Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE DS – If x and y are positive integers, what is the value of…

If x and y are positive integers, what is the value of…

Solution:

We must determine the value of √x + √y.

Statement One Alone: 

x + y = 15

Although it may seem tempting to take the square root of x, y, and 15, we actually cannot do that. The only way statement one would be sufficient is if we knew the actual values of x and y. Since we do not know those values, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone: 

√(xy) = 6

We can square both sides of the equation √(xy) = 6 to get:

xy = 36

However, since we do not know the individual values of x and y, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together: 

Using the information in statements one and two we have two equations:

x + y = 15

xy = 36

Using these two equations we can determine a value for x and y. Let’s start by isolating x in the first equation.

x = 15 – y

We now can substitute 15 – y for x in the equation xy = 36.

(15 – y)y = 36

15y – y^2 = 36

y^2 – 15y + 36 = 0

(y – 12)(y – 3) = 0

y = 12 or y = 3

When y = 12, we see that x = 3 and when y = 3 we see that x = 12. For either solution set, the value of √x + √y  is √12 + √3. Both statements together are sufficient to determine a value for √x + √y.

Answer: C 

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