The median of a certain data set of five numbers is 24.5. If a value k

Question

The median of a certain data set of five numbers is 24.5. If a value k is added to each number in the data set, then the new median becomes 28.5. What is the value of k?

A. 1
B. 2
C. 3
D. 4
E. 5

Archit3110 · Answer

median of 5 digits/5 = 24.5
sum of 5 digits= 122.5

when K is added then the median = 28.5
and sum= 5*28.5= 142.5

difference ; 142.5-122.5= 20 
since k is 5 times added so 20/5 = 4 IMO D

testcracker · Answer

hi

how can you conclude that "sum of 5 digits= 122.5" ?

thanks

Archit3110 · Answer

Sum of digits = "median/avg" * no of terms

In this case 24.5×5= 122.5 will.be sum.of 5 digits ..

Hope this helps..

Posted from my mobile device

testcracker · Answer

Archit3110

Well, the set can be,

1 , 2, 22.5, 23, 24

will you now think, the sum is 122.5 ...?

thanks

pranav0073 · Answer

5 term set - median is the middle term = 24.5
if k is added to each term - median is still the the middle trerm = 24.5 + k = 28.5

=> k = 4

Archit3110 · Answer

The median of a certain data set of five numbers is 24.5. If a value k is added to each number in the data set, then the new median becomes 28.5. What is the value of k?

A. 1
B. 2
C. 3
D. 4
E. 5

median of 5 digits/5 = 24.5
sum of 5 digits= 122.5

when K is added then the median = 28.5
and sum= 5*28.5= 142.5

difference ; 142.5-122.5= 20 
since k is 5 times added so 20/5 = 4 IMO D

hi

how can you conclude that "sum of 5 digits= 122.5" ?

thanks

Archit3110

Well, the set can be,

1 , 2, 22.5, 23, 24

will you now think, the sum is 122.5 ...?

thanks

NO it won't be..
Actually what I did is : for an odd set of equally spaced integers the avg of the set is always equal to the median . For eg 2,3,4 avg =median and if we add same no to all then also the avg = median stays same if 1 is added 3,4,5 ...
I used this logic to solve...

Posted from my mobile device

testcracker · Answer

median of 5 digits/5 = 24.5
sum of 5 digits= 122.5

when K is added then the median = 28.5
and sum= 5*28.5= 142.5

difference ; 142.5-122.5= 20 
since k is 5 times added so 20/5 = 4 IMO D

hi

how can you conclude that "sum of 5 digits= 122.5" ?

thanks

Archit3110

Well, the set can be,

1 , 2, 22.5, 23, 24

will you now think, the sum is 122.5 ...?

thanks

NO it won't be..
Actually what I did is : for an odd set of equally spaced integers the avg of the set is always equal to the median . For eg 2,3,4 avg =median and if we add same no to all then also the avg = median stays same if 1 is added 3,4,5 ...
I used this logic to solve...

Posted from my mobile device

I got it

but this is not an equally spaced set

thanks

Archit3110 · Answer

hi

how can you conclude that "sum of 5 digits= 122.5" ?

thanks

Archit3110

Well, the set can be,

1 , 2, 22.5, 23, 24

will you now think, the sum is 122.5 ...?

thanks

NO it won't be..
Actually what I did is : for an odd set of equally spaced integers the avg of the set is always equal to the median . For eg 2,3,4 avg =median and if we add same no to all then also the avg = median stays same if 1 is added 3,4,5 ...
I used this logic to solve...

Posted from my mobile device

I got it

but this is not an equally spaced set

thanks

Well it's not specifically given in question stem that it's not equally spaced ..
This was the only way I could think of while of solving this question, if you have any other better way to.solve kindly do share..

testcracker · Answer

Archit3110

Well, the set can be,

1 , 2, 22.5, 23, 24

will you now think, the sum is 122.5 ...?

thanks

NO it won't be..
Actually what I did is : for an odd set of equally spaced integers the avg of the set is always equal to the median . For eg 2,3,4 avg =median and if we add same no to all then also the avg = median stays same if 1 is added 3,4,5 ...
I used this logic to solve...

Posted from my mobile device

I got it

but this is not an equally spaced set

thanks

Well it's not specifically given in question stem that it's not equally spaced ..
This was the only way I could think of while of solving this question, if you have any other better way to.solve kindly do share..

hey its okay
I have tried the problem as follows

since a fixed number is added to every number of the set, this addition will affect all the numbers equally, for example, the difference between 4 and 6 is 2, now if 4 is added to each number, the numbers become 8 and 10, and the difference is still 2

so, I have just subtracted 24.5 from 28.5 to get 4

hope this helps and is clear!
thanks and cheers!

The median of a certain data set of five numbers is 24.5. If a value k

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The median of a certain data set of five numbers is 24.5. If a value k

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards