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largest of seven

by sanju09 » Tue Mar 03, 2009 4:39 am
Is the largest of seven consecutive integers an odd number?

(1) The product of the integers is even.

(2) The sum of the integers is zero.
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by DanaJ » Tue Mar 03, 2009 4:51 am
1 means that there is at least one even number among the seven consecutive numbers, which is actually quite obvious, since of any two consecutive numbers you have one that is even.

2 actually tells you that the integers are 3 on each side of zero. This can be demonstrated using the progression formula:
Consider a = smallest
then the next one will be a + 1, third will be a + 2 and so on, until you reach the seventh, which will be a + 6. The sum of these integers will be :
a + a + 1 + ... + a + 6 = 7a + 1 + 2 + ... + 6 = 7a + 21. This has to be 0, making 7a = -21, with a = -3. So the numbers will be -3, -2, -1, 0, 1, 2, and 3.
However, I suggest just thinking of the whole thing logically: in order for the sum of consecutive integers to be zero, they have to basically "eliminate" one another, which only happens when they're symetrically on the sides of zero.
So 2 is sufficient for us to know that the greatest number is 3, which is indeed an odd number.

B will be my answer.
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