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# Marta bought several pencils. Each pencil was either 23

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Manager
Joined: 15 Jul 2008
Posts: 205
Marta bought several pencils. Each pencil was either 23 [#permalink]

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17 Aug 2008, 14:51
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Marta bought several pencils. Each pencil was either 23 cents or 21 cents. How many 23 cent pencils did Marta buy ?

1) Marta bought 6 pencils in all
2) Total value of pencils Marta bought was 130 cents.

OA = B

For this one, my work was very crude and shoddy. Am looking for an elegant and generalized approach.
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Joined: 30 Apr 2008
Posts: 1863
Location: Oklahoma City
Schools: Hard Knocks

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17 Aug 2008, 18:04
This is the type of question that you just have to start adding the numbers and trying difference combinations and see which ones work.
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17 Aug 2008, 20:07
statement 1 : obviously not suff

stetemet 2 : total number of pencils are not more than 6 ( 21 * 7 > 130 )

possible unit digits of 23 x = 3, 6, 9, 5, 8 when x = 1,2,3,4,5,6 respectively
possible unit digits of 21y = 1, 2, 3, 4, 5, 6 when y = 1,2,3,4,5,6 respectively

unit digit of 23x + 21y = 0, only possible with 6,4 combination ... (5,5) and (8,2) are not possible as x+y will be more than 6.

Suff... B
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Joined: 15 Jul 2008
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18 Aug 2008, 09:59
durgesh79 wrote:
statement 1 : obviously not suff

stetemet 2 : total number of pencils are not more than 6 ( 21 * 7 > 130 )

possible unit digits of 23 x = 3, 6, 9, 5, 8 when x = 1,2,3,4,5,6 respectively
possible unit digits of 21y = 1, 2, 3, 4, 5, 6 when y = 1,2,3,4,5,6 respectively

unit digit of 23x + 21y = 0, only possible with 6,4 combination ... (5,5) and (8,2) are not possible as x+y will be more than 6.

Suff... B

Thanks... this is exactly what i was looking for..
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Joined: 07 Nov 2007
Posts: 1789
Location: New York

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18 Aug 2008, 11:28
bhushangiri wrote:
Marta bought several pencils. Each pencil was either 23 cents or 21 cents. How many 23 cent pencils did Marta buy ?

1) Marta bought 6 pencils in all
2) Total value of pencils Marta bought was 130 cents.

OA = B

For this one, my work was very crude and shoddy. Am looking for an elegant and generalized approach.

total pencil cost =130 --> implies that all pencils are <7 . (130<21*7=147) and >5 (130> 23*5= 115)
so there are 6 pencils
Assume all pencils cost 21 then total cost 21*6=126.
difference between 23 and 21 =2
130-126=2*2

two 23 cent pencils and four 21 cent pencils.

B.
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Re: DS   [#permalink] 18 Aug 2008, 11:28
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