shahdevine wrote:What is the value of positive integer m?
(1) The remainder when any integer is divided by m is less than 5.
(2) The remainder when any integer is divided by m is an even number.
OA after some discussion.
Target question: What is the value of positive integer m?
Statement 1: The remainder when any integer is divided by m is less than 5.
Useful rule concerning remainders:
When positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
Given the above rule, statement 1 basically tells us that m is less than or equal to 6.
So,
m could equal 6, 5, 4, 3, 2 or 1
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The remainder when any integer is divided by m is an even number.
How is this possible?
If we're not sure, let's IGNORE statement 2 and see what happens with different values of m.
m = 5. If we divide some positive integer by 5, the remainder will be 4, 3, 2, 1, or 0 (some odd and some even)
m = 4. If we divide some positive integer by 4, the remainder will be 3, 2, 1, or 0 (some odd and some even)
m = 3. Here, the remainder will be 2, 1, or 0 (some odd and some even)
m = 2. Here, the remainder will be 1, or 0 (one odd and one even)
m = 1. The remainder will be 0 (EVEN) AHA!!!
This is the
only case where the remainder MUST BE EVEN.
So, it must be true that
m = 1
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
