In 2013, Mohammads work weeks consisted of 2, 4, or 5 days of work.

Question

In 2013, Mohammad’s work weeks consisted of 2, 4, or 5 days of work. If his entire year consisted of exactly 25 weeks of 2 workdays, 13 weeks of 4 workdays, and 12 weeks of 5 workdays, which of the following is closest to his average number of days worked per week for the year?

A. 3
B. 3.25
C. 3.75
D. 4
E. 4.5

Kudos for a correct solution.

A. 3
B. 3.25
C. 3.75
D. 4
E. 4.5

Kudos for a correct  solution .

Cadaver · Answer

B - 3.25

Total days worked 50 + 52 + 60 = 162

Total Weeks 25+13+!2 = 50

Avg 162/50 = 3.25

chetan2u · Answer

ans B 3.25.. ans is too straight forward to be correct..
 so may be missing something here
 if i take the entire year to be 52 weeks ans will be closer to 3.1, which would mean ans is A..3

buddyisraelgmat · Answer

Total days worked 50 + 52 + 60 = 162

Total Weeks 25+13+!2 = 50

Avg 162/50 = 3.24

Ans - B

harshpopo26 · Answer

according to the question, we have 50 weeks=350 days. question asks for per week for the year, i think we should add two more weeks to divide by..
50+52+60=162/52 =3.11

A

TudorM · Answer

Hi Bunuel,

This is a weighted average problem.

We will weigh every of the number of weeks with its number of workdays accordingly:

(25 x 2 + 13 x 4 + 12 x 5) / 25 + 13 + 12 = 162/ 50 = 324 / 100 = approx 3.25

CORRECT RESPONSE B

kdatt1991 · Answer

The question stem is asking for 'average number of days worked per week for the year' which means the total number of days worked within the year/the total number of weeks in that year. The total number of days worked in that year: (2*25) + (4*13) + (5*12) = 162 The total number of weeks in that year: 25 + 13 + 12 = 50 Therefore 'average number of days worked per week for the year' = 162/50..... 81/25 which is (9/5)*(9/5) and thus is slightly less than (2)*(2) = 4. So it is approx. 3.75! I think the answer is C. Please consider giving me KUDOS if you felt this post was helpful! Thanks.

EMPOWERgmatRichC · Answer

Hi All,

This is an awkwardly worded question, since it's not perfectly clear if we're supposed to consider a year to be 52 weeks OR if we're only supposed to consider the 50 weeks that Mohammad actually worked. The GMAT tends to be far more meticulous with the wording of its questions.

Hi kdatt1991,

You have to be MORE careful with your estimations and generalizations....

9/5 = 1.8

So (9/5)(9/5) = (1.8)^2

If you do that calculation, you'll find that your estimation is incorrect (and that you're leaning towards one of the wrong answers). When dealing with future questions, if the answers are relatively "close" together, you have to do precise work to make sure that you're getting the correct answer.

GMAT assassins aren't born, they're made,
Rich

peachfuzz · Answer

I agree with Rich.
Hmmm sneaky question. Do we count the 2 weeks where he presumably worked 0 days? I did because the question asked for days worked per week for the year (52 weeks).

(2*0 + 12*5 + 13*4 + 25*2) / 52 = 3.1

Answer: A

The answer choice 3 is still unusual given its relatively far away from 3.1

PareshGmat · Answer

Answer = B. 3.25

Average  = \frac{25*2 + 13*4 + 12*5}{25+13+12} = \frac{162}{50} = \frac{324}{100} \approx{3.25}

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

We can use our knowledge of weighted average to solve. Mohammad worked a total of 50 weeks (25 + 13 + 12), so 25/50 of them consisted of 2 work days, 13/50 of 4 workdays, and 12/50 of 5 workdays. If we reduce the fractions we then have: 1/2 * 2 + 13/50 * 4 + 6/25 * 5, or 1 + 26/25 + 6/5. We can convert to a common denominator (25/25 + 26/25 + 30/25 = 81/25) or decimals (1 + 1.04 + 1.2), but either way we end up with an average of 3.24, which is closest to B. Alternatively, we can recognize that 50% of his weeks had 2 workdays and the other 50% had 4 or 5, so the correct answer should be pretty close to the average of 2 and 4.5, which is conveniently 3.25.

In 2013, Mohammads work weeks consisted of 2, 4, or 5 days of work.

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