paranoidvik wrote:

Each day at Dan’s new job, he earns $10 more than the day before. If he just completed his 15 th day of work, how much did he earn on his first day?

(1) His total earnings for the three most recent work days equal $690.

(2) His total earnings for the three most recent work days exceed his total earnings for the first three work days by $360

This is one of those questions where it is easy to determine data sufficiency than it is to actually solve. Remember the important rule: on DS questions don't try to find the answer unless you absolutely have to in order to test the sufficiency of the statement.

Here's my approach to this problem:

First, I determine what data would be needed to answer the question.

I know:

-he has worked 15 days.

-his pay increases by $10/day (on day 15 it is $140 more than on day 1)

I need to know:

-what was his day 1 pay

Start with statement 1 by itself:

If I know his total earnings for the last 3 days ($690), then I should be able to determine the his pay on day 15 with this formula...

x= day 15 pay

x+x-10+x-20 = 690

If I solve for x then I would know the day 15 pay. And then I just need to subtract 140 from x to get day 1 pay.

Statement 1 is sufficient, so I can eliminate B, C and E.

Now to test Statement 2:

Total earnings for the last 3 days exceeds first three days by $360. In equation form...

x = day 15 pay

(x+x-10+x-20)=(x-120+x-130+x-140)+360

Can you solve for x here? The answer is no - not without more information, because x cancels itself out (or becomes equal to itself). Look:

(x+x-10+x-20)=(x-120+x-130+x-140)+360

3x-30=3x-390+360

3x-30=3x-30

Therefore, statement 2 is insufficient. Eliminate D.

Correct answer: A