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How many different 3-digit numbers are greater than 299 and

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by Brent@GMATPrepNow » Fri Mar 15, 2019 1:09 pm
BTGmoderatorLU wrote:Source: Magoosh

How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

A. 222
B. 245
C. 291
D. 315
E. 343

The OA is B
Take the task of creating the 3-digit numbers and break it into stages.

Stage 1: Select the first digit (hundreds digit)
Since the first digit can be 3, 4, 5, 7 or 9, we can complete stage 1 in 5 ways

Stage 2: Select the second digit (tens digit)
Since the second digit can be 0, 2, 3, 4, 5, 7 or 9, we can complete stage 2 in 7 ways

Stage 3: Select the third digit (units digit)
Since the third digit can be 0, 2, 3, 4, 5, 7 or 9, we can complete stage 3 in 7 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a 3-digit number) in (5)(7)(7) ways (= 2445 ways)

Answer: B
--------------------------

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Cheers,
Brent
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by Scott@TargetTestPrep » Tue Mar 19, 2019 6:02 pm
BTGmoderatorLU wrote:Source: Magoosh

How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

A. 222
B. 245
C. 291
D. 315
E. 343

The OA is B
The first (or hundreds) digit has 5 choices (digits 3 to 9, excluding 6 and 8). Each of the second (or tens) and the third (or units) digits has 7 choices (digits 0 to 9, excluding 1, 6 and 8). Therefore, the number of 3-digit numbers greater than 299 that do not contain the digits 1, 6, or 8 is

5 x 7 x 7 = 245

Answer: B

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