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Each day at Dan’s new job, he earns $10 more than the day before

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Each day at Dan’s new job, he earns $10 more than the day before  [#permalink]

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New post 25 Nov 2014, 09:29
4
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

45% (01:22) correct 55% (00:56) wrong based on 226 sessions

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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

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Re: Each day at Dan’s new job, he earns $10 more than the day before  [#permalink]

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New post 25 Nov 2014, 10:31
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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
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Re: Each day at Dan’s new job, he earns $10 more than the day before  [#permalink]

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New post 23 Aug 2015, 11:11
OA:

Note that the daily increase is consistent: he always earns $10 more each day. This is essentially a consecutive integer problem (although, in this case, there are increments of 10, not 1). Use f to represent Dan’s earnings on the first day. Express his earnings on subsequent days as f + 10, f + 20, f + 30, … f + 140.

(1) SUFFICIENT: This statement provides the sum of the most recent three days:

(f + 120) + (f + 130) + (f + 140) = $690
3f + 390 = $690
3f = $300
f = $100

Dan earned $100 on his first day.

(2) INSUFFICIENT: This statement provides the difference between the totals for the first three days and the last three days:

First three days = (f) + (f + 10) + (f + 20) = 3f + 30
Last three days = (f + 120) + (f + 130) + (f + 140) = 3f + 390
Last three days − First three days = (3f + 390) − (3f + 30) = $360

This statement is always true, regardless of how much Dan made on the first day. (This information can be determined from the question stem alone!)

The correct answer is (A).
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Re: Each day at Dan’s new job, he earns $10 more than the day before  [#permalink]

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New post 09 Sep 2018, 02:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Each day at Dan’s new job, he earns $10 more than the day before &nbs [#permalink] 09 Sep 2018, 02:05
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