Home » Test Prep » PSAT Test » What is the remainder if 3a + 5 is divided by 3?
If a positive integer a is divided by 7, the remainder is 4. What is the remainder if 3a + 5 is divided by 3?
A. 5
B. 6
C. 2
D. 3
E. 4
Correct Answer: C
Explanation/Reference:
Explanation:
The best way to solve this problem is to plug in an appropriate value for a. For example, plug-in 11 for a because 11 divided by 7 will give us a remainder of 4.
Then 3a + 5, where a = 11, gives us 38. Then 38 divided by 3 gives a remainder of 2.
The algebra method is as follows:
a divided by 7 gives us some positive integer b, with a remainder of 4.
Thus, a/7 = b 4/7 a/7 = (7b + 4)/7 a = (7b + 4) then 3a + 5 = 3 (7b + 4) + 5 (3a + 5)/3 = [3(7b + 4) + 5]/3 = (7b + 4) + 5/3The first half of this expression (7b + 4) is a positive integer, but the second half of this expression (5/3) gives us a remainder of 2.
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