If (a + 3) / 5 is an integer, what is remainder when ‘a’ is divided by 5?
A)2
E) cannot be determined
The answer is A. The explanation said that if you subsitute a by 7 and divided it by 5, you will get 2. But I answered E because I tried subsituting a by 2. 2+3 equals an integer when divided by 5 but when 2 is divided by 5, tgere will be no remainder. Am I right ?
2/5 = 0 with remainder 2.
I didnt understand your explanation. Can you elaborate more ? @MITer94
When you divide 2 by 5, you get a quotient of 0 with a remainder of 2.
@gameplayer1234 What happens if a = -3? The quantity (-3 + 3)/5 is still an integer which satisfies the first clause of the problem, but what is the “remainder” when -3 is divided by 5?
In a more formal setting, the quotient and remainder are defined the following way: if we divide an integer a by a nonzero integer m, then there exists a unique pair of integers (q,r) (think “quotient”, “remainder”) such that a = qm + r and 0 ≤ r < |m|. The quotient is q and the remainder is r.
In your example where a = 2, we have 2 = 05 + 2, so the quotient is 0 and the remainder is 2. In my example where a = -3, we have -3 = (-1)5 + 2 so the remainder is still 2.
To expand on that, the complete set of integers a that work are {…, -8, -3, 2, 7, …} which is called a residue class modulo 5. But you don’t really need to know what modulo or residue classes mean for the SAT…but might be an interesting read anyway.
Thank you for such a perfect explanation @MITer94
Do you prefer the officisl college board tests or the the barrons test ??
In terms of preparation
I’m not that familiar with either source, but general consensus on CC seems to be to use the official CB materials first.