If a, b, c are three numbers on the number line shown above , is c between a and b.

Probably the best way to solve this problem is to pick some smart numbers. Notice that from the diagram we have that \(a<b\).

(1) b <0. Clearly insufficient since we know nothing about c.

(2) a-b>c. If \(a=-10\) and \(b=-1\), then \(-10-(-1)=-9>c\). Now, is \(c=-9.5\), then the answer is YES but if \(c=-100\), then the answer is NO. Not sufficient.

(1)+(2) Example from (2) is still valid, so even when we consider the two statements together we cannot answer the question. Not sufficient.

Answer: E.
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For (1) and (2):
From (2), we know that \(0>a-b>c\) and from (1) that \(b<0.\)
Place \(a,b\) and \(a-b\) on the number line (see the attached drawing).
You can see that \(c\) can be between \(a\) and \(a-b\) (which means that \(c\) is between \(a\) and \(b\)) or on the left of \(a\) (meaning \(c\) is not between and \(b\)).
Not sufficient.

Answer E.

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Bunuel I also interpret that from diagram a<b but in the official explanation they took a=0 and b =-2 isnt it strange?

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Hi Gurpreet, in your screenshot I dont see the line segment where points 'A' and 'B' are marked like in the original question. In the original question the line segment is given with the points positioned in it. So that makes a difference. These questions are similar, not identical.

I have not posted the real question. I have just posted the explanation. And the question is exactly same.
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Taking into consideration the diagram in the question, it's not strange it's just wrong.
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Answer is E.

Any tips on how to pick smart numbers for this question?

I have a question here if I may

Should we assume that a,b are given in order, that is as shown in the number line? I understood that one should trust the order of points shown either on number lines or graphs according to GMAT

Please confirm
Thanks!
Cheers
J

Yes, from the diagram we can derive that a<b.
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I did it this way

Note: One can trust the relative position of graphs/lines in DS as per OG.

Statement 1:

b<0. Clearly Insufficient

Statement 2:

a-b>c --> a>b+c

Insufficient again

Both (1) and (2) together

Let's pick some numbers.

Since b<0 and b>a, then let's say a=-2 and b=-1

Now then replacing we have that c<-1.
Thus 'c' could be either between 'a' and 'b' or to the left of 'a'

Answer: E

Hope it helps
Cheers!
J

From the OA, I would say that we cant... look at the examples in (2). a > b

Answer ExplanationClose
Determine if c lies between a and b on the number line.

(1) It is given that b < 0, but nothing is known about a and c; NOT sufficient.
(2) Given that a – b > c, it is possible that c lies between a and b (for example, a = 0, b = –2, and c = –1) and it is possible that c does not lie between a and b (for example, a = 0, b = –2, and c = 1); NOT sufficient.

Given (1) and (2) together, the examples given in (2) above show that both statements together are NOT sufficient to determine if c lies between a and b.

The correct answer is E;
both statements together are still not sufficient.
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Bunuel, if I consider a<b (as mentioned in the number line), then the value of c is always coming out to be < a, ie. on the far left, can u pls give some numbers that negate this?

If \(a=-10\) and \(b=-1\), then \(-10-(-1)=-9>c\). Now, is \(c=-9.5\), then the answer is YES but if \(c=-100\), then the answer is NO.
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(1) and (2) by itself are clearly insufficient.

(1&2)

\(b < 0\)
\(c < a - b < 0\)

Since we know \(a < b\), c may be between \(a and b\) or \(c < a\). We're never told anything about c aside from the fact that it's less than \(a - b\). INSUFFICIENT.

Answer is E.
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While the answer is E, just wanted to add that c can actually be on the right of b as well- i.e.

If \(a-b>\) c AND \(b > a\)

Then we can have 3 cases:

1. c lies between a and b, i.e. \(a <c <b\). Sample numbers a = -2, c = -1.5 , b = -1.
2. c lies on the left of a, i.e. \(c< a< b \). Sample numbers c = -3, a = -2, b = -1
3. c lies on the right of b, i.e. \(a < b < c\). Sample numbers a = -3, b = -2.5 , c = -1

Not sure why no other answer had mentioned the 3rd case

Q. Stem: Is c between a and b?

St(1) b < 0:

No information on c is provided. Insufficient. Eliminate A and D.

St(a - b > c:

If a=-5 and b=-1 then a-b = -4 and should be greater than c.

If c= -4.1 then it is less than -4 and is b/w a and b and hence the answer to Q.Stem is Yes.

If c= -5.1 then it is not less than -4 and is not b/w a and b and hence the answer to Q.Stem is No.

We have contradicting answers. Insufficient. Eliminate B.

Combining 1 & 2,
b = -1 and the inputs of St(2) here will provide the same result.

Insufficient. Eliminate C.

(option c)

Takeaway: Use data that can be recycled on GMAT, so that you need not create new data points for checking every answer choice.


D.S
GMAT SME


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