The sum of five consecutive integers is 35. How many of the five consecutive integers are prime numbers?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
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n is not 5 but 7.

Let the numbers be, n, n+1, n-1, n+2 and n-2; adding them we get=> n*5=35, so n is 7,

Numbers: 7,8,6,9,5; Primes: 5 and 7.

Both approaches are correct and yield the same result

First Approach: -
If we assume numbers as n, n+1, n+2, n+3 and n+4 then
n+n+1+n+2+n+3+n+4 = 5n+10 = 35
n=25/5 = 5

Numbers are 5,6,7,8 & 9
5 & 7 are prime

IMO C

Second Approach: -
If we assume numbers as n, n+1, n+2, n-1 and n-2 then
n+n+1+n+2+n-1+n-2 = 5n = 35
n=35/5 = 7

Numbers are 5,6,7,8 & 9
5 & 7 are prime

IMO C

But the end result of both approaches is the same.

It is better to assume 5 consecutive integers as n-2 ,n-1, n, n+1, n+2 since it eases the calculations in most cases.
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mean=35/5=7
sequence=5,6,7,8,9
2
C

The sum of 5, 6, 7, 8, and 9 is 35. Of these five numbers, 5 and 7 are prime numbers.

Answer: C
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