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# On the number line shown, is zero between 'a' and 'c'?

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On the number line shown, is zero between 'a' and 'c'?  [#permalink]

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20 May 2018, 06:16
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Difficulty:

95% (hard)

Question Stats:

26% (02:19) correct 74% (02:03) wrong based on 86 sessions

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On the number line shown, is zero between 'a' and 'c'?

(1) The distance of 'a' from zero is greater than the distance of 'c' from zero.
(2) The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.

Source: ExpertsGlobal

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Re: On the number line shown, is zero between 'a' and 'c'?  [#permalink]

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21 May 2018, 06:54
1
seed wrote:
Attachment:
Question.JPG

On the number line shown, is zero between 'a' and 'c'?

(1) The distance of 'a' from zero is greater than the distance of 'c' from zero.
(2) The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.

Source: ExpertsGlobal

If we can establish that 'a' and 'c' are of opposite signs, the answer is Yes. Alternatively, if we can establish that 'a' and 'c' are of the same sign, the answer is No. In either case, the data is sufficient. If we cannot establish either, the data is not sufficient. The question stem has drawn the number line. So, a < b < c.

Statement 1: The distance of 'a' from zero is greater than the distance of 'c' from zero.
Example: a = -4, c = -1. The distance of 'a' from zero is greater than the distance of 'c' from zero. Zero is not in between 'a' and 'c'.
Counter example: a = -2, c = 1. The distance of 'a' from zero is greater than the distance of 'c' from zero. Zero is in between 'a' and 'c'.

Statement 1 alone is not sufficient.

Statement 2: The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.
Example: a = -5, c = -1 and b = -3. a < b < c. |a - c| = 4. |(-b) - c| = 4. Zero does not lie between 'a' and 'c'. (In all such cases, c will be the arithmetic mean of 'a' and '-b')
Counter example: a = -1, b = 1, c = 2. a < b < c. |a - c| = 3. |(-b) - c| = 3. Zero lies between 'a' and 'c'. (In all such cases, a = -b.)

Statement 2 alone is not sufficient.

Statements together: The distance of 'a' from zero is greater than the distance of 'c' from zero and The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'
Example: a = -5, c = -1 and b = -3. a < b < c. Satisfies condition in both statements. Zero does not lie between 'a' and 'c'.
Counter example: 'a' has to be negative. 'c' has to be positive.
If a is negative and c is positive and if |a - c| = |(-b) - c| then it is possible only when a = -b.
That is 'a' and 'b' have the same magnitude but are of opposite signs. So, |a - 0| = |b - 0|. And if b < c as given in the number line, |a - 0| will not be greater than |c - 0|. It is not possible to find a counter example.
a = -1, b = 1, c = 2 clearly shows that distance between -1 and 0 is not greater than 2 and 0.

The counter example is not possible when we combine the two statements.
We can conclude that zero does not lie between 'a' and 'c'.

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Re: On the number line shown, is zero between 'a' and 'c'?  [#permalink]

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01 Sep 2018, 02:06
seed wrote:
Attachment:
Question.JPG

On the number line shown, is zero between 'a' and 'c'?

(1) The distance of 'a' from zero is greater than the distance of 'c' from zero.
(2) The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.

Source: ExpertsGlobal

The solution provided in the thread is good, and I find it doable till 2 equations that is for options 'A' and 'B'...from 'C' onward it got difficult, I mean during actual exam its difficult to find the numbers to fit in YES/NO both situations.
Kindly help to solve the question in an easier and more doable method.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9446
Location: Pune, India
Re: On the number line shown, is zero between 'a' and 'c'?  [#permalink]

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02 Sep 2018, 01:56
3
seed wrote:
Attachment:
Question.JPG

On the number line shown, is zero between 'a' and 'c'?

(1) The distance of 'a' from zero is greater than the distance of 'c' from zero.
(2) The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.

Source: ExpertsGlobal

---------- a ---------------------------------- b ----------- c ---------

On the number line shown, is zero between 'a' and 'c'?

(1) The distance of 'a' from zero is greater than the distance of 'c' from zero.

We can have 0 at 3 different places relative to 'a' and 'c'.

Case 1: -----0----- a ---------------------------------- b ----------- c ---------
Case 2: ---------- a ---------------------0------------- b ----------- c ---------
Case 3: ---------- a ---------------------------------- b ----------- c -----0----

But the first case is not possible since then a would be definitely closer to 0 than c would be. Cases 2 and 3 are both possible so this stmnt alone is not sufficient.

(2) The distance between 'c' and 'a' is the same as the distance between 'c' and '-b'.
If the distance between c and a is the same as distance between c and -b, -b can be at 2 places around c such that

Case 1: ---------- a and -b ----------------0---------------- b ----------- c ---------
a and -b are at the same point and 0 is between a and c somewhere.

Case 2: ---------- a ---------------------------------- b ----------- c ---------- 0 ------------------------- (-b) -----------
-b is to the other side of c (same distance away as a is to c) and 0 is somewhere to the right of c.

Again, 2 cases are possible so this stmtn alone is not sufficient.

Using both,

Case 1 of stmnt 2 becomes invalid because distance of a from 0 is equal to distance of b from 0 and hence this is less than distance of c from 0. This contradicts stmnt 1.
Only case 2 of stmnt 2 is possible in which 0 is to the right of c.
Hence, this is sufficient.

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Re: On the number line shown, is zero between 'a' and 'c'?  [#permalink]

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24 Jun 2019, 04:50
Statement 1: There are 2 possibilities. Either 0 lies between a and c OR 0 lies to the right hand side of C. So statement 1 is not sufficient. Option A and D are eliminated

Statement 2: There again 2 possibilities. Either 0 lies to the left hand side of b or right hand side of b and 0 lies between a and c only when 0 is in left hand side of b. Not sufficient. Option B is eliminated.

when we introduce statement 2 to 2 possibilities of statement 1, we will find that 0 cannot lie to the left hand side of b. So 0 is on right side of b and since distance between b and c is smaller than half the distance of a and c, we know that 0 will also lie on right hand side of B. Thus we know the answer to the question "if 0 lies between a and c".

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Re: On the number line shown, is zero between 'a' and 'c'?   [#permalink] 24 Jun 2019, 04:50
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