Bunuel wrote:
If |a – b| = 6 and |b – c| = 15, then what is the value of |c|?
(1) |a – c| = 9
(2) |b| = 9
We are given the distance between point a and point b and the distance between point b and point c
|a - b| = 6
Let's plot this over a number line, there can be two scenarios
Case 1: 'a' lies to the right of 'b' and the distance between 'a' and 'b' = 5
--------- b ----------- a ---------
Case 2: 'a' lies to the left of 'b' and the distance between 'a' and 'b' = 5
--------- a ----------- b ---------
|b - c| = 15
Just as in the above case, we can two scenarios one in which 'c' lies to the left of 'b' and in the other case 'c' lies to the right of 'b'. We can use the cases created above and superimpose this information.
Case 1(a): 'c' lies to the right of 'b' and the distance between 'c' and 'b' = 15
--------- b ----------- a --------- c ---------- ⇒ Distance between 'a' and 'c' = 9
Case 1(b): 'c' lies to the left of 'b' and the distance between 'c' and 'b' = 15
--------- c ----------- b --------- a ----------
Case 2(a): 'c' lies to the right of 'b' and the distance between 'c' and 'b' = 15
--------- a ----------- b --------- c ----------
Case 2(b): 'c' lies to the left of 'b' and the distance between 'c' and 'b' = 15
--------- c ----------- a --------- b ---------- ⇒ Distance between 'a' and 'c' = 9
Statement 1(1) |a – c| = 9The distance between 'a' and 'c' is 9. The information correlates to Case 1(a) and Case 2(b)
We need to find |c| (i.e distance between '0' and 'c')
In any of the above four cases, we didn't consider the position of zero, nor did that matter to us. Hence, merely knowing that the distance between 'c' and 'a' = 6, at max we can narrow the relative position of 'a', 'b', and 'c'. We still don't know nor can we find out the position of zero on the number line, and without that information, we cannot find the distance between c and 0.
Hence, statement 1 is not sufficient.
Statement 2(2) |b| = 9The distance between 0 and b is 9. The information is not sufficient as zero can lie to the right of b or it can lie to the left of b and based on the position of zero, we can find the distance between 0 and c.
CombinedFrom
statement 1,
We have the following two cases -
Case 1(a): --------- b ----------- a --------- c ----------
Case 2(b): --------- c ----------- a --------- b ----------
From
statement 2,
Zero can either be to the right of 'b' as shown in the below two cases
Case 1(a): --------- b ----------- a --- 0 ----- c -------------- ⇒ |c| = 6
Case 2(b): --------- c ----------- a --------- b ----------0 ---- ⇒ |c| = 24
Zero can either be to the left of 'b' as shown in the below two cases
Case 1(a): -- 0 --------- b ----------- a --------- c ---------- ⇒ |c| = 24
Case 2(b): --------- c ----- 0 ---- a --------- b -------------- ⇒ |c| =6
As we are getting two answers upon combining, the statements combined are not sufficient.
Option E