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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Sun Oct 20, 2013 12:49 am

How is the answer D and not B
I am missing something with option 1. Please explain how option 1 is sufficient.[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 20, 2013 12:49 am

mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Sun Oct 20, 2013 1:24 am

Website W receives orders for its products every day. What is the Standard Deviation of the number of orders that Website W received daily for the past 5 days?
a) The Average(Arithmetic Mean) number of orders that Website W received per day for the past 5 days is equal to the greatest of the numbers of orders that Website W received daily for the past 5 days.
b) The range of the numbers of orders that Website W received daily for the past 5 days is equal to 0.

Q: SD = ?

St1: Max value = mean value (for a period of 5 days). This statement essentially states that all the data values are same, thus SD = 0.
SUFFICIENT

St2: Max - Min (for 5 days) = 0, thus when the data values are placed in ascending order all the values are again same. SD = 0
SUFFICIENT

Answer D

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Sun Oct 20, 2013 1:37 am

mevicks wrote:
Website W receives orders for its products every day. What is the Standard Deviation of the number of orders that Website W received daily for the past 5 days?
a) The Average(Arithmetic Mean) number of orders that Website W received per day for the past 5 days is equal to the greatest of the numbers of orders that Website W received daily for the past 5 days.
b) The range of the numbers of orders that Website W received daily for the past 5 days is equal to 0.
Q: SD = ?

St1: Max value = mean value (for a period of 5 days). This statement essentially states that all the data values are same, thus SD = 0.
SUFFICIENT

St2: Max - Min (for 5 days) = 0, thus when the data values are placed in ascending order all the values are again same. SD = 0
SUFFICIENT

Answer D

Hi Mate,

Is there any rule which says if the Mean=max value then all the numbers are same or just testing value will do the job in this case.

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mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Sun Oct 20, 2013 1:59 am

rakeshd347 wrote: Hi Mate,

Is there any rule which says if the Mean=max value then all the numbers are same or just testing value will do the job in this case.

There is no rule as such but the statement is easy to visualize if you break it down into simple steps:

1) receives orders for its products every day --> Ok. So atleast we have some number of orders everyday for a period of 5 days
2) mean value is usually below the maximum value, but wait here I see that mean is actually equal to the max and also the number of days are not just one! so all the values have to be that last value. (the orders have to be +ive integers so (x+x+x+x+x)/5 = x)

If you want to consider pure algebra:
Let the orders in increasing order be a, b, c, d, MAX
(note that a < b < c < d < MAX)

(Sum of all the orders) = 5 * MAX
Now the only way the sum of the 5 numbers could be equal to five times the MAX number is that they all are MAX.
ie a = b = c = d = MAX

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Oct 20, 2013 8:27 am

Great explanation, Vivek!

A big takeaway here is that, when it comes to Standard Deviation, the GMAT LOVES to test one's knowledge of the fact that standard deviation = 0 when all of the numbers in a set are identical.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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sahilchaudhary: Master | Next Rank: 500 Posts; Posts: 153; Joined: Mon Apr 11, 2011 7:13 amFollowed by: 7 members; Location: India; Thanked: 22 times; GMAT Score:540

by sahilchaudhary » Mon Oct 21, 2013 1:05 am

A states that average per day for last 5 days = greatest in last 5 days. It means that same no. of products was received on all 5 days. So S.D = 0.

B states that range is 0. It means that max and min values are same, which implies that all values are same. So S.D. = 0.

So, the answer is D

Sahil Chaudhary
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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members; Thanked: 50 times

by rakeshd347 » Mon Oct 21, 2013 2:10 am

Brent@GMATPrepNow wrote:Great explanation, Vivek!

A big takeaway here is that, when it comes to Standard Deviation, the GMAT LOVES to test one's knowledge of the fact that standard deviation = 0 when all of the numbers in a set are identical.

Cheers,
Brent

Hi Brent,

I knew that same numbers will have 0 SD. However, i got confused with the fact that Mean=Largest number means that all numbers are same. Specially with time limit under test conditions. vivek explained it though as clear as possible.

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