Brent@GMATPrepNow wrote:How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149
B) 150
C) 159
D) 199
E) 200
Here's a different approach:
There are
499 integers from 1 to 499 inclusive.
Let's determine how many of those
499 integers DO NOT meet the condition of beginning with a 3, ending with a 3, or both
1-digit integers that DO NOT begin with a 3, end with a 3, or both
1, 2, 4, 5, 6, 7, 8, and 9
TOTAL =
8
2-digit integers that DO NOT begin with a 3, end with a 3, or both
In the tens position, we can have 1, 2, 4, 5, 6, 7, 8, or 9 (
8 possibilities)
In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 (
9 possibilities)
TOTAL number of 2-digit integers that DO NOT begin with a 3, end with a 3, or both = (
8)(
9) =
72
3-digit integers that DO NOT begin with a 3, end with a 3, or both
In the hundreds position, we can have 1, 2, or 4 (
3 possibilities)
In the tens position, we can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 (
10 possibilities)
In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 (
9 possibilities)
TOTAL number of 3-digit integers that DO NOT begin with a 3, end with a 3, or both = (
3)(
10)(
9) =
270
So, the TOTAL number of integers that DO NOT meet the given condition =
8 +
72 +
270 =
350
TOTAL number of integers that MEET the given condition
So, the =
499 -
350 = 149
Answer: A
Cheers,
Brent
