himu wrote:If @ represents the tens digit of integer n = 194,7@6, what is @?
(1) n is divisible by 4
(2) n is divisible by 3
Target question: What is the value of digit @?
Statement 1: 194,7@6 is divisible by 4
A number is divisible by 4 if the number created by the last two digits is divisible by 4.
For example, we know that 8712 is divisible by 4 since 12 is divisible by 4
Similarly, we know that 14788 is divisible by 4 since 88 is divisible by 4
So, if 194,7@6 is divisible by 4, then it must be the case that @6 is divisible by 4
Since 16, 36, 56, 76, and 96 are all divisible by 4, @ could equal 1, 3, 5, 7 or 9.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 194,7@6 is divisible by 3
A number is divisible by 3 if the sum of its digits is divisible by 3
For example, we know that 732 is divisible by 3 since its digits add to 12, and 12 is divisible by 3.
Similarly, we know that 111,123 is divisible by 3 since its digits add to 9, and 9 is divisible by 3.
So, if 194,7@6 is divisible by 3, then it must be the case that the sum of 1+9+4+7+@+6 must be divisible by 3
So, @ could equal 0, 3, 6 or 9.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 tells us that @ could equal 1, 3, 5, 7 or 9
Statement 2 tells us that @ could equal 0, 3, 6 or 9
So, the statements combined tell us that @ could equal 3 or 9
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
