OG 2020: Question No. 305
If m and n are integers, what is the value of m + n?
- (x + m) (x + n) = x2 + 5x + mn and x ≠ 0.
- mn = 4
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topic | Algebra |
| Sub-Topic | Simple Algebraic Expression |
| Difficulty | Easy – Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- The numbers m and n are integers.
We need to determine
- The value of m + n
As we have no other information about the values of m and n from the question stem, let us analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, (x + m) (x + n) = x2 + 5x + mn and x ≠ 0
Simplifying the above equation, we get
- (x + m) (x + n) = x2 + 5x + mn
Or, x2 + (m + n) x + mn = x2 + 5x + mn
Or, (m + n) x = 5x
Or, m + n = 5 [as x ≠ 0]
As we can determine the value of m + n, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 2, mn = 4
- However, from this statement we cannot determine either the individual values of m and n or their sum.
Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from statement 1 individually, this step is not required.
Hence, the correct answer choice is option A.
