# Practice GMAT Data Sufficiency Question

If 10x + 10y + 16x2 + 25y2 = 10 + Z, what is the value of x + y?
1. Z = (4x)2 + (5y)2
2. x = 1
 A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
1. Evaluate Statement (1) alone.
1. Substitute Z into the equation:
10x + 10y + 16x2 + 25y2 = 10 + Z
10x + 10y + 16x2 + 25y2 = 10 + (4x)2 + (5y)2
10x + 10y + 16x2 + 25y2 = 10 + 16x2 + 25y2
10x + 10y = 10
10(x+y) = 10
x + y = 1
2. Statement (1) is SUFFICIENT.
2. Evaluate Statement (2) alone.
1. Substitute the information you know (i.e, x = 1) into the equation:
10x + 10y + 16x2 + 25y2 = 10 + Z
10(1) + 10y + 16(1)2 + 25y2 = 10 + Z
10y + 25y2 + 10 + 16 = 10 + Z
25y2 + 10y + 16 - Z = 0
2. 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.
3. Statement (2) is NOT SUFFICIENT.
3. Since Statement (1) alone is SUFFICIENT but Statement (2) alone is NOT SUFFICIENT, answer A is correct.