If the sum of 7 consecutive integers is x, which of the following must be true?
If the sum of 7 consecutive integers is x, which of the following must be true?
I. x is an even number
II. x is an odd number
III. x is a multiple of 7
Answer/Solution
III only
Steps/Work
I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 7p + 14 = 7 (p+2) => divisible by 7. There this must be true in all cases.
Therefore B is the answer.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 7p + 14 = 7 (p+2) => divisible by 7. There this must be true in all cases.
Therefore B is the answer.