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nafiul9090
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anuprajan5
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Assume d to be day hour and n to be night hours
a - Day rate
b - Night rate
b=1.2a - Given - condition 1
Statement 1 - Insifficient. There can be many combinations to suit d + n = 55
Statement 2 -
d*a = = 0.5(da+nb)
Simplifying and using condition 1
we should get 5d=6n. We have a relation between the hours. But we do not know total hours.
Combining Statement 1 and 2
d + n = 55
d + 5/6 d = 55
we will get d = 30 hours and n to be 25 hours. Hence C.
Just to verify assume $5 as day rate and $6 as night rate (1.2 times day rate), we get day pay for the month to be 30*5 = 150 and total to be 30*5+25*6 = 300.
And day pay for the whole month is 50% of the whole month pay. (150/300)
Regards
Anup
a - Day rate
b - Night rate
b=1.2a - Given - condition 1
Statement 1 - Insifficient. There can be many combinations to suit d + n = 55
Statement 2 -
d*a = = 0.5(da+nb)
Simplifying and using condition 1
we should get 5d=6n. We have a relation between the hours. But we do not know total hours.
Combining Statement 1 and 2
d + n = 55
d + 5/6 d = 55
we will get d = 30 hours and n to be 25 hours. Hence C.
Just to verify assume $5 as day rate and $6 as night rate (1.2 times day rate), we get day pay for the month to be 30*5 = 150 and total to be 30*5+25*6 = 300.
And day pay for the whole month is 50% of the whole month pay. (150/300)
Regards
Anup
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GMATGuruNY
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To determine the ratios implied by the problem, PLUG IN.nafiul9090 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?
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.
Let the day shift rate = $5 per hour.
Since the night shift rate is 20% higher, the night shift rate = 5 + .2(5) = $6 per hour.
Statement 1: x = 55.
No way to determine the number of hours worked on the day shift.
Statement 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.
Let the total pay for each shift = the LCM of 5 and 6 = $30.
Since $30 is earned during the day shift at a rate of $5 per hour, the number of day shift hours = 30/5 = 6 hours.
Since $30 is earned during the night shift at a rate of $6 per hour, the number of night shift hours = 30/6 = 5 hours.
Thus, of every 11 hours worked, the fraction worked during the day = 6/11.
No way to determine the exact number of day shift hours.
Statements 1 and 2 combined:
Number of day shift hours = (6/11)55 = 30.
SUFFICIENT.
The correct answer is C.
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minkathebest
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Hello GMATguruNY, thank you for the great suggestion on plug-in! This still took me a while with the plug-in because I did not know which variables I should let numbers for.
As a general rule do you try and not let numbers for what is being asked? So, we rule out trying to let a number for hours in the day shift.
But we let numbers for everything else in the problem.
I guess, I am trying to see how I can navigate my way around plugging-in. This seems like a good problem to experiment with.
As a general rule do you try and not let numbers for what is being asked? So, we rule out trying to let a number for hours in the day shift.
But we let numbers for everything else in the problem.
I guess, I am trying to see how I can navigate my way around plugging-in. This seems like a good problem to experiment with.
Hi Mitch,
I tried the same problem the way you solved , But i took 3 mins to solve it I was wondering whether there is any relation between the ratios
6: 5 is the salary/ hour ratio . Can it be 5: 6 the number of hours ratio ??
applied the time to speed (const distance ) link here, I'm just curious.Please answer .
Thanks
I tried the same problem the way you solved , But i took 3 mins to solve it I was wondering whether there is any relation between the ratios
6: 5 is the salary/ hour ratio . Can it be 5: 6 the number of hours ratio ??
applied the time to speed (const distance ) link here, I'm just curious.Please answer .
Thanks
Hi Mitch,
I did the problem the way you solved , But i took 3 mins to solve it I was wondering whether there is any relation between the ratios
6: 5 is the salary/ hour ratio . Can it be 5: 6 the number of hours ratio ??
applied the time to speed (const distance ) link here, I'm just curious.Please answer .
Thanks
I did the problem the way you solved , But i took 3 mins to solve it I was wondering whether there is any relation between the ratios
6: 5 is the salary/ hour ratio . Can it be 5: 6 the number of hours ratio ??
applied the time to speed (const distance ) link here, I'm just curious.Please answer .
Thanks
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GMATGuruNY
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Nice work.AnuGmat wrote:Hi Mitch,
I tried the same problem the way you solved , But i took 3 mins to solve it I was wondering whether there is any relation between the ratios
6: 5 is the salary/ hour ratio . Can it be 5: 6 the number of hours ratio ??
applied the time to speed (const distance ) link here, I'm just curious.Please answer .
Thanks
In statement 2, the time ratio (6/5) is equal to the reciprocal of the rate ratio (5/6) because the SAME AMOUNT is earned during each shift.
However, if the same amount is NOT earned during each shift, then the time ratio will NOT be equal to the reciprocal of the rate ratio.
Consider an extreme case:
Grace's gross pay for the hours she worked on day shift last month was exactly 99% of her total gross pay for last month.
Here, since close to 100% of the total gross pay is earned during the day shift, close to 100% of the total number of hours must be worked during the day shift.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
