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# Data Sufficiency Pack 2, Question 4) On a number line...

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EMPOWERgmat Instructor
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Data Sufficiency Pack 2, Question 4) On a number line...  [#permalink]

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01 Nov 2015, 16:40
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Difficulty:

55% (hard)

Question Stats:

59% (01:47) correct 41% (01:42) wrong based on 140 sessions

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QUANT 4-PACK SERIES Data Sufficiency Pack 2 Question 4 On a number line...

On a number line (not shown), the points a, b and c are placed in order (from left to right). Is the product of a and b less than the product of b and c?

(1) c is to the right of 0.
(2) The product of b and c is not positive

48 Hour Window Answer & Explanation Window
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** CEO Joined: 20 Mar 2014 Posts: 2635 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 01 Nov 2015, 17:33 2 2 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Data Sufficiency Pack 2 Question 4 On a number line... On a number line (not shown), the points a, b and c are placed in order (from left to right). Is the product of a and b less than the product of b and c? (1) c is to the right of 0. (2) The product of b and c is not positive 48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4-Pack series Scroll Down For Official Explanation Good question +1 Question mentions that a,b,c are arranged in this order ---> a<b<c. We need to know whether ab<bc? Per statement 1, c is to the right of 0 ---> Clearly not sufficient. Consider 2 cases: a<0, b<0 and c>0 --> "no" a<0, b>0 and c>0 --> maybe. Per statement 2, bc $$\neq$$ positive quantity ---> 2 cases, either bc = 0 or bc<0 For case bc= 0 --> possible cases are: a<0, b=0 , c>0 ---> "no" for is ab<bc a<0, b<0 , c=0 ---> "no" for is ab<bc For case bc<0 --> possible case is: a<0, b<0, c>0 (you can not have b>0 and c<0) ---> "no" for is ab<bc Thus statement 2 is sufficient. B is the correct answer. Intern Joined: 10 Oct 2012 Posts: 25 Re: Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 01 Nov 2015, 17:46 1 very good question and I will provide my solution the question states that a b and c are in that order in the number line and so the question asks us whether a*b>b*c so now we could do this using a diagram with the number line and ploting, pluging numbers for different scenarios or well by using logic. I went by using a bit mix of both. here it goes. Statement 1 says that C>0 or well c is positive. This is insufficient because we know nothing about a and b and about the relative distances with respect to each one and to 0 ---------------------------------------- 0 -------------------------- a____ b___c; or a__b___________c this showing relative distances and asuming all are right to 0 additionally a also could be negative or b could be negative or even 0 thereby giving us different solutions. Statement 2 is more subtle but again inufficient and we can prove this through counter example ------------------------ 0 a b c ------------------------ 0 a b c ------------------------ 0 a b c These diagrams tell us that the product of b and c is not positive, meaning it could be negative or EVEN ZERO and above all we know nothing about a with respect to b. If c is 0 then a and b are negative and thus their prduct be greater than that of b and c but if B is 0 then the product is the same COMBINING BOTH STATEMENTS STILL ARE INSSUFICIENT AND THUS ANSWER IS E Using the same scenarios described before, we can have a * b = b * c if b is 0 or a * b > b * c if b is negative. Hope you like my explanation Please send some kudos CEO Joined: 20 Mar 2014 Posts: 2635 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Re: Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 01 Nov 2015, 17:51 mmelendez wrote: very good question and I will provide my solution the question states that a b and c are in that order in the number line and so the question asks us whether a*b>b*c so now we could do this using a diagram with the number line and ploting, pluging numbers for different scenarios or well by using logic. I went by using a bit mix of both. here it goes. Statement 1 says that C>0 or well c is positive. This is insufficient because we know nothing about a and b and about the relative distances with respect to each one and to 0 ---------------------------------------- 0 -------------------------- a____ b___c; or a__b___________c this showing relative distances and asuming all are right to 0 additionally a also could be negative or b could be negative or even 0 thereby giving us different solutions. Statement 2 is more subtle but again inufficient and we can prove this through counter example ------------------------ 0 a b c ------------------------ 0 a b c ------------------------ 0 a b c These diagrams tell us that the product of b and c is not positive, meaning it could be negative or EVEN ZERO and above all we know nothing about a with respect to b. If c is 0 then a and b are negative and thus their prduct be greater than that of b and c but if B is 0 then the product is the same COMBINING BOTH STATEMENTS STILL ARE INSSUFICIENT AND THUS ANSWER IS E Using the same scenarios described before, we can have a * b = b * c if b is 0 or a * b > b * c if b is negative. Hope you like my explanation Please send some kudos Your interpretation of statement 2 is not correct. You are given that the sequence is a,b,c (left to right) ---> a<b no matter what. The 3 cases above that you have mentioned for statement 2 will all give a "no" to "is ab<bc" making statement 2 sufficient. Intern Joined: 10 Oct 2012 Posts: 25 Re: Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 01 Nov 2015, 18:05 1 Engr2012 Math Forum Moderator You are actually wrong!!! ------A-----B------0-----C--------- You forgot the second scenario where B equals 0 . If B=O THEN A*B is the same as B*C.. ------A-----B=0------C the fact that a product is not positive means that the product can be negative or equal to 0 Hope this clarifies very well!! Kudos CEO Joined: 20 Mar 2014 Posts: 2635 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 01 Nov 2015, 18:09 2 mmelendez wrote: Engr2012 Math Forum Moderator You are actually wrong!!! ------A-----B------0-----C--------- You forgot the second scenario where B equals 0 . If B=O THEN A*B is the same as B*C.. ------A-----B=0------C the fact that a product is not positive means that the product can be negative or equal to 0 Hope this clarifies very well!! Kudos You are not understanding what the question actually asks. "Is ab<bc"is what is getting asked. Any scenario that gives you ab= bc will be a "no" to the question asked. All the 3 scenarios that you mention for statement 2 do give you 1 answer of "no" and that is all you need to determine that this statement is sufficient. I'm not denying your interpretation of bc is not positive. But you are not answering the questions getting asked. Hope this clears the confusion. Manager Joined: 26 Nov 2014 Posts: 94 Re: Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 02 Nov 2015, 12:34 1 The points a, b and c are placed in order (from left to right), so a<b<c. Is ab<bc? St 1: c is to the right of 0. So C is positive. a<0 and b can be negative or positive. If a=-1, b=1, c=2, ab<bc. Yes. If a=-2, b=-1, c=1, ab<bc. No. St 2: The product of b and c is not positive. $$bc\leq{0}$$. both of them can't be positive or negative together. if b=-1, c=1, bc=-1, consider a=-2. so ab<bc. No if b=0, c=1, bc=0, consider a=-1, so ab<bc. No This is sufficient. Ans B. _________________ Consider Kudos for my post, if it is helpful. TIA EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12857 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Data Sufficiency Pack 2, Question 4) On a number line... [#permalink] ### Show Tags 03 Nov 2015, 22:01 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Data Sufficiency Pack 2 Question 4 On a number line... On a number line (not shown), the points a, b and c are placed in order (from left to right). Is the product of a and b less than the product of b and c? (1) c is to the right of 0. (2) The product of b and c is not positive 48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4-Pack series Scroll Down For Official Explanation Hi All, This DS question can be solved with a variety of different approachess, including TESTing VALUES, drawing pictures or using Number Properties. TESTing VALUES will offer the most immediate evidence for the correct answer, so I'll approach this prompt in that way. To start, we're told that the variables A, B and C appear on a number line IN THAT ORDER. By extension, that means A < B < C. We're asked if (A)(B) < (B)(C). This is a YES/NO question. (1) C is to the right of 0. This Fact tells us that C is POSITIVE, but we don't know anything about the values of A and B. IF.... C = 2 B = 1 A = 0 Then (0)(1) IS < (1)(2) and the answer to the question is YES. IF.... C = 2 B = 0 A = -1 Then (-1)(0) is NOT < (0)(2) and the answer to the question is NO. Fact 1 is INSUFFICIENT (2) The product of B and C is NOT positive IF (B)(C) is NOT positive, then it's either 0 or it's NEGATIVE. We'll have to work through several possibilities to properly assess Fact 2: To start, let's look at the two possibilities that involve a 0.... IF.... C = 2 B = 0 A = -1 Then (-1)(0) is NOT < (0)(2) and the answer to the question is NO. IF.... C = 0 B = -1 A = -2 Then (-2)(-1) is NOT < (-1)(0) and the answer to the question is NO. Next, we'll look at the possibility of a NEGATIVE product. Here, C would have to be positive and B would have to be negative. By extension, A would ALSO have to be negative. IF.... C = 2 B = -1 A = -2 Then (-1)(-2) is NOT < (-1)(2) and the answer to the question is NO. In ALL possible scenarios, the answer to the question is NO. Fact 2 is SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Data Sufficiency Pack 2, Question 4) On a number line...  [#permalink]

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11 Nov 2015, 06:28
My approach: ab<bc only when b > 0

1) c > 0, nothing about b --->insufficient

2) bc is not positive
--> bc = 0 --> either b = 0 (no) or c = 0 so b < 0 (no)
or bc < 0 --> b <0 (no)

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Re: Data Sufficiency Pack 2, Question 4) On a number line...  [#permalink]

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23 Dec 2017, 07:37
given : a < b < c
question : ab < bc ?
=> ab - bc < 0 ?
=> b(a - c) < 0 ?
=> case 1: b < 0 and a > c ? or case 2: b > 0 and a < c ?
if we observe, case 1 is not valid, as given a < c
so question is : b > 0 && a < c ?

Statement 1: c is to right of zero
no idea about b > 0 and a < 0 => insufficient

Statement 2 : bc <= 0
=> also since b < c, if bc <= 0, then b < 0 && c >= 0 => sufficient to answer question b > 0 && a < c ? as NO

Re: Data Sufficiency Pack 2, Question 4) On a number line... &nbs [#permalink] 23 Dec 2017, 07:37
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