Practice GMAT Data Sufficiency Question
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If 10x + 10y + 16x^{2} + 25y^{2} = 10 + Z, what is the value of x + y?
 Z = (4x)^{2} + (5y)^{2}
 x = 1
Correct Answer: A

Evaluate Statement (1) alone.
 Substitute Z into the equation:
10x + 10y + 16x^{2} + 25y^{2} = 10 + Z
10x + 10y + 16x^{2} + 25y^{2} = 10 + (4x)^{2} + (5y)^{2}
10x + 10y + 16x^{2} + 25y^{2} = 10 + 16x^{2} + 25y^{2}
10x + 10y = 10
10(x+y) = 10
x + y = 1  Statement (1) is SUFFICIENT.
 Substitute Z into the equation:

Evaluate Statement (2) alone.
 Substitute the information you know (i.e, x = 1) into the equation:
10x + 10y + 16x^{2} + 25y^{2} = 10 + Z
10(1) + 10y + 16(1)^{2} + 25y^{2} = 10 + Z
10y + 25y^{2} + 10 + 16 = 10 + Z
25y^{2} + 10y + 16  Z = 0  At this point, we reach a wall. Since we do not know what Z equals, we cannot solve for Y. Without a value for Y, we cannot find x + y.
 Statement (2) is NOT SUFFICIENT.
 Substitute the information you know (i.e, x = 1) into the equation:
 Since Statement (1) alone is SUFFICIENT but Statement (2) alone is NOT SUFFICIENT, answer A is correct.
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