Manhattan problem

[pink_08]

Why if the values are in percents, we can assign a value of 100 for the total number of interns in the calculation..

I got this doubt when solving the below problem.

I tried using values - 1000 and got the same result. But for the number 30, I got different one.

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?


pink

[cbenk121]

Answer is 89%.

We need to figure out the # of not tired people who work < 6 hours, and > 6 hours.

We're given:

>> # of not tired people who work < 6 hours = 75% = 75 people (assume there's 100 total people to make math easy)

>> # of total people < 6 hours = 80.
>>>>This means that the # of people who sleep > 6 hours = 20.

>> 70% of people who sleep > 6 hours are not tired.
>>>>70% * 20 = 14.

We now know the # of not tired people both < 6 hours and > 6 hours. 75 + 14 = 89.

Since we assumed there were 100 total people, 89 / 100 * 100 = 89%

-----------------

Oops, looks like I misplaced some information. Always double check your work...

Answer is 19%.

We need to figure out the # of not tired people who work < 6 hours, and > 6 hours.

We're given:

>> # of tired (was formally non-tired) people who sleep < 6 hours = 75% = 75 people (assume there's 100 total people to make math easy)

>> # of total people who sleep < 6 hours = 80.
>>>>We can calculate the # of non-tired people who sleep < 6 hours = 5 (need to calculate this now)
>>>>This also means that the total # of people who get > 6 hours of sleep = 20.

>> 70% of people who sleep > 6 hours are not tired.
>>>>70% * 20 = 14.

We now know the # of not tired people both < 6 hours and > 6 hours. 5 + 14 = 19.

Since we assumed there were 100 total people, 19 / 100 * 100 = 19%

------------------------------

I agree with Stuart - you should get same percentage values no matter which numbers you use, as long as you're consistent. Show your math for both 1000, and 30, and perhaps we can help you further.

[pink_08]

Answer is 19.

My question is not about how to solve the problem. But more on , Why should we take 100 as the total value for percent problems,... We get the same 19 as the answer for 1000 but not for 30...

[Stuart@KaplanGMAT]

Answer is 19.

My question is not about how to solve the problem. But more on , Why should we take 100 as the total value for percent problems,... We get the same 19 as the answer for 1000 but not for 30...

Show your math; you should be getting the same answer no matter which numbers you select.

We take 100 because it's the simplest number to work with when percents are involved.

[viidyasagar]

Isn't there an error in the Q, if the answer is 19%....

IMO, if the Q were worded as , At a certain hospital, 75% of the interns who received fewer than 6 hours of sleep, reported feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

In its current form -

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

I think the answer is 14%......any takers...

75% of the interns receive fewer than 6 hours of sleep and report feeling tired...

Therefore 25% sleep more than 6 hours.....infact, the question in its current form is grammatically wrong...

Somebody help

[viidyasagar]

Sorry, kindly ignore previous post...... question is correct..answer is 19%

[biker317]

19%

Use the double set matrix
Final equation we need is
Not tired>6 hrs+Not tired<6hrs=?
70% of 20%+5%=14%+5%=19%

remember its "75% of the interns receive fewer than 6 hours of sleep " not who received as vidyasagar changed it to..big diifference..hope this helps.

[gmatmachoman]

Guys,

It seems I am not getting it right..Plz help me!

[sanju09]

Why if the values are in percents, we can assign a value of 100 for the total number of interns in the calculation..

I got this doubt when solving the below problem.

I tried using values - 1000 and got the same result. But for the number 30, I got different one.

At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?


pink

below links discuss the same problem

https://www.beatthegmat.com/tired-interns-t18055.html

https://www.beatthegmat.com/tired-interns-t28561.html

When everything is dealt in percent, 100 is the best option for the total, but anything in place of 100 won't hamper the result provided special care was taken in calculations and conversions.

[sanju09]

Guys,

It seems I am not getting it right..Plz help me!

...and what's the issue with you, thegentlegmatmachoman?

[gmatmachoman]

Guys,

It seems I am not getting it right..Plz help me!

...and what's the issue with you, thegentlegmatmachoman?

sanju bhai, plz do post the steps to solve it.. My brain is not working..heheheh!!

[sanju09]

Guys,

It seems I am not getting it right..Plz help me!

...and what's the issue with you, thegentlegmatmachoman?

sanju bhai, plz do post the steps to solve it.. My brain is not working..heheheh!!

Lo phir...

Split 100 people in two categories, < 6 and ≥ 6, then split each category to two sub-categories, reporting tired (RT) and not reporting tired (NRT).

First line guarantees that the category < 6 has 75 interns who contribute to the grand sub-category, RT. And the third line confirms that the category < 6 has 80 interns in total. If it's so, then 5 of category < 6 contribute to the grand sub-category, NRT, and that the category ≥ 6 must have 20 interns in total, and of those 20, 0.70 × 20 = 14 contribute to the grand sub-category, NRT, and hence the remaining 0.30 × 20 = 6 contribute to the grand sub-category, RT.

Now, what percent of the interns report no feelings of tiredness during their shifts? Or, answer grand NRT, which is 5 from the category < 6, and 14 from the category ≥ 6, which totals to [spoiler]19[/spoiler].

[spoiler]One more thing, Govind...

I am surprised to see the given problem as a Manhattan problem. This was in fact posted by me on this forum the last year, under heading "feelings of fatigue", which I am not able to find now on this forum even after trying the search option many times after reading this thread. Don't know what's happening around![/spoiler]