If N is a positive, three-digit integer, what is the hundreds digit of N?
(1) The hundreds digit of N+120 is 7.
(2) The tens digit of N+15 is 9
Here's the rationale behind my answer above.
Target question: What is the hundreds digit of N?
Statement 1: The hundreds digit of N+120 is 7
Let's examine the range of possible values for N.
N can be as small as 580 (since 580+120=700) and N can be as large as 679 (since 679+120=799)
So,
580 < N < 679
As we can see,
the hundreds digit of N can be either 5 or 6
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The tens digit of N+15 is 9
Since there's no information about the hundreds digit, we immediately know that statement 2 is NOT SUFFICIENT.
However, let's see what we can conclude from statement 2.
If the tens digit of N+15 is 9, then N can be as small as ?75 (since ?75+15=?90), and N can be as large as ?84 (since ?84+15=?99)
Aside: The question mark represents the unknown hundreds digit
So,
?75 < N < ?84
Statements 1 and 2 combined
Statement 1 tells us that
580 < N < 679
Statement 2 tells us that
?75 < N < ?84
At this point, we can spot some possible values of N that will yield conflicting answers to the
target question.
Case a: N =
582, in which case
the hundreds digit is 5
Case b: N =
679, in which case
the hundreds digit is 6
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
