fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 14)
Answer: [spoiler]____ (C)__ [/spoiler]
Statement 1:
Case 1: a=0 and b=1, with the result that a+b = 0+1 = 1
In this case, a³+b³ = 0³ + 1³ = 1
Case 2: a=2 and b=-1, with the result that a+b = 2-1 = 1
In this case, a³+b³ = 2³ + (-1)³ = 7
Since a³+b³ can be different values, INSUFFICIENT.
Statement 2:
Case 3: a=1 and b=1, with the result that a²+b² = 1²+1² = 2
In this case, a³+b³ = 1³ + 1³ = 2
Case 4: a=-1 and b=-1, with the result that a²+b² = (-1)²+(-1)² = 2
In this case, a³+b³ = (-1)³ + (-1)³ = -2
Since a³+b³ can be different values, INSUFFICIENT.
Statements combined:
Squaring a+b = 1, we get:
a² + b² + 2ab = 1
Substituting a²+b²=2 into the red equation above, we get:
2 + 2ab = 1
2ab = -1
ab = -0.5
Multiplying a²+b²=2 by a+b=1, we get:
(a²+b²)(a+b) = 2*1
a³ + b³ + a²b + ab² = 2
a³ + b³ + ab(a+b) = 2
Substituting ab=-0.5 and a+b=1 into the blue equation above, we get:
a³ + b³ + (-0.5)(1) = 2
a³ + b³ = 2.5
SUFFICIENT.
The correct answer is
C.
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