Last month Grace worked, and was paid for, a total of x hours. Some of

Question

Last month Grace worked, and was paid for, a total of x hours. Some of the hours were on the day shift and the remainder of the hours were on the night shift. Her hourly pay is 20% higher for the night shift than for the day shift. How many hours did Grace work on the day shift last month?

(1) x = 55

(2) Grace’s gross pay for the hours she worked on the day shift last month was exactly 50% of her total gross pay for last month.

ID 15269

Bunuel · Accepted Answer

Last month Grace worked, and was paid for, a total of x hours. Some of the hours were on day shift and the remainder were on the night shift. Her hourly pay is 20% higher for the night shift than for the day shift. How many hours did Grace work on the day shift last month?

Say her hourly pay was $p for the day shift and $1.2p for the night shift.

(1) x = 55. Clearly insufficient: we need to know how these 55 hours are split between the day shift hours and the night shift hour.

(2) Grace's gross pay for the hours she worked on day shift last month was exactly 50% of her total gross pay for last month. Not sufficient.

(1)+(2) Say Grace worked  h  hours on the day shift and  55-h  hours on the night shift. Thus, her pay for the the hours she worked on day shift is $ ph  and the total gross pay is $ ph+(55-h)*1.2p . From (2) we have that  ph=0.5(ph+(55-h)*1.2p)  --> reduce by  p :  h=0.5(h+(55-h)*1.2) . We have 1 variable, so we can solve for it. Sufficient.

Answer: C.

Nwsmith11 · Answer

Same concept but seemed a little quicker and more logical for me:

Given 1 and 2 individually are obviously insufficient....d=day shift hours, n=night shift hours , p=hourly pay and m=monthly pay

d+n=x 
 pd+1.2pn=m 
 pd=1.2pn 
 d=1.2n 
 1.2n+n=x=55

Thus we can solve and the answer is C

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fozzzy · Answer

would it make a difference if we had switched it the other way around 55-h as day and h as night for this particular question? Suppose the statement was a little different lets say

(2) Grace's gross pay for the hours she worked on day shift last month was exactly 70% of her total gross pay for last month

how would the variables change?

Bunuel · Answer

It does not matter we denote the day or night shift with h. The point is that we can solve for h hence we can get for 55-h too.

NoHalfMeasures · Answer

VeritasPrepKarishma ,

You have written some incredibly perceptive blog posts on weighted averages. Do you think we can apply weighted average concept to such problems as well? Thanks

NoHalfMeasures · Answer

St2 of the above kind that ‘gives us relation between a part and the whole’ can be easily expressed into a relation between the two parts. IMO this skill is nicely rewarded on the gmat. For instance in the above example St2 says day shift pay is 50% of the total, meaning –

Day shift pay = night shift pay

d*w = (x-d)*w*1.2 …where d= day shift hrs w=day shift pay rate

putting x=55 from st1

d*w = (55-d)*w*1.2

At this point we know that we can get rid of w and calculate d. Thus st1+st2 are SUFF. Ans C

What if st2 instead gave some different percentage “Grace's gross pay for the hours she worked on day shift last month was exactly 40% of her total gross pay for last month.”

We can (Day Shift Pay)/40% = Total and (Night shift Pay)/60%= Total

=> d*w/0.4 = {(x-d)*w*1.2}/0.6

Similarly if st2 instead gave some crazy fraction “Grace's gross pay for the hours she worked on day shift last month was exactly 7/13 of her total gross pay for last month.”
We can (Day Shift Pay)/(7/13) = (Night shift Pay)/(6/13)

SnorLax_7 · Answer

Hi @Bunuel/  KarishmaB

Can we take Pay as '1' for Day shift and solve this ? I hve seen in many DS question that having 2 variables ultimately lead to Option 'E'. Is there any trick we can find out when to use '1' and when to use variable ?

Thanks !

KarishmaB · Answer

You can take pay as 1 and solve it because this variable ultimately gets cancelled off.

Statement 2 says 
Earnings from day work = Earnings from night work
d * Pay = (x - d)* 1.2 * Pay

'Pay' cancels off on both sides so you could have taken pay as 1 or 100 or whatever else you wished to.

d = (x - d)* 1.2
Given x in statement 1, we can find the value of d and that is why both statements are sufficient together.

KarishmaB · Answer

8 years too late to reply but still, yes, I would use weighted averages here. I would say that the ratio of day pay : night pay is 5 : 6 and in statement 2, we are essentially given that C1w1 = C2w2 and hence, the weights (number of hrs of each) must be in the ratio 6:5. Knowing from statement 1 that total number of hrs is 55, we can find the number of day hrs as 30 and night hrs as 25. Hence answer (C) Check this post and this video for weighted averages. I will try to put up a video solution of this interesting question too. https://anaprep.com/arithmetic-weighted-averages/ https://www.youtube.com/watch?v=_GOAU7moZ2Q

Fish181 · Answer

To answer the question, how many HOURS did she work on day shift, you must have a hard number and not just ratios/percentages.

To answer the question, you must also know *something* about the pay.

From this alone you should deduce you can't solve with just one or the other.

Both together:

You're given day + night = 55

You're given gross pay equals each other.

At this point, you know you need those two different criteria listed at the top and you're given both of these criteria when together.

Logically, this is sufficient. You don't really need to even solve to recognize this. Now i'm not saying this is as thorough as you should aim to be but when you're staring down a timer on the real test sometimes you don't have enough time to deal in absolutes.

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