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

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Last month Grace worked, and was paid for, a total of x hour [#permalink] New post 17 Jan 2013, 05:50
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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.
[Reveal] Spoiler: OA

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Re: Last month Grace worked, and was paid for, a total of x hour [#permalink] New post 17 Jan 2013, 06:13
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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.

Answer: C.
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Kudos [?]: 157 [0], given: 543

Re: Last month Grace worked, and was paid for, a total of x hour [#permalink] New post 26 Jan 2013, 19:52
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.

Answer: C.


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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Math Expert
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Joined: 02 Sep 2009
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Kudos [?]: 18313 [0], given: 2345

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Re: Last month Grace worked, and was paid for, a total of x hour [#permalink] New post 28 Jan 2013, 00:00
Expert's post
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.

Answer: C.


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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

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Joined: 28 Apr 2013
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GMAT Date: 08-03-2013
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Kudos [?]: 11 [1] , given: 1

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Re: Last month Grace worked, and was paid for, a total of x hour [#permalink] New post 06 Jun 2013, 16:53
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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] 06 Jun 2013, 16:53
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