Algebra - Data Sufficiency - Help me solve this

[raghavan]

Hi,

Pls help me to solve this problem.

What is the value of xy?
1) y = x + 1
2) y = x^2 + 1

[ksb]

Hi Raghavan

The answer and explanation to your query

The correct answer is Choice (E)

The question asks you to evaluate if the value of xy can be found using the information provided in the two statements.

From statement 1, we know that y = x + 1. Therefore, xy = x(x+1) = x^2 + x. There will be infinite values for xy. So, statement 1 alone is not sufficienct.

Therefore, we can eliminate answer choices A and D and narrow down our answer choices to B, C or E.

Let us look at statement 2. y = x^2 + 1. Therefore, xy = x(x^2 + 1). Therefore, the value of xy = x^3 + x. Again there can be infinite values for xy. Therefore, statement 2 alone is not sufficient. Eliminates answer choice B.

Now, let us combine the two statements, y = x + 1 and y = x^2 + 1.
i.e, x + 1 = x^2 + 1

Simplifying, we get x^2 - x = 0 or x(x - 1) = 0
Either x = 0 or x = 1.

If x = 0, then we can conclude that xy = 0.
On the contrary if x = 1, then xy = 1 * (1 + 1) = 2.

As we get two answers for the value of xy, we cannot conclusively find out the answer to the value of xy

Hence, Answer choice (E) is the correct answer.

Best wishes

KSB
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