Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #37

7

If x and y are positive integers

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

2 Explanations

1

John Robertson

Used test cases, SQR(X)+SQR(Y)=?

1) x+y = 15, could be for x & y, 10 and 5, 9 and 4, etc. Can't get a lock on what x and y are, IS

2) SQR(xy)=6. Indicates xy=36, as only solution for that perfect square to =6 is SQR(36).
But, you can get for xy: 6x6, 9x4, 12x3, etc.
IS

1&2) knowing x+y=15, and SQR(xy)=6, 12+3=15, satisfies (1), and 12x3=36, satisfies (2). Without solving for SQR(x)+SQR(y), you know x and y are definitely 12 and 3 in either order, and it could be solved out.
S, (D)

Feb 16, 2017 • Comment

2

What is the value of X^0.5 + Y^0.5?

Recognise that squaring the original (X^0.5 + Y^0.5?)^2 leads to X + 2(XY)^0.5 + Y. Knowing the value of the latter is one step away from answering the question.

1: X + Y = 15
In X + 2(xy)^0.5 + Y, this statement does not answer the value of 2(XY)^0.5
Insufficient

2: (XY)^0.5 = 6
In X + 2(XY)^0.5 + Y, this statement does not answer the value of X + Y
Insufficient

1 & 2: Using both statements we can solve X + 2(XY)^0.5 + Y
-> 15 + 2*(6) = 27
-> X^0.5 + Y^0.5 = 27^0.5 = (3*9)^0.5 = 3 * (3)^0.5

Sep 23, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

Thanks for sharing your solution :) Nice work!

Sep 23, 2016 • Reply

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Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.


Section 6.3 Data Sufficiency

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