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# If 20 Swiss Francs is enough to buy 9 notebooks and 3

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Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]  15 Jul 2012, 04:50
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sayak636 wrote:
Bunuel... I have a doubt in regard to this question. Is it possible to add or subtract two equations, each with an inequality? Say, for example, if X + Y <= A and Z+ W<=B, then can we say that X-Z+Y-W<=A-B and X+Y+Z+W<=A+B?

If so, then S1 tells us that 7n+5p<=20 and we know that 3n+p<=20/3; if we subtract one from the other, we get 4n+4p<=40/3, or n +p<=10/3. Does this mean that S1 is sufficient?

Thanks.

OA for this question is B and it's correct.

As for your solution, notice that:

You can only add inequalities when their signs are in the same direction:

If a>b and c>d (signs in same direction: > and >) --> a+c>b+d.
Example: 3<4 and 2<5 --> 3+2<4+5.

You can only apply subtraction when their signs are in the opposite directions:

If a>b and c<d (signs in opposite direction: > and <) --> a-c>b-d (take the sign of the inequality you subtract from).
Example: 3<4 and 5>1 --> 3-5<4-1.

So, we can not subtract 3n+p<=20/3 from 7n+5p<=20 since the signs are in the same direction.

Hope it helps.
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Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]  21 Aug 2012, 04:41
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Guys...sorry for bothering but can anyone help me in understanding the bunuel's explanation.
I just don't understand that if we can replace 2 notebooks with 2 pencils, then why can't be substitute 3 notebooks with 3 pencils.
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Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]  12 Sep 2013, 14:37
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Re: Tricky Inequality [#permalink]  13 Sep 2013, 04:11
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Bunuel wrote:
Hussain15 wrote:
If 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils, is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils?

(1) 20 Swiss Francs is enough to buy 7 notebooks and 5 pencils.
(2) 20 Swiss Francs is enough to buy 4 notebooks and 8 pencils.

Given 9n+3p\leq20, question is 12n+12p\leq40 true? Or is 6n+6p\leq20 true? So basically we are asked whether we can substitute 3 notebooks with 3 pencils. Now if p<n we can easily substitute notebooks with pencils (equal number of notebooks with pencils ) and the sum will be lees than 20. But if p>n we won't know this for sure.

But imagine the situation when we are told that we can substitute 2 notebooks with 2 pencils. In both cases (p<n or p>n) it would mean that we can substitute 1 (less than 2) notebook with 1 pencil, but we won't be sure for 3 (more than 2).

(1) 7n+5p\leq20. We can substitute 2 notebooks with 2 pencils, but this not enough. Not sufficient.

(2) 4n+8p\leq20. We can substitute 5 notebooks with 5 pencils, so in any case (p<n or p>n) we can substitute 3 notebooks with 3 pencils. Sufficient.

Responding to a pm:

First of all, it is a tricky question. What makes it different from the run of the mill similar questions is the use of "is enough". Had the question said 9N and 3P cost 20 Swiss francs, life would have been much easier. Then your complain "I just don't understand that if we can replace 2 notebooks with 2 pencils, then why can't be substitute 3 notebooks with 3 pencils" would be totally justified.
The problem here is that we know that 9N and 3P cost less than or equal to 20 Swiss Francs.

So why does Bunuel say "We can substitute 2 notebooks with 2 pencils, but this not enough."? I can try to answer this question of yours using an example.

Say 1 N costs 1.5 SF and 1 P costs 1.85 SF
Then 9N and 3P cost 19.05 SF (which is less than 20 SF)

7N and 5P cost 19.75 SF. (So even though 1P costs more than 1N, 2P can substitute 2N because total cost is less than 20 SF. Obviously 1P can substitute 1N since there was enough leeway for even 2P in place of 2N)
But 6N and 6P cost 20.1 SF. (Now we see that 3P cannot substitute 3N. This time it crossed 20 SF)

I hope this answers why we can substitute 2P in place of 2N but not 3P in place of 3N.
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 16 Oct 2013 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink] 03 Nov 2013, 12:02 Hi, I am still having some problems with this question. If 20 SF can buy 9N and 3P, with statement 1 20 SF can buy 7N and 5P, it shows that we can switch 2N for 2P? So if we double it to 40SF then with 40SF we can buy 14N and 10P with statement 1, so why cant we still change 2N for 2P and get 40SF to buy 12N and 12P Math Expert Joined: 02 Sep 2009 Posts: 15224 Followers: 2565 Kudos [?]: 15885 [0], given: 1575 Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink] 03 Nov 2013, 12:04 Expert's post Allen122 wrote: Hi, I am still having some problems with this question. If 20 SF can buy 9N and 3P, with statement 1 20 SF can buy 7N and 5P, it shows that we can switch 2N for 2P? So if we double it to 40SF then with 40SF we can buy 14N and 10P with statement 1, so why cant we still change 2N for 2P and get 40SF to buy 12N and 12P Please read the whole discussion. For example, check here: if-20-swiss-francs-is-enough-to-buy-9-notebooks-and-89226-40.html#p1266613 _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 3781 Location: Pune, India Followers: 813 Kudos [?]: 3244 [1] , given: 138 Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink] 06 Nov 2013, 20:08 1 This post received KUDOS Expert's post Allen122 wrote: Hi, I am still having some problems with this question. If 20 SF can buy 9N and 3P, with statement 1 20 SF can buy 7N and 5P, it shows that we can switch 2N for 2P? So if we double it to 40SF then with 40SF we can buy 14N and 10P with statement 1, so why cant we still change 2N for 2P and get 40SF to buy 12N and 12P Yes, the word 'enough' makes it a challenging question. Check out the detailed discussion of this concept here: http://www.veritasprep.com/blog/2013/09 ... -of-words/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]  26 Nov 2013, 05:26
VeritasPrepKarishma wrote:
Allen122 wrote:
Hi, I am still having some problems with this question.

If 20 SF can buy 9N and 3P, with statement 1 20 SF can buy 7N and 5P, it shows that we can switch 2N for 2P?

So if we double it to 40SF then with 40SF we can buy 14N and 10P with statement 1, so why cant we still change 2N for 2P and get 40SF to buy 12N and 12P

Yes, the word 'enough' makes it a challenging question. Check out the detailed discussion of this concept here: http://www.veritasprep.com/blog/2013/09 ... -of-words/

THANK YOU!

This is the best explanation I have seen so far!

Thks!
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Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3   [#permalink] 26 Nov 2013, 05:26
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