Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1243
Concentration: Strategy, General Management

If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
15 Jan 2010, 10:01
Question Stats:
21% (01:43) correct 79% (02:29) wrong based on 1841 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Aug 2009
Posts: 5938

If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
15 Jan 2010, 10:45
B.... stem tells us 20>9n+3p... or 40>18n+6p...(i) we are asked is 40>12n+12p?.. (ii) So it is asked " Can we replace (1812) or 6 notebooks with 126 or 6 pencils. Logically.. In every equation we have 20 Swiss franc buying 12 items, with different combinations of notebooks and pencils Initial equation gives more notebooks and lesser pencils, but the Q asks if 6 of each can be purchased in 20 Swiss franc. 1) 20>7n+5p In Original equation 20>=9n+3p and 20>=7n+5p, number of notebooks is more than number of pencils. So n<p or n>p.. LOGICALLY in both cases number of notebooks is MORE than number of pencils insuff 2). 20>4n+8p from stem number of notebooks could be more and this eq tells us that pencils can be MORE.. so, we can say that any type of combinations of 12 items from 4 to 8 ( 48, 57,66,75,84) is possible Hence 6 each is possible suff B
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
GMAT online Tutor



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: Tricky Inequality [#permalink]
Show Tags
15 Jan 2010, 15:06
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. Answer: B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Status: The last round
Joined: 18 Jun 2009
Posts: 1243
Concentration: Strategy, General Management

Re: Tricky Inequality [#permalink]
Show Tags
15 Jan 2010, 21:51
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. Answer: B. Thanks Bunuel!! OA is "B" Kudos!! Just wanna know that you solved this problem conceptually and no algebric approach is used. How did you know that this will be done without using algebra.
_________________
[ From 470 to 680My Story ] [ My Last Month Before Test ] [ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: Tricky Inequality [#permalink]
Show Tags
17 Jan 2010, 02:09



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345

Re: Tricky Inequality [#permalink]
Show Tags
30 Jan 2010, 15:27
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. I like Bunuel's approach above. One can also do: S1: Say notebooks are free, and pencils cost $4 each. Then the answer is 'no'. On the other hand, if pencils and notebooks are both free, the answer is 'yes'. Not sufficient. S2: * From the stem, we can buy 3 notebooks and 1 pencil for < 20/3 francs. * From S2 we can buy 2 notebooks and 4 pencils for < 10 francs. * Adding, we can buy 5 notebooks and 5 pencils for < 50/3 francs. * Thus, we can buy 12 notebooks and 12 pencils for < (12/5)(50/3) = 40 francs. The answer is B.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Manager
Status: Prepping for the last time....
Joined: 28 May 2010
Posts: 153
Location: Australia
Concentration: Technology, Strategy
GPA: 3.2

Re: Tricky Inequality [#permalink]
Show Tags
04 Sep 2011, 21:40
Well, I tried in a different way and got B. from stem and 1 9n+3p <=20 and 7n+5p <=20 => 16n+8p <=40 => 2n+p <=5 From this, we can get values for n,p (1,2) (1,3) and (2,1) Subsituting these values in required inequality 12n+12p<=40 we can see that (1,3) does not satisfy the inequality. So A is insufficient Coming to B, 9n+3p<=20 and 4n+8p<=20 which imply that 13n+11p <=40 possible values for n and p are (1,2) and (2,1) Substituting these values in 12n+12p<=40, both the values satisfy the inequality..hence B is sufficient.
_________________
Two great challenges: 1. Guts to Fail and 2. Fear to Succeed



Intern
Joined: 14 May 2011
Posts: 9

Re: Tricky Inequality [#permalink]
Show Tags
04 Sep 2011, 22:30
Hi,
I solved using the below method.
statement from the stem is 20>= 9(n) + 3(p)
The greatest value of n is 2.2 with p being very small. the greatest value of p is 6.33 with n being very small. If n = 2.2 and p is small then $40 is enough to purchase 12 notes and 12 pencils.However if p = 6 then the pencils alone will cost $72 and $40 will not be enough.
Statement 1 : 20>= 7n + 5p
Look at the greatest values for n and p again (keeping in mind the statements caps them at 2.2 and 6.3 respectively) N could be 2.8 in statement 1 but the cap is 2.2 by the original stem. p could be 3.9 from this statement. As stated above $40 will be enough when n = 2.2 and now check p= 3.9 to see that 12(3.9) is already over $40  since you can get two answers this is insufficient.
Statement 2 says 20>= 4n + 8p
using the same logic  the greatest n = 2.2 (from the stem) but the greatest p can only be 2.5.
when n=2.2, $40(2.2 * 12 )will be enough.When p = 2.5,$40 (2.5 * 12) will be enough again.
Though I solved it.I'm interested in understanding bunuel's conceptual way to solve the problem.Can some one please elaborate bunuel's method.



Board of Directors
Joined: 01 Sep 2010
Posts: 3424

Re: Tricky Inequality [#permalink]
Show Tags
29 Feb 2012, 09:50
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. Answer: B. After what you said all is clear but to figure out this tough question alone with your pencil in two minutes or less is quite difficult. I think as usual you have a really amazing approach , really flexible. Basically we have to cover the difference between 9n and 6n = 3 AND 6p and 3p = 31) 9n  7n = 2 and 5p  3 p = 2 2) 9n  4n = 5 AND 8p  3p = 5 B it is. I hope this kind of approach is not prone of errors but seems clear.
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Manager
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 96
Concentration: Strategy, General Management
GPA: 3.6
WE: Consulting (Computer Software)

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
01 Mar 2012, 00:08
Hi Buneul, Quote: 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. For the second statement 9n+3P<=20 and 4n+8p<=20. if i solve these two inequaities i get n<=1. N cant be negative or zero so n=1 with n=1 i can p<=11/3 p=1,2,3 and n1 this stmt wud be insufficient then?



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
01 Mar 2012, 00:21
shankar245 wrote: Hi Buneul, Quote: 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. For the second statement 9n+3P<=20 and 4n+8p<=20. if i solve these two inequaities i get n<=1. N cant be negative or zero so n=1 with n=1 i can p<=11/3 p=1,2,3 and n1 this stmt wud be insufficient then? Please notice the following: 1. OA is B; 2. n and p can be zero, why not? We can have charity shop which gives either notebooks or pencils (or both) for free; 3. Values of n and p (prices of 1 notebook and 1 pencil respectively) are not necessary to be integers. Reconsider your solution according to above. Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 01 Jan 2011
Posts: 20
Location: Kansas, USA
Schools: INSEAD, Wharton

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
14 Jul 2012, 23:36
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 XZ+YW<=AB 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.



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
15 Jul 2012, 05:50
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 XZ+YW<=AB 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 \(<\)) > \(ac>bd\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). So, we can not subtract 3n+p<=20/3 from 7n+5p<=20 since the signs are in the same direction. Hope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: Tricky Inequality [#permalink]
Show Tags
13 Sep 2013, 05:11
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. Answer: B. 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.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 15 Sep 2013
Posts: 1
Concentration: Statistics, Entrepreneurship
GPA: 3.06
WE: Business Development (Other)

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
16 Feb 2014, 16:57
He is my solution which I find more formal.
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.
What we have: (A) 20 ≥ 9n+3p → 20 ≥ 3(n+p) + 6n
What we need to prove is: (B) 40 ≥ 12n+12p → 40/12 ≥ n+p → n+p ≤ 10/3
Let's see the first statements: (1) 20 ≥ 7n+5p → 20 ≥ 5(n+p)+2n we can not combine (1) with (A) to prove or disprove (B) Unsufficient
The second statement is: (2) 20 ≥ 4n+8p → 20 ≥ 4(n+p)+4p Let's combine it with (A) so we can find the solution: 20 ≥ 3(n+p)+6n x 2 20 ≥ 4(n+p)+4p x 3 → 40 ≥ 6(n+p)+12n + 60 ≥ 12(n+p)+12p = 100 ≥ 18(n+p)+12p+12n → 100 ≥ 30(n+p) → n+p ≤ 10/3 Which is exactly what we need to prove (B). (2) is Sufficient.
So the answer is B.



Intern
Joined: 07 Mar 2014
Posts: 1
Concentration: Finance, Marketing

Re: Tricky Inequality [#permalink]
Show Tags
13 Mar 2014, 05:42
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.  From given equation 9n + 3p < 20 i.e 3n + 1p < 20/3  eq 1 (1) 7n + 5p < 20  eq 2 Subtracting eq 1 from eq 2, we get 4n+4p < 40/3 i.e 12n+12p < 40 (multiplying through out by 3). SUFFICIENT. (2) 4n + 8p < 20 i.e 2n + 4p < 10  eq 3 Adding eq 1 with eq 3, we get, 5n +5p < 50/3 i.e 12n + 12p < 40 (multiplying through out by 12/5). SUFFICIENT. Ans : D Kindly clarify if the approach is correct



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: Tricky Inequality [#permalink]
Show Tags
13 Mar 2014, 06:16
kuttu88 wrote: 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.  From given equation 9n + 3p < 20 i.e 3n + 1p < 20/3  eq 1 (1) 7n + 5p < 20  eq 2 Subtracting eq 1 from eq 2, we get 4n+4p < 40/3 i.e 12n+12p < 40 (multiplying through out by 3). SUFFICIENT. (2) 4n + 8p < 20 i.e 2n + 4p < 10  eq 3 Adding eq 1 with eq 3, we get, 5n +5p < 50/3 i.e 12n + 12p < 40 (multiplying through out by 12/5). SUFFICIENT. Ans : D Kindly clarify if the approach is correct Actually it isn't. The correct answer is (B). You cannot subtract inequalities like this. e.g. 2 < 8 ... (I) 3 < 15 ...(II) (I)  (II) 1 < 7 not true The best is to only add inequalities when they have the same inequality sign. To see how to solve this question, check: http://www.veritasprep.com/blog/2013/09 ... ofwords/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 16 Feb 2014
Posts: 20

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
13 Apr 2014, 22:24
Why should an inequality approach has to be followed for this qn?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
13 Apr 2014, 23:57
krishna789 wrote: Why should an inequality approach has to be followed for this qn? Because the question says that "20 Swiss Francs is enough to buy 9 notebooks and 3 pencils" This means that 9 notebooks and 3 pencils may cost anything less than or equal to 20 SF. They could cost 18 SF, 10 SF or 20 SF etc. Hence you need to use inequalities. Check out the link I gave above. On that, I have discussed how this question is different from other questions in which we make equations.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 28 May 2014
Posts: 57

Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3 [#permalink]
Show Tags
01 Aug 2014, 10:20
Bunuel,
Doesn't " 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils" come down to 9n + 3p =20? Why are we taking the equation as 9n+3P <= 20 ? Please explain. Thanks




Re: If 20 Swiss Francs is enough to buy 9 notebooks and 3
[#permalink]
01 Aug 2014, 10:20



Go to page
1 2
Next
[ 28 posts ]



