Data Sufficiency Pack 1, Question 4) John is paid X dollars

John paid x dollars for fist 8 hours =8x.

Next paid 1.5x dollars for 4 hours = 6x.

thereafter , 12 hours paid 2x for one hour

from statement 1
John paid 280 on monday two possibilities are there

1 , 14x=280, x=20 , john worked for 12 hours

or2, 20x=280, x=14, john worked for 17hours.

from statement 2,
john worked for additional 2 hours he would have paid 80 dollars.
not sufficient.

combining both statement , john worked for 2 hours he paid 40 dollars per hour,
It satisfies 1st possbility in 1st statement . next 12 hours he paid 2x of the amount, x= 20 satisify the solution


so option C is correct.

Hi All,

This prompt gives us a changing pay rate depending on the total number of hours that John works in a given day:

1) For the first 8 hours, he earns X dollars per hour
2) For the next 4 hours after that, he earns 1.5X dollars per hour
3) For any time over 12 hours, he earns 2X dollars per hour

We're told that X is an integer. We're asked for the number of hours that John worked on Monday. TESTing VALUES will help to define the possibilities here....

1) John was paid a total of $280 for his work on Monday.

This information allows for a number of different possibilities....

IF...
X = $35
Then (8 hours)($35/hour) = $280 and the answer to the question is 8

IF...
X = $20
Then (8 hours)($20/hour) + (4 hours)($30/hour) = $280 and the answer to the question is 12

IF...
X = $14
Then (8 hours)($14/hour) + (4 hours)($21/hour) + (3 hours)($28/hour) = $280 and the answer to the question is 15
Fact 1 is INSUFFICIENT

2) If John had worked 2 additional hours, then he would have made an additional 80 dollars.

IF...
X = $40
Then any 2 additional hours (up to 8 hours) would have gained him (2 hours)($40/hour) = $80; the answer to the question is any integer 3 through 8 inclusive.

IF....
X = $20
Then (8 hours)($20/hour) + (4 hours)($30/hour) = $280 and an extra 2 hours would have gained him (2 hours)($40/hour); the answer to the question is 12
Fact 2 is INSUFFICIENT

Combined, we know...
John was paid a total of $280 for his work on Monday.
If John had worked 2 additional hours, then he would have made an additional 80 dollars.

Since John earns $X/hour for the first 8 hours, the extra two hours CANNOT have been paid at $40/hour. 7 hours at $40/hour would = $280, but working past 8 hours would have made the second 'extra' hour 1.5X (or $60/hour at that rate), which does NOT match up with the increase of $80. This means that John MUST have worked some total over 8 hours (and at a rate that was LESS than $40/hour). Based on the restriction that X is an INTEGER, the only option that 'fits' is when X = 20.

At X = 20, the John would have worked 12 hours to earn $280 (8 hours at $20/hour + 4 hours at $30/hour). The extra two hours would have been at 2X dollars/hour (or $40/hour), so the extra two hours would equal $80 total.
Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

I wonder why x = 2, 4, 6 are not included in your analysis!

Please elaborate! Many thanks

Hi leanhdung,

On many DS questions, using small positive integers is a great way to quickly prove whether a pattern exists in a given Fact or not. However, with this question, you run into a couple of issues with that idea. First, there are only 24 hours in the day so there is a limit to the number of hours he can work on Monday (and only so much money that John could earn on that day). Second, the two Facts introduce information that implies that John is paid significantly MORE than $2/hour, $4/hour, $6/hour, etc. so those numbers are NOT a great option to start with.

GMAT assassins aren't born, they're made,
Rich

Ugh I was so so so close to getting this question correct, but made the amateur mistake of thinking that information from Stmt 1 is from the original question stem.

And chose B instead of C.

Hi HappyQuakka,

You're not the first person to make that mistake when dealing with a DS prompt (and you won't be the last), so that's not a big deal at this point. It's important to absorb THAT lesson though. You'll find that with the proper Tactics and organizational skills, most GMAT questions are actually fairly straight-forward, but it takes time to develop all of the necessary skills to to get to that 'ability level.' Certain GMAT questions (such as DS) don't have a 'safety net' - meaning that if you make a little mistake, you won't realize it (you'll just convince yourself that one of the wrong answers is the correct one). This is one of the reasons why note-taking is so important; if you're doing work 'in your head', then you are more likely to miss out on a vital detail (or make a silly mistake) that will cost you some easy points. Remember the error you made from this question as you continue to practice DS and I bet that you'll be far less likely to make that same mistake again.

GMAT assassins aren't born, they're made,
Rich

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.