DS: MEDIAN

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Tue Sep 13, 2011 12:24 am

Q: OF THE 200 NO, 76% ARE LESS THAN OR EQUAL TO 80. IS THE MEDIAN NO. LESS THAN 70 ?

A: OF THE NO. GREATER THAN 70, 60% ARE LESS THAN OR EQUAL TO 80
B: OF THE NO. GREATER THAN 70, 40% ARE GREATER THAN 80

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Source: Beat The GMAT — Data Sufficiency | Tue Sep 13, 2011 12:24 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue Sep 13, 2011 1:19 am

76% means 152 <= 80. or 48>80 Thus median <=80
let no. > 70=x.
b) then 40/100 * x = 48 or x = 120.
Thus 120 numbers >70 and 80 numbers <=70.
Still 70 can be a median if around 20 members = 70. Insufficient
a)as 60% <=80 it means 40%>80
A and b are same...
IMO E

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Tue Sep 13, 2011 2:07 am

we convert everything into numbers: of the 200 NO, 152 NO are <= value 80. Is the median less than value 70? OR 100 and 101 NO-s' average is < value 70?
we need to find whether 52 and 51 No-s are <= value 80? OR 51.5 NO-s <=80?
lets see our statements now

st(1) value 70 < 60%X <= value 80, where X is the NO within 70-80 interval. If 60% of is 52 NO, then 40% must be >80. But it's only 34-35 NO-s are >80. So the median is definitely above 70, as we need more NO-s (more than 51-51 NO-s) to be grabbed within interval 70-80.

st(2) the same as st(1) with reverse application

d

[email protected] wrote:Q: OF THE 200 NO, 76% ARE LESS THAN OR EQUAL TO 80. IS THE MEDIAN NO. LESS THAN 70 ?

A: OF THE NO. GREATER THAN 70, 60% ARE LESS THAN OR EQUAL TO 80
B: OF THE NO. GREATER THAN 70, 40% ARE GREATER THAN 80

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1947: Master | Next Rank: 500 Posts; Posts: 215; Joined: Sat Jun 14, 2008 4:24 pmFollowed by: 1 member; Thanked: 13 times

by 1947 » Tue Sep 13, 2011 7:36 am

looks like a very tough question.....
apart from just solution please post the approach and time it should take..

my take is E.....both A and B are giving same information.....and combined also can not solve....
I took 5+ minutes

Thanks

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[email protected]: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Tue Sep 13, 2011 9:36 am

1947 wrote:looks like a very tough question.....
apart from just solution please post the approach and time it should take..

my take is E.....both A and B are giving same information.....and combined also can not solve....
I took 5+ minutes

Thanks

cant get the method please explain

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1947: Master | Next Rank: 500 Posts; Posts: 215; Joined: Sat Jun 14, 2008 4:24 pmFollowed by: 1 member; Thanked: 13 times

by 1947 » Tue Sep 13, 2011 9:54 am

[email protected] wrote:
1947 wrote:looks like a very tough question.....
apart from just solution please post the approach and time it should take..

my take is E.....both A and B are giving same information.....and combined also can not solve....
I took 5+ minutes

Thanks

cant get the method please explain

This is the number line

x1........70.......x100......80..........x200

x152=80
so between 80 and x200 there are 48 numbers
Say between 70 and x200 there are Y numbers
Now statement B says between 80 and x200 there are 0.4Y numbers
i.e. 0.4Y = 48 so Y=120
so median can 70 also or anything more than 70 and less than 80
B insuff

A says same thing as B

so A,b together insuff .....so E

Please do tell the source and difficulty level if u know... Thanks

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TwiceBitten: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Dec 06, 2010 7:38 pm; Thanked: 1 times

by TwiceBitten » Sun Sep 18, 2011 7:52 pm

We know that there are total 200 numbers.
152 are less than or equal to 80 and 48 are more than 80.

A - of the Numbers greater than 70, 60% are less than or equal to 80.
40% of the numbers above 70 are more than 80.
But we know that numbers above 80 are 48. Hence 40% = 48. 100% = 120.

Hence 120 numbers are above 70.Hence median has to be more than 70. Sufficient.

B - In the same manner explained above, sufficient.

Hence answer is D

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dhonu121: Master | Next Rank: 500 Posts; Posts: 316; Joined: Sun Aug 21, 2011 6:18 amFollowed by: 6 members; Thanked: 16 times

by dhonu121 » Mon Sep 19, 2011 12:53 pm

Here is the number line
-----70--80------------
Now since 76% are <=80 median is definetely <80
To answer the question that whether median<70, we need to know the number of total number that are below 70.
None of A and B give that information.
Both A and B talk about the same thing.Also, the information that they give is relative, not absolute.
They just tell about the relative number based on the number of numbers that are between 70 and 80.
Hence this info is of no use.
THus E

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