GreenlightTestPrep 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

*I'll post a full solution in 2 days

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 both1, 2, 4, 5, 6, 7, 8, and 9

TOTAL =

82-digit integers that DO NOT begin with a 3, end with a 3, or bothIn 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) =

723-digit integers that DO NOT begin with a 3, end with a 3, or bothIn 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) =

270So, the TOTAL number of integers that DO NOT meet the given condition =

8 +

72 +

270 =

350TOTAL number of integers that MEET the given condition

So, the =

499 -

350 = 149

Answer: A

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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