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# Last month Grace worked, and was paid for, a total of x hour

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Director
Joined: 29 Nov 2012
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Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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17 Jan 2013, 06:50
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55% (hard)

Question Stats:

70% (02:10) correct 30% (02:08) wrong based on 351 sessions

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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?

(1) x = 55
(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.
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Re: Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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17 Jan 2013, 07:13
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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.

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Director
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Posts: 740
Re: Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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26 Jan 2013, 20:52
Bunuel wrote:
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.

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?
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Posts: 55271
Re: Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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28 Jan 2013, 01:00
fozzzy wrote:
Bunuel wrote:
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.

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?

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.
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Re: Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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06 Jun 2013, 17:53
2
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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Re: Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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15 Dec 2015, 11:29
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
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Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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15 Dec 2015, 12:17
1
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)
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Re: Last month Grace worked, and was paid for, a total of x hour  [#permalink]

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24 Mar 2018, 12:57
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Re: Last month Grace worked, and was paid for, a total of x hour   [#permalink] 24 Mar 2018, 12:57
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