The average of a set of five distinct prime numbers is 10. If the medi

Question

The average of a set of five distinct prime numbers is 10. If the median of the set is 7, which of the following is the greatest possible value for a number in the set?

A. 13
B. 17
C. 19
D. 23
E. 29

neha283 · Answer

Set of 5 prime numbers with median 7 and mean 10
2,5,7,13,23. 
Largest number possible is 23.

Archit3110 · Answer

set = 2+5+7+13+23=50
IMO D

Manat · Answer

why was 3 not included in the set?

junii · Answer

@Buneul, pls can you explain is there any principle or logic?

medic19 · Answer

Organize the information and let x, y, z, w be the other 4 numbers that are not 7. With the information provided x + y + z + w = 43. Test out the numbers in the answers provided for W and work from there with x and y needing to be less than 7 and z and w needing to be greater than 7. You can also try different values for z as your work along (the values for x and y are much easier to test mentally as they include only 2,3,5). So when you get to the correct answer (D) you can see that 23 +   + 5 + 2 = 43, and you would have needed to test out different values for z (or 13).

lacktutor · Answer

I think we need to focus on answer choices. If a+b+7+c+d=50 and all set numbers are distinctive prime numbers(let’s say d is the greatest one), we can take all small prime numbers for a,b and c(a=2,b=3 and c=11) to get the value of d as the greatest prime number. So, we got d=27. That means d cannot be 29. 
Well, next big number is D(23). Is there any possible values for set numbers which d can be 23? Yes, {2,5,7,13,23} is the only choice. Answer choice D.

Posted from my mobile device

nick1816 · Answer

a<b<c<d<e are 5 prime numbers
a+b+c+d+e=50, Only possible when one of them is even. Hence a=2
We know median is 7, so c=7.
b can take only 2 values 3 or 5
Case 1- When b=3
2+3+7+d+e=50
d+e=38
We want to maximize e, Hence we have to minimize d.
if d=11 then e=27 not a prime
if d=13 then e=25 not a prime
if d=17 then e=21 not a prime
if d=19 then e=19 e and d must be distinct
Hence there is no value of d and e (d<e) are possible in this case

Case 2- When b=5
2+5+7+d+e=50
d+e=36
When d=11, e=25 not a prime
When d=13, e=23 (Bingo)

Vivek1707 · Answer

Key point to note in this question is that the question talks about  DISTINCT prime numbers 
To find the max value you need to minimize the other values

We know that the median is 7 Hence
a + b + 7 c + d = 50

Now to find the max value start minimizing the values of a and b, subtract the sum of a + b + 7 from 50 and test answer choices

For instance smallest two prime numbers are 2 , 3 so a = 2 , b = 3
2 + 3 + 7 + c + d = 50

Now c + d = is 50 - 2 - 3 - 7 = 38 
Now if you minus the answer choices one by one from 38 you will notice that none of them give you a prime number except 19 but since you need DISTINCT prime numbers 19 is not valid. Since we dint get an answer here try the next set of prime numbers

Next higher set of prime numbers for a and b would be take 2 , 5 
2 + 5 + 7 + c + d = 50 
So c + d = 36
Now 36 - 29 = 7 but wont work cause we need distinct nos
36 - 23 = 13 prime number works ---> done

The average of a set of five distinct prime numbers is 10. If the medi

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