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27 Jun 2010, 01:33
1
3
00:00

Difficulty:

85% (hard)

Question Stats:

33% (00:56) correct 67% (01:41) wrong based on 33 sessions

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The cost of 22 CDs, 25 pens & 7 erasers is $142. What is the cost of 1 CD, 1 pen & 1 eraser? (1) The cost of 7 CDs & 6 erasers is$ 23.
(2) The cost of 5 CDs & 6 pens is $31. Intern Joined: 19 Feb 2010 Posts: 5 Re: The cost of 22 CDs, 25 pens & 7 erasers is$ 142. What is the cost of [#permalink]

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27 Jun 2010, 05:37
mikioso wrote:

please analyse the question carefully..... I have put it under 700+ level questions...
SVP
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1869
Concentration: General Management, Nonprofit
Re: The cost of 22 CDs, 25 pens & 7 erasers is $142. What is the cost of [#permalink] ### Show Tags 27 Jun 2010, 14:35 The answer is C. Given in question: $$22x + 25y + 7z = 142$$ Asked to find: $$x+y+z$$ Statement 1: $$7x+6z = 23$$ Clearly this is insufficient. There are many values of x and y which can satisfy this equation. So we are down to B C or E for answer choices Statement 2: $$5x+6y = 31$$ This is also insufficient by itself. So now putting both together and using initial equation from question. $$22x + 25y + 7z = 142$$ $$7x+6z = 23$$ $$5x+6y = 31$$ Three equations and three variables. Solvable. Hence the answer is C. apex1umt wrote: Question: The cost of 22 CDs, 25 pens & 7 erasers is$ 142. What is the cost of 1 CD, 1 pen & 1 eraser?

1. The cost of 7 CDs & 6 erasers is $23. 2. The cost of 5 CDs & 6 pens is$ 31.
Intern
Joined: 19 Feb 2010
Posts: 5

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28 Jun 2010, 20:32
1
5c + 6p =31
so 15c+ 18p=93..(1)
22c+25p+7e=142..(2)
(2)-(1)
7c+7p+7e=49
c+p+e=7
Manager
Joined: 05 Jul 2008
Posts: 132
GMAT 2: 740 Q51 V38
Re: The cost of 22 CDs, 25 pens & 7 erasers is $142. What is the cost of [#permalink] ### Show Tags 30 Jun 2010, 23:13 3 apex1umt wrote: Question: The cost of 22 CDs, 25 pens & 7 erasers is$ 142. What is the cost of 1 CD, 1 pen & 1 eraser?

1. The cost of 7 CDs & 6 erasers is $23. 2. The cost of 5 CDs & 6 pens is$ 31.

Verry tricky. It must be B
22C + 25P+7E= 7(C+P+E)+ 15C+18P= 7(C+P+E)+3(5C+6P)=7(C+P+E)+ 93
SO C+P+E= 7

22C + 25P+7E= 25(C+P+E)-3C-18E=25(C+P+E)-3(C+6E) INSUF
I need 3 more Kudos, Kudo me if OA is B
Manager
Joined: 16 Jun 2010
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01 Jul 2010, 06:24
Good solution David Archuleta. I looked for tricks to manipulate, but completely forgot that I could commonly factorize the 7 from this equation. Good job, +1 from me.

Devashish: I think only practice can help you solve the equations. I think the easiest way to start practicing for these problems is to get the given equation in terms of what you want. In this case:

You want $$x+y+z$$ and you're given $$22x+25y+7z$$ The only way you can split this into something of the form $$a(x+y+z)$$ is by taking the 7 out common and breaking it down as suggested.

I'm afraid there's no real shortcut guarantee to getting this type of problem, only practice helps.
Manager
Joined: 05 Jul 2008
Posts: 132
GMAT 2: 740 Q51 V38

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01 Jul 2010, 11:04
@David: Thanks a very obvious point, and still missed all the time.
@whiplash2411: Thanks, it makes sense and should be the starting point the next time I start solving a 3-variable equation.
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Please give me kudos, if you like the above post.
Thanks.

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Joined: 21 Jun 2010
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27 Jul 2010, 05:48
If x, y, and z respectively the unit price of CD, pen, and eraser, we have: 22x+25y+7z=142$We would like to know the price of 1CD, 1 pen, and 1 eraser, in other words x+y+z ? The first equation can be written as 7*(x+y+z)+(15x+18y)=142$
So if we know how much 15x+18y is, the question can be answered.

On the other hand, statement 2 give us 5x+6y=31, or 15x+18y=93.
Therefore statement 2 is sufficient.
_________________

Hardworkingly, you like my post, so kudos me.

Senior Manager
Joined: 25 Feb 2010
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28 Jul 2010, 02:20
Hi.. Guys... I think you have got the exact funda of the question.........

Moreover I am recently done with my GMAT and have scored a 710 with 51 (Quant) & 34(verbal) and 5 in AWA...
Though 34 seems or rather is low, but I have no more patience to give the exam again.... I would rather better the profile then appear again..

Best of luck to you guys....
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Re: The cost of 22 CDs, 25 pens & 7 erasers is $142. What is the cost of [#permalink] ### Show Tags 20 Sep 2017, 06:04 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: The cost of 22 CDs, 25 pens & 7 erasers is$ 142. What is the cost of   [#permalink] 20 Sep 2017, 06:04
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