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but not the median?

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by sanju09 » Fri Nov 04, 2011 3:27 am
Melissa runs the 50-yard dash five times, with times of 5.4 seconds, 5.6 seconds, 5.4 seconds, 6.3 seconds, and 5.3 seconds. If she runs a sixth dash, which of the following would change the mean and mode of her scores, but not the median?
(A) 5.3 seconds
(B) 5.4 seconds
(C) 5.5 seconds
(D) 5.6 seconds
(E) 6.3 seconds
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by yasha_gmat » Fri Nov 04, 2011 4:08 am
IMO : A

Below is how I solved it
Median = 5.4 ( Should not change )
Mode = 5.4 ( Should change )
Mean = 5.6 ( Should Change )

I took cue from the answer choice after this point
Mode has to change, so the option 5.4 is ruled out
We know that Median should not change, but any value greater than 5.4 would change the median
( E.g 5.4+5.5 / 2 = 5.45 , 5.4+5.6 / 2 = 5.5 )
So the only other option is 5.3

Cross verify With 5.3 as the 6th value,
Median = 5.4+5.4/2 = 5.4 ( Not Changed )
Mode = 5.3 & 5.4 ( Changed )
Mean = 5.55 ( Changed )

OA Please?
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by GmatKiss » Fri Nov 04, 2011 4:15 am
IMO: A
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by user123321 » Fri Nov 04, 2011 4:25 am
is it A?

Can't be 6.3 or 5.5 because median will change
Can't be 5.4 because mode remains unchanged
Can't be 5.6 because mean remains unchanged

So should be 5.3 because median wont change & mean,mode will change.

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by sanju09 » Fri Nov 04, 2011 4:45 am
yasha_gmat wrote:IMO : A

Below is how I solved it
Median = 5.4 ( Should not change )
Mode = 5.4 ( Should change )
Mean = 5.6 ( Should Change )

I took cue from the answer choice after this point
Mode has to change, so the option 5.4 is ruled out
We know that Median should not change, but any value greater than 5.4 would change the median
( E.g 5.4+5.5 / 2 = 5.45 , 5.4+5.6 / 2 = 5.5 )
So the only other option is 5.3

Cross verify With 5.3 as the 6th value,
Median = 5.4+5.4/2 = 5.4 ( Not Changed )
Mode = 5.3 & 5.4 ( Changed )
Mean = 5.55 ( Changed )

OA Please?
You are correct!

Melissa’s mean time for the �rst �ve dashes is 5.6. Her times, in order from least to greatest, are: 5.3, 5.4, 5.4, 5.6, and 6.3. The middle score, or median, is 5.4. The number that appears most often, the mode, is 5.4. A score of 5.3 will mean that the mean will decrease and that the mode will no longer be 5.4 alone. The mode will now be 5.3 and 5.4. The median, however, will remain 5.4.
The mind is everything. What you think you become. –Lord Buddha



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Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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