$ be the number of used books.

Given: $$15n+10u=125 => 3n+2u = 25$$

$$=>u = \frac{(25-3n)}{2}$$

Since $$n$$ can only take integral Values, the Possible values of $$n$$ = 1, 3, 5, and 7. Corresponding values of $$u$$ = 11, 8, 5, and 2

So the possible values of $$(n, u)$$ are - { (1, 11) , (3,8) , (5,5), and (7,2) }

To find the possible profits Substitute $$(n, u)$$ in $$5n+2u$$. we find apart from E all answer choices hold true.

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Kudos [?]: 46 [0], given: 149

Re: M22-12   [#permalink] 19 Oct 2017, 09:44
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# M22-12

Moderators: chetan2u, Bunuel

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