buoyant wrote:If k is an even integer, what is the remainder when k is divided by 10?
(1) The remainder when k is divided by 5 is equal to the remainder when k is divided by 10.
(2) The remainder is greater than 3.
[spoiler]OA:C[/spoiler]
Target question: What is the remainder when k is divided by 10?
This question is a good candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Let's make a few observations:
2
4 divided by 10 equals 2 with remainder
4
7
0 divided by 10 equals 7 with remainder
0
8
6 divided by 10 equals 8 with remainder
6
2 divided by 10 equals 0 with remainder
2
As you can see, the remainder (when we divide by 10) will always be the same as the UNITS digit of k. So, we can write....
REPHRASED target question: What is the units digit of k?
Given: k is an EVEN integer
Since k is an EVEN integer, then we know that, the UNITS digit of k will be
0, 2, 4, 6, or 8.
Statement 1: The remainder when k is divided by 5 is equal to the remainder when k is divided by 10.
Let's examine all possible cases:
case a: units digit of k is
0: When k is divided by
5, the remainder is 0. When k is divided by
10, the remainder is also 0. So,
the units digit of k COULD be 0
case b: units digit of k is
2: When k is divided by
5, the remainder is 2. When k is divided by
10, the remainder is also 2. So,
the units digit of k COULD be 2
case c: units digit of k is
4: When k is divided by
5, the remainder is 4. When k is divided by
10, the remainder is also 4. So,
the units digit of k COULD be 4
case d: units digit of k is
6: When k is divided by
5, the remainder is 1. When k is divided by
10, the remainder is 6. So,
the units digit of k CANNOT be 6
case e: units digit of k is
8: When k is divided by
5, the remainder is 3. When k is divided by
10, the remainder is 8. So,
the units digit of k CANNOT be 8
Since
the units digit of k COULD be 0, 2 or 4, statement 1 is NOT SUFFICIENT
Statement 2: The remainder [when k is divided by 10] is greater than 3.
In other words, the
units digit of k COULD be 4, 6 or 8
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
the units digit of k COULD be 0, 2 or 4
Statement 2 tells us that
the units digit of k COULD be 4, 6 or 8
The ONLY possible scenario that satisfies BOTH statements is that
the units digit of k MUST be 4
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
