alltimeacheiver wrote:What is the median number of employees assigned per project for the projects at Company Z?

(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

P=number of projects, M=median number of employees for all projects, E=number of employees per each project (all projects are considered), M=PE //midpoint, where PE is given in ascending (or descending order)
st(1) E>=4 and PE/4>=P*4 --> E/4>=4, E>=16 As the number of employees per each project may be >=16 we can not ascertain the exact value;
st(2) E=<2 and 7*PE/20=<P*2 --> E=<40/7 As the number of employees per each project may be =<40/7 we can not ascertain the exact value;
Combined st(1&2): given we have 25%+35%=60% and 100%-60%=40% <-- data about 40% of the projects is missing, hence we can not decide if 40% of projects falls within which interval.

IOM E

Anurag@Gurome wrote:Question 1:

Both the statements separately are NOT SUFFICIENT to answer the question.

Next combine both the statements: (1) covers the possibilities when there are 4 or more employees in each project, and (2) covers the possibilities when there are 2 or fewer employees in each project. This implies that no. of employees not covered for each project is 3. Therefore, 100% - (25% + 35%) = 40% of the projects have 3 employees assigned to each project. So, combining the statements is SUFFICIENT.

The correct answer is C.

@Anurag: why we shouldn't make assumption that the number of employees not covered for 40% of projects is >3 or =<1. Please explain what suggests in st(1) or (2), combined to imply x=3. 40% could be placed anywhere on the number line.

Anurag@Gurome wrote:Question 1:

Both the statements separately are NOT SUFFICIENT to answer the question.

Next combine both the statements: (1) covers the possibilities when there are 4 or more employees in each project, and (2) covers the possibilities when there are 2 or fewer employees in each project. This implies that no. of employees not covered for each project is 3. Therefore, 100% - (25% + 35%) = 40% of the projects have 3 employees assigned to each project. So, combining the statements is SUFFICIENT.

The correct answer is C.

Anurag,... can you please where the 3 is coming from. Thanks.

>=4 means {4,5,6} and =<2 means {1,2}
it can also be the case that none of the projects has 3 employees assigned. Please show me precise condition for 3.

Anurag@Gurome wrote:

Night reader wrote: @Anurag: why we shouldn't make assumption that the number of employees not covered for 40% of projects is >3 or =<1. Please explain what suggests in st(1) or (2), combined to imply x=3. 40% could be placed anywhere on the number line.

Statement 1: 25% of the project at company Z can have 4, 5, 6, 7, 8... employees.
Statement 2: 35% of the project at company Z can have 0, 1, or 2 employees.

# of employees: (0 to 2) (3) (> 4)
% of projects: (1 to 35%) (36% to 75%) (76% to 100%)

It can be seen that projects on either side of the 50% will have 3 employees. Therefore, 40% of the projects will have 3 employees and so the median value is 3.

Agree it's C

25% have 4+
35% have 1 or 2

40% of the projects left unaccounted for.

Would have to be 3 employees. If no project had 3 employees assigned to it then 40% of the projects would be left uaccounted for

40% may be anything, it's not specified in the problem

rros0770 wrote:Agree it's C

25% have 4+
35% have 1 or 2

40% of the projects left unaccounted for.

Would have to be 3 employees. If no project had 3 employees assigned to it then 40% of the projects would be left uaccounted for

25% assigned to either 4, 5, 6, 7, 8, 9, 10, 11....etc
35% assigned to 0, 1 or 2
40% left unnaccounted for.

Median would be the 50% mark, which would then fall under the 3 employee category

I'm under the impression it has to be 3 employees, I can't derive any other scenario in which this would not be the case, as we've already accounted for the 0 employees, 1 employee, 2 employee, and essentially the 4 employee to infinity employee scenarios...


What scenario would this be different for?

Got it- I see where our opinions differ here Night Reader:


Quoting you:
">=4 means {4,5,6} and =<2 means {1,2}
it can also be the case that none of the projects has 3 employees assigned. Please show me precise condition for 3. "


I believe the 2nd statetment would encompass none (0) ,1 or 2 employees

VERY TOUGH ONE.
More explanations please how is no. 3 derived

Anurag@Gurome wrote:

Night reader wrote: @Anurag: why we shouldn't make assumption that the number of employees not covered for 40% of projects is >3 or =<1. Please explain what suggests in st(1) or (2), combined to imply x=3. 40% could be placed anywhere on the number line.

Statement 1: 25% of the project at company Z can have 4, 5, 6, 7, 8... employees.
Statement 2: 35% of the project at company Z can have 0, 1, or 2 employees.

# of employees: (0 to 2) (3) (> 4)
% of projects: (1 to 35%) (36% to 75%) (76% to 100%)

It can be seen that projects on either side of the 50% will have 3 employees. Therefore, 40% of the projects will have 3 employees and so the median value is 3.

For the first one it is simple,

35% is either 0,1,2 ====>> 65% is >2 or

65% is 3,4,5,6,etc. but we know 4,5,6,etc. is 25% thus 40% must be 3.

Median is the middle number so the 49 and 51 % must be 3 employees. Hence, C is the answer for this.



Had the 25% been for only 4 employees, then the answer would be undefined.

I hope I helped.

A train traveled from station X to station Y at a constant speed of 88 feet per second. Is the distance that the train traveled from station X to station Y greater than 40 miles? (1 mile = 5,280 feet)

(1) It took less than 45 minutes for the train to travel from station X to station Y
(2) It took more than 42 minutes for the train to travel from station X to station Y

We can let d = the distance between station X and station Y. We need to determine whether d > 40 miles.
Since the distance is given in miles but the speed, or rate, is given in feet per second, we need to convert the distance from miles to feet. Since 1 mile = 5,280 feet, 40 miles = 40 x 5,280 = 211,200 feet.

Since rate x time = distance and we have a rate of 88 ft/s, we can change the question to:

Is 88t > 211,200 feet?

Is t > 2,400 seconds?

Since 2,400 seconds = 2,400/60 = 40 minutes, the question becomes:

Is t > 40 minutes?

Statement One Alone:

It took less than 45 minutes for the train to travel from station X to Station Y.

Since less than 45 minutes could mean 42 minutes or 38 minutes, statement one does not tell us whether t > 40 minutes. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

It took more than 42 minutes for the train to travel from station X to Station Y.

Statement two tells us that t is greater than 40 minutes.

Answer: B