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rss GMAT Practice Question (One of Hundreds)
n is an integer and n2 is divisible by 28. Which of the following must be true?
I. n2 is divisible by 49.
II. n is divisible by 4.
III. n2/28 is divisible by 7.
Correct Answer: C
The equation for an arithmetic sequence is an = a1 + d(n-1)
  1. It is important to realize that given the statement that n is an integer, it is impossible for n2 to have only one of any individual factor. For example if n were 6 = 3*2, then n2 would be 36 = 2*2*3*3. In other words, the number of occurrences of each individual factor is doubled.
  2. n2 is a multiple of 28 so we know that n2 has at least one factor of 7 and two factors of 2 (28 = 7*2*2). We also know from the above paragraph that n2 cannot just have one factor of 7, therefore n2 has at least two sevens in its factor tree.
  3. I. n2 has at least two factors of 7, so n2 must have a factor of 49.

    II. n2 could be 7*7*2*2 = 196 which would make n = 14. This is not divisible by 4.

    III. n2 has at least two factors of 7, so when you divide by 28, a number with only one factor of 7, at least one factor of 7 remains. Therefore n2/28 is divisible by 7.
  4. I and III are correct so the answer is C.