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# Marta bought several pencils. If each pencil was either a

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Senior Manager
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Marta bought several pencils. If each pencil was either a [#permalink]  16 Nov 2009, 20:52
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Marta bought several pencils. If each pencil was either a $0.23 pencil or a$0.21 pencil, how many $0.23 pencils did Marta buy? 1) Marta bought a total of 6 pencils 2) The total value of the pencils Marta bought was$1.30

OA will be posted in 24 hours
Manager
Joined: 13 Aug 2009
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Kudos [?]: 81 [0], given: 16

Re: Pencils [#permalink]  16 Nov 2009, 22:34
let x = number of $0.23 pencils let y = number of$0.21 pencils

Statement 1 gives us:
x+y=6
one equation, one unknown... INSUFFICIENT

Statement 2 gives us:
.23x+.21y=1.30
one equation, one unknown... INSUFFICIENT

Statements 1 and 2:
two equations, two unknowns... SUFFICIENT

Manager
Joined: 11 Sep 2009
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Kudos [?]: 218 [0], given: 6

Re: Pencils [#permalink]  17 Nov 2009, 01:31

Let's represent the number of $0.21 pencils bought as: m Let's represent the number of$0.23 pencils bought as: n

Statement 1: Marta bought a total of 6 pencils.

The combination of 6 pencils could be anything. Clearly, insufficient.

Statement 2: The total value of the pencils Marta bought was $1.30. This can be solved intuitively, but I'll show the process that I go through mentally: 0.21m + 0.23n = 1.30 0.21(m+n) + 0.02n = 1.30 n = [1.30 - 0.21(m+n)] / 0.02 Clearly, n must be less than m+n, but also greater than or equal to 0. Also, (m+n) must be an even number, otherwise n is not an integer. (m+n) = 2, n = 44 (NOT POSSIBLE) (m+n) = 4, n = 23 (NOT POSSIBLE) (m+n) = 6, n = 2 (OKAY) (m+n) = 8 n = -19 (NOT POSSIBLE) Therefore, sufficient. GMAT Instructor Joined: 24 Jun 2008 Posts: 978 Location: Toronto Followers: 281 Kudos [?]: 799 [0], given: 3 Re: Pencils [#permalink] 17 Nov 2009, 07:46 chicagocubsrule wrote: Marta bought several pencils. If each pencil was either a$0.23 pencil or a $0.21 pencil, how many$0.23 pencils did Marta buy?
1) Marta bought a total of 6 pencils
2) The total value of the pencils Marta bought was $1.30 OA will be posted in 24 hours You can also look at this as follows: if she bought 7 pencils, she would spend at least 7*0.21 =$1.49. If she bought 5 pencils, she would spend at most 5*0.23 = $1.15. So if she spent$1.30, as we learn from Statement 2 alone, she must have bought exactly 6 pencils. So Statement 2 is sufficient alone (once we know that she bought 6 pencils, there can only be one combination of $0.23 and$0.21 pencils that give a total cost of $1.30, since the more$0.23 pencils she buys, the greater the cost will be).
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Re: Pencils [#permalink]  17 Nov 2009, 08:07
Quote:
You can also look at this as follows: if she bought 7 pencils, she would spend at least 7*0.21 = $1.49. If she bought 5 pencils, she would spend at most 5*0.23 =$1.15. So if she spent $1.30, as we learn from Statement 2 alone, she must have bought exactly 6 pencils. So Statement 2 is sufficient alone (once we know that she bought 6 pencils, there can only be one combination of$0.23 and $0.21 pencils that give a total cost of$1.30, since the more \$0.23 pencils she buys, the greater the cost will be).

Good approach.
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Re: Pencils   [#permalink] 17 Nov 2009, 08:07
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