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

## what should be the answer

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### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

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

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

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

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

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

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770

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

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

### GMAT/MBA Expert

- Brent@GMATPrepNow
- GMAT Instructor
**Posts:**16207**Joined:**Mon Dec 08, 2008 6:26 pm**Location:**Vancouver, BC**Thanked**: 5254 times**Followed by:**1268 members**GMAT Score:**770