Data Sufficiency Pack 3, Question 4 If |a - b| = 6...

Hi All,

This is a high-difficulty level DS prompt that requires thoroughness and the willingness to prove whether more than one answer to the question exists or not. Since we're dealing with several absolute value calculations, we'll have to consider multiple possibilities (positive and negative) to get to the correct answer.

From the outset, we're given two absolute value equations to work with (|a - b| = 6 and |b - c| = 15). We're asked for the value of |c|.

From the two Facts, it appears that Fact 2 will be considerably easier to deal with (since it limits b to just two possible values), so I'm going to start there.

2) |b| = 9

This Fact tells us that b can equal 9 or -9, so we should do a bit of work to see how those two values would impact the other two variables...

When b = - 9, c can equal two possibilities:

-9 - c = 15
c = - 24
So |c| = |-24| = 24

or

-9 - c = -15
c = 6
So |c| = |6| = 6
Fact 1 is clearly INSUFFICIENT

Before moving on to Fact 1 though, I'm going to do a bit more work to figure out what the variable a could equal....

When b = -9...

a - (-9) = 6
a = -3

or

a - (-9) = -6
a = -15

When b = +9...

a - (9) = 6
a = 15

or

a - (9) = -6
a = 3

1) |a - c| = 9

Since we've done a number of different calculations in Fact 2, we should look to see if any of them will also 'fit' Fact 1.

IF...
a = -3
b = -9
c = 6
Then all 3 of the absolute value equations (the two in the prompt and the one in Fact 1) are satisfied and the answer to the question is |6| = 6.

IF...
a = -15
b = -9
c = -24
Then all 3 of the absolute value equations (the two in the prompt and the one in Fact 1) are satisfied and the answer to the question is |-24| = 24.
Fact 1 is INSUFFICIENT.

Combined, we already have two sets of values that fit ALL of the given information and provide two different solutions (see above).
Combined, INSUFFICIENT

Final Answer: