Math, asked by nupurpatel2405, 9 months ago

Solution of the system : 17x + 9y = 31, 9x + 11y = 29 is : (a) x = –2, y = –1 (b) x = –2, y = 1 (c) x = 2, y = 1 (d) x = 2, y = –1

Answers

Answered by mpuja1508

Answer:

If m and n are integers, what is the value of m + n? – OG 2020 Question #305 with Solution

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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

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Source OG 2020

Type Data Sufficiency

Topic Algebra

Sub-Topic Simple Algebraic Expression

Difficulty Easy – Medium

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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.

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