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DS: Arithmetic salary problem

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by me_1234 » Wed Dec 17, 2014 2:43 pm
From Leland's gross pay of p dollars last week, t percent was deducted for taxes and then s dollars was deducted for savings. What amount of Leland's gross pay last week remained after these two deductions?

1/ p - s = 244

2/ pt = 7552


Answer: C both statements together are sufficient


I understand why C works here, but can someone show me how to solve this algebraically if this was a Problem Solving question?
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by GMATGuruNY » Wed Dec 17, 2014 2:57 pm
melanie.espeland wrote:From Leland's gross pay of p dollars last week, t percent was deducted for taxes and then s dollars was deducted for savings. What amount of Leland's gross pay last week remained after these two deductions?

1/ p - s = 244

2/ pt = 7552
Pay after the two deductions = p - (t/100)p - s.

Rephrase the expression above in terms of the two statements (p-s and pt):
p - (t/100)p - s = p - s - pt/100.

Question stem, rephrased:
What is the value of p - s - pt/100?

Statement 1: p-s = 244
No information about pt/100.
INSUFFICIENT.

Statement 2: pt = 7552
No information about p-s.
INSUFFICIENT.

Statements combined:
p - s - pt/100 = 244 - 7552/100.
SUFFICIENT.

The correct answer is C.
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by me_1234 » Wed Dec 17, 2014 4:41 pm
Thanks
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