Data Sufficiency Question: What is the absolute value of the sum of two numbers?

**(1) The product of the two numbers is 12.**

**(2) One number is 1 less than the other number.**

- Statement (1) alone is enough to answer the question. However, statement (2) alone is not sufficient to answer the question asked.
- Statement (2) alone is enough to answer the question, but statement (1) alone is not sufficient to answer the question asked.
- Both statements (1) and (2) together suffice to answer the question asked. However, neither statement ALONE is sufficient.
- Each statement alone suffice to answer the question asked.
- Statements (1) and (2) together are not sufficient to answer the question asked, and extra data specific to the problem are required.

## Solution to The Data sufficiency Question : What Is The Absolute Value Of The Sum Of Two Numbers

The correct answer is choice (C). Calling one number a and the other number b, statement (1) alone tells us only that ab = 12, but gives no information about their sum. Hence, the right answer choice could be either options to (B), (C), or (E).

Statement (2) alone tells us that the relationship between the two numbers can be written as a = b-1, but gives no information about their sum. As a result, the correct answer choice must be (C) or (E). By considering statements (1) and (2) together, you can substitute b-1 for a in the equation ab = 12:

b(b-1)= 12

b²-b= 12

b²-b-12 = 0

You can get the binomial factors of the above equation by factoring the quadratic equation. Then solving the binomial factors as linear equations easily:

(b+3)(b-4)=0

b=-3 or b=4

You can factor the quadratic expression into two binomial factors, then find the roots of the equation – that is, the possible values of b.

Hence, either b = 4 and a = 3, with sum 7, or b = -3 and b = -4, with sum -7.

We conclude the following:

- The absolute value of the sum of the two numbers in either case is 7.
- Statement (1) and (2) together provide only one answer to the question.
- Hence, the correct answer is (C)

## Another Approach to Solve This Data Sufficiency Problem

You can also approach this problem to solve it less formally. According to statement (1), you can think of some numbers that satisfy statement (1). The following pairs should occur to you using only integers: (1,12), (3,4), (2,6), (-1,-12), (-3,-4), (-2,-6). As there are more than one possibility, then you can rule out choice (A) and (D). On the other hand, statement (2) presents many possibilities. So, rule out choice (B) as well. Therefore, we are left with choice (D) and (E). Working with statement (1) and (2) together, we can rule out all integer pairs except (3,4) and (-3,-4). The absolute sum of either integer pair is 7. This makes choice (C) the right answer. But what about non-integer numbers?

To answer this question, you may require trial and error or intuition. Try a few non-integer pairs to make sure that none works.

**Also Read: Data Sufficiency: How Many Quarts Of Oil Will A Car Burn**

## Final Word

There were two approaches to solve the above mentioned data sufficiency problem. The first one is where you should your math skills to find the end result. The second one is where you need to use trial and error or intuition to get the end results. The first approach will yield a 100% solution but it is a time consuming approach. Whereas, the second one will require more trials to satisfy yourself with the right answer; but it may be a faster approach.