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# If 2 elemenst are dropped from setX{-10,-8,0,6,7},what will

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If 2 elemenst are dropped from setX{-10,-8,0,6,7},what will [#permalink]

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23 Mar 2011, 22:42
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If 2 elemenst are dropped from setX{-10,-8,0,6,7},what will be the %age change in its mean?

1.The median of the set will remain same .
2.The range will decrease by3.
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23 Mar 2011, 22:51
IMO C

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23 Mar 2011, 23:06
AnkitK wrote:
If 2 elemenst are dropped from setX{-10,-8,0,6,7},what will be the %age change in its mean?

1.The median of the set will remain same .
2.The range will decrease by3.

1.
-10,0,-7
-8,0,6
Have different means.
Not Sufficient.

2.
Range will become 14. Only possible when -10,7 are dropped.
-8,0,6
Mean = -2/3
Sufficient.

Ans: "B"
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23 Mar 2011, 23:12
Wow thanks fluke !

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23 Mar 2011, 23:24
Dear Fluke could you throw some light your answer.Also y hase you taken -7 when it 7 in the set ?
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23 Mar 2011, 23:54
AnkitK wrote:
Dear Fluke could you throw some light your answer.Also y hase you taken -7 when it 7 in the set ?

{-10,-8,0,6,7}

Typo. It is -10,0,7.

The stem says two elements are taken out. Find out the mean.

1. Median remains unaltered even after those two elements are taken out.
Original Median = 0 for {-10,-8,0,6,7}
If median remains unchanged, we are sure that the two elements that are taken out must be one each from pair {-10,-8} and {6,7}

Possible sets will be:
{-10,0,6},{-10,0,7},{-8,0,6},{-8,0,7} each having different means. Thus, we can't find the exact mean after two element are removed.
Not Sufficient.

2. The range will decrease by 3 after two elements are removed.

What is the original range: maximum-minimum= 7-(-10) = 17. It should be reduced by 3 making the new range 14.

For what combination of the set of the three will make the range=14. Only when minimum=-8 and maximum=6;
Range=6-(-8)=14.

Meaning thereby, the two elements that were removed were indeed {-10,7} and the set becomes {-8,0,6} making the mean = -2/3.
We found the exact mean here.
Sufficient.

If you want the brute force method, it is going to take some time.
In how many ways can you remove two elements from a set of 5. $$C^{5}_{2}=10 ways$$
{-10,-8,0,6,7}

Total possible ways to remove two elements:
{-10,-8} leaves {0,6,7}. Range= (7-0) = 7 != 14
{-10,0} leaves {-8,6,7}. Range= (7-(-8)) = 15 != 14
{-10,6} leaves {-8,0,7}. Range= (7-(-8)) = 15 != 14
{-10,7} leaves {-8,0,6}. Range= (6-(-8)) = 14 = 14. Possible
{-8,0} leaves {-10,6,7}. Range= (7-(-10)) = 17 != 14
{-8,6} leaves {-10,0,7}. Range= (7-(-10)) = 17 != 14
{-8,7} leaves {-10,0,6}. Range= (6-(-10)) = 16 != 14
{0,6} leaves {-10,-8,7}. Range= (7-(-10)) = 17 != 14
{0,7} leaves {-10,-8,6}. Range= (6-(-10)) = 16 != 14
{6,7} leaves {-10,-8,0}. Range= (0-(-10)) = 10 != 14

You can see that there is just one possible way.
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24 Mar 2011, 02:34
(1)

Mean = (-18 + 13)/5 = -5/5 = -1

Median = 0

So -10 and 7 go or -8 and 0 go, and mean will be different in each case, so insufficient

(2)

Range = 7 - (-10) = 17

New range which is less than previous range by 3 = 6 - (-8) = 14 which means -10 and 7 go, so answer - B.
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Re: mode Ds   [#permalink] 24 Mar 2011, 02:34
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