Data Sufficiency

swerve wrote:Every month, Harriet draws three paychecks from three jobs. The greatest paycheck incurs a thirty-five percent income tax, while the other two paychecks incur twenty-five percent income tax each. Is the total amount of tax deducted from the three paychecks greater than thirty percent of the total of the paychecks before tax deduction?

1) Harriet's biggest salary is $4000, and the next largest salary is $1500.
2) Harriet's smallest salary is $1000.

The OA is A

Source: Economist GMAT

Say the greatest paycheck is $x, and the other two paychecks are $y and $z, respectively.

Tax on the greatest paycheck = 35% of x = 35%x;
Tax on one of the smaller paycheck = 25% of y = 25%y;
Tax on another of the smaller paycheck = 25% of z = 25%z

We have to determine whether

35%x + 25%y + 25%z > 30%(x + y + z)

x > y + z

Question rephrased: Is x > y + z?

Let's take each statement one by one.

1) Harriet's biggest salary is $4000, and the next largest salary is $1500.

=> x = $4000, y = $1500. Since y is the next largest salary, z must be less than equal to 1500. Say we consider z = 1500.

Thus, x > y + z => 4000 > 1500 + 1500 => 4000 > 3000. The answer is Yes. Sufficient.

2) Harriet's smallest salary is $1000.

Say z is the smallest salary = $1000

Case 1: Say y = 2000 and x = 2500.
x > y + z => 2500 ? 2000 + 1000 => 2500 < 3000. The answer is No.

Case 2: Say y = 4000 and x = 2500.
x > y + z => 4000 ? 2000 + 1000 => 4000 > 3000. The answer is Yes.

Insufficient.

The correct answer: A

Hope this helps!

-Jay
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