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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 am; Location: Delhi; Thanked: 1 times; Followed by:5 members

ds percents and time distance

by alltimeacheiver » Fri Feb 11, 2011 2:59 am

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.

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

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Source: Beat The GMAT — Data Sufficiency | Fri Feb 11, 2011 2:59 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Fri Feb 11, 2011 4:09 am

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.

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by Anurag@Gurome » Fri Feb 11, 2011 4:24 am

Question 2:

Distance traveled by train in 1 min (or 60 sec) = 88 Ã— 60 = 5,280 feet or 1 mile (as 1 mile = 5,280 feet), which implies time taken by the train to travel 40 miles = 40 minutes or the question can be transformed to "Does the train take more than 40 minutes to travel from station X to Y?"
(1) It took less than 45 minutes for the train to travel from station X to station Y is definitely NOT SUFFICIENT.

(2) It took more than 42 minutes for the train to travel from station X to station Y implies the answer to the main question is "yes". So, statement 2 is SUFFICIENT.

The correct answer is B.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pm; Thanked: 127 times; Followed by:10 members

by Night reader » Fri Feb 11, 2011 5:17 am

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

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pm; Thanked: 127 times; Followed by:10 members

by Night reader » Fri Feb 11, 2011 5:20 am

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.

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by Anurag@Gurome » Fri Feb 11, 2011 5:38 am

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.

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earnest10: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sun Apr 25, 2010 1:37 pm; Thanked: 1 times

by earnest10 » Fri Feb 11, 2011 6:07 am

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.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pm; Thanked: 127 times; Followed by:10 members

by Night reader » Fri Feb 11, 2011 6:09 am

>=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.

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rros0770: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Mar 14, 2008 1:39 pm; Thanked: 3 times

by rros0770 » Fri Feb 11, 2011 10:55 am

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

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pm; Thanked: 127 times; Followed by:10 members

by Night reader » Fri Feb 11, 2011 11:06 am

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

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rros0770: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Mar 14, 2008 1:39 pm; Thanked: 3 times

by rros0770 » Fri Feb 11, 2011 11:25 am

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?

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rros0770: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Mar 14, 2008 1:39 pm; Thanked: 3 times

by rros0770 » Fri Feb 11, 2011 11:33 am

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

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gmatapril: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Fri Jan 28, 2011 1:08 pm

by gmatapril » Fri Feb 11, 2011 1:43 pm

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.

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cyrwr1: Master | Next Rank: 500 Posts; Posts: 218; Joined: Sat Jul 24, 2010 2:43 pm; Thanked: 5 times

by cyrwr1 » Mon Feb 14, 2011 6:41 pm

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.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Tue Dec 19, 2017 9:38 am

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

Jeffrey Miller
Head of GMAT Instruction
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