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

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.
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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.
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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.
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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.

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

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)

Answer B

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

Answer (B)

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