Problem Solving

sana.noor wrote:How many even number of 4 digits can be formed with the figures 3,4,7,8 if repetitions are allowed?

64
128
12
256
255

Is it 128

Take the task of building 4-digit numbers and break it into stages.

Stage 1: Select the thousands digit
There are 4 digits to choose from (3, 4, 7 or 8), so we can accomplish stage 1 in 4 ways

Stage 2: Select the hundreds digit
Since repetitions are allowed, there are 4 digits to choose from (3, 4, 7 or 8), so we can accomplish stage 2 in 4 ways

Stage 3: Select the tens digit
We can accomplish stage 3 in 4 ways

Stage 4: Select the units digit
Since the 4-digit number must be even, the units digit must be EITHER 4 or 8
So we can accomplish stage 4 in 2 ways

By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus create a 4-digit number) in (4)(4)(4)(2) ways ([spoiler]= 128 ways[/spoiler])

Answer: B

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

sana.noor wrote:How many even number of 4 digits can be formed with the figures 3,4,7,8 if repetitions are allowed?

64
128
12
256
255

Is it 128

Take the task of building 4-digit numbers and break it into stages.

Stage 1: Select the thousands digit
There are 4 digits to choose from (3, 4, 7 or 8), so we can accomplish stage 1 in 4 ways

Stage 2: Select the hundreds digit
Since repetitions are allowed, there are 4 digits to choose from (3, 4, 7 or 8), so we can accomplish stage 2 in 4 ways

Stage 3: Select the tens digit
We can accomplish stage 3 in 4 ways

Stage 4: Select the units digit
Since the 4-digit number must be even, the units digit must be EITHER 4 or 8
So we can accomplish stage 4 in 2 ways

By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus create a 4-digit number) in (4)(4)(4)(2) ways ([spoiler]= 128 ways[/spoiler])

Answer: B

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

sana.noor wrote:How many even number of 4 digits can be formed with the figures 3,4,7,8 if repetitions are allowed?

64
128
12
256
255

Is it 128

Take the task of building 4-digit numbers and break it into stages.

Stage 1: Select the thousands digit
There are 4 digits to choose from (3, 4, 7 or 8), so we can accomplish stage 1 in 4 ways

Stage 2: Select the hundreds digit
Since repetitions are allowed, there are 4 digits to choose from (3, 4, 7 or 8), so we can accomplish stage 2 in 4 ways

Stage 3: Select the tens digit
We can accomplish stage 3 in 4 ways

Stage 4: Select the units digit
Since the 4-digit number must be even, the units digit must be EITHER 4 or 8
So we can accomplish stage 4 in 2 ways

By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus create a 4-digit number) in (4)(4)(4)(2) ways ([spoiler]= 128 ways[/spoiler])

Answer: B

Cheers,
Brent

Aside: For more information about the FCP, we have a free video on the subject: https://www.gmatprepnow.com/module/gmat-counting?id=775

Hmmm, looks like the BTG server is acting up