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# Sam spent a total of \$6.00 on pens and pencils. How many pen

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Intern
Joined: 09 Mar 2013
Posts: 10
Location: India
Sam spent a total of \$6.00 on pens and pencils. How many pen  [#permalink]

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Updated on: 01 May 2013, 02:52
2
6
00:00

Difficulty:

95% (hard)

Question Stats:

49% (02:23) correct 51% (02:04) wrong based on 266 sessions

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Sam spent a total of \$6.00 on pens and pencils. How many pens did he buy?

(1) The price of 2 pens was \$0.10 less than the price of 3 pencils
(2) The average price of 1 pen and 1 pencil was \$0.35

OA : E

But as per me its C. Can any one help.

Thanks
Rohan

Originally posted by rohanchowdhary on 01 May 2013, 01:59.
Last edited by Bunuel on 01 May 2013, 02:52, edited 2 times in total.
Renamed the topic and edited the question.
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Joined: 16 Dec 2011
Posts: 286
Re: Sam spent a total of \$6.00 on pens and pencils. How many pen  [#permalink]

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01 May 2013, 04:09
2
rohanchowdhary wrote:
Sam spent a total of \$6.00 on pens and pencils. How many pens did he buy?

(1) The price of 2 pens was \$0.10 less than the price of 3 pencils
(2) The average price of 1 pen and 1 pencil was \$0.35

Let's say unit price of pen and pencil are p and q respectively and number of pen and pencil are x and y respectively.
So, we have 4 unknown values and we know that px + qy = 6.00

1) Given that 2p + 0.1 = 3q. However, we cannot solve for 4 unknowns with 2 equations. Insufficient.

2) Given that (p + q) / 2 = 0.35 ==> p + q = 0.7 However, we cannot solve for 4 unknowns with 2 equations. Insufficient.

Together: From the equations 2p + 0.1 = 3q and p + q = 0.7, we get that p = 0.4 and q = 0.3.
Substituting these values into px + qy = 6.00, we get that 0.4x + 0.3y = 6.0
Now we can have different sets of values for x and y (e.g., 3 & 16; 6 & 12) which would satisfy the equation 0.4x + 0.3y = 6.0
Insufficient.

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Re: Sam spent a total of \$6.00 on pens and pencils. How many pen  [#permalink]

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07 May 2015, 16:05
Hi All,

This is an interesting DS question in that YOUR instinct will probably be to take an algebraic approach and assume that you know how many pencils and pens there are. However, there is NO INFORMATION about the number of either, there's just information about the PRICE of each.

Most Test Takers would quickly deduce that the two Facts are individually insufficient. Combining them will help you to figure out the PRICE of each pen and of each pencil (40 cents per pen and 30 cents per pencil), but you still do NOT know how many of each were purchased.

There are several different combinations of pens and pencils that will total \$6.00.

For example:
6 pens and 12 pencils
9 pens and 8 pencils
Etc.

Combined, INSUFFICIENT

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Re: Sam spent a total of \$6.00 on pens and pencils. How many pen  [#permalink]

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29 Aug 2017, 23:29
this is not too hard, since combination of 2 statements only yield the price of each item, it is not enough to find the number of pens or pencils.
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Re: Sam spent a total of \$6.00 on pens and pencils. How many pen  [#permalink]

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20 Dec 2018, 13:33
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Re: Sam spent a total of \$6.00 on pens and pencils. How many pen   [#permalink] 20 Dec 2018, 13:33
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