Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How many 5 digit numbers can be created if the following [#permalink]

Show Tags

13 Aug 2007, 05:10

1

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

57% (03:17) correct
43% (01:08) wrong based on 169 sessions

HideShow timer Statistics

How many 5 digit numbers can be created if the following terms apply: the leftmost digit is even, the second is odd, the third is a non even prime and the fourth and fifth are two random digits not used before in the number?

Left most can be chosen from 2,4,6,8 ( 4 ways)
2nd one
Can be split into
a)When 9 is chosen then 1 ways is how 2nd digit is chosen and 3rd digit then can be chosen from 1,3,5,7 (4ways)

b)and when 9 is not chosen then 2nd digit can be chosen from ( 4 ways)
and 3rd in 4 ways

First digit: (2, 4, 6, 8)
Second : (1, 3, 5, 7, 9)
Third : (1, 3, 5, 7)

then the last two digits have to be digits that haven't be used.

BUT, we can't assume we're used three digits already. The second and third digit can be the same one. We could have it startout as 233 and that would fall within the rules.

I don't know how to come to the correct answer, but I'm fairly positive that we can't say 4*5*4*7*6

If we consider the five digits to be {a,b,c,d, &e}

a is even, so that leaves us with four options [2,4,6,or 8]

b is odd, so that leaves us with five options [1,3,5,7,or 9]

c is a non-even prime, so that leaves us with three options [3,5, or 7]

and d & e are random digits that are not repeated which leaves us with the possibility of eight and seven random possibilities;

with that said, if we multiply the various options together we get the total outcomes possible.

4*5*3*8*7 = 3360

Answer is C!

I agree with the 4*5*3 (forgot about 1 not being prime) but what about after that? don't you have to take into account that under some circumstances you won't have 8 choices left? what if the first digits are 235...this leaves us with only 7 choices for the 4th digit and 5 for the 5th. don't we have to take this into account at all?

[quote="eschn3am"][quote="VAGMAT"]If we consider the five digits to be {a,b,c,d, &e}

a is even, so that leaves us with four options [2,4,6,or 8]

b is odd, so that leaves us with five options [1,3,5,7,or 9]

c is a non-even prime, so that leaves us with three options [3,5, or 7]

and d & e are random digits that are not repeated which leaves us with the possibility of eight and seven random possibilities;

with that said, if we multiply the various options together we get the total outcomes possible.

4*5*3*8*7 = 3360

Answer is C![/quote]

I agree with the 4*5*3 (forgot about 1 not being prime) but what about after that? don't you have to take into account that under some circumstances you won't have 8 choices left? what if the first digits are 235...this leaves us with only 7 choices for the 4th digit and 5 for the 5th. don't we have to take this into account at all?[/quote]

The question says "How many numbers..." I understood the question to read that is the max number of possibilities that are possible. So, it's possible that to get the max number of possibilities, out of ten possibile numbers for the fourth and fifth digits, the first number and the third numbers could be the same, and the second be an odd number so that leaves 8 possibilities for the fourth number and 7 possibilities for the fifth number.

If we consider the five digits to be {a,b,c,d, &e}

a is even, so that leaves us with four options [2,4,6,or 8]

b is odd, so that leaves us with five options [1,3,5,7,or 9]

c is a non-even prime, so that leaves us with three options [3,5, or 7]

and d & e are random digits that are not repeated which leaves us with the possibility of eight and seven random possibilities;

with that said, if we multiply the various options together we get the total outcomes possible.

4*5*3*8*7 = 3360

Answer is C!

I agree with the 4*5*3 (forgot about 1 not being prime) but what about after that? don't you have to take into account that under some circumstances you won't have 8 choices left? what if the first digits are 235...this leaves us with only 7 choices for the 4th digit and 5 for the 5th. don't we have to take this into account at all?

I am getting 2688
4*3*8*7+4*12*7*6
there are 3 combinations when 2nd and 3rd digit are same and 12 combinations when they are different, accordingly available choices for 4th digit are 8 and 7 respectively, similarly for 5th digit, they are 7 and 6 respectively.

I am not following..either its too late in the day or my brain is just plain ol..fried

beckee529 wrote:

racha24 wrote:

eschn3am wrote:

VAGMAT wrote:

If we consider the five digits to be {a,b,c,d, &e}

a is even, so that leaves us with four options [2,4,6,or 8]

b is odd, so that leaves us with five options [1,3,5,7,or 9]

c is a non-even prime, so that leaves us with three options [3,5, or 7]

and d & e are random digits that are not repeated which leaves us with the possibility of eight and seven random possibilities;

with that said, if we multiply the various options together we get the total outcomes possible.

4*5*3*8*7 = 3360

Answer is C!

I agree with the 4*5*3 (forgot about 1 not being prime) but what about after that? don't you have to take into account that under some circumstances you won't have 8 choices left? what if the first digits are 235...this leaves us with only 7 choices for the 4th digit and 5 for the 5th. don't we have to take this into account at all?

I am getting 2688 4*3*8*7+4*12*7*6 there are 3 combinations when 2nd and 3rd digit are same and 12 combinations when they are different, accordingly available choices for 4th digit are 8 and 7 respectively, similarly for 5th digit, they are 7 and 6 respectively.

Great catch! Of course this question is not that straightforward! What is the OA?

If we consider the five digits to be {a,b,c,d, &e}

a is even, so that leaves us with four options [2,4,6,or 8]

b is odd, so that leaves us with five options [1,3,5,7,or 9]

c is a non-even prime, so that leaves us with three options [3,5, or 7]

and d & e are random digits that are not repeated which leaves us with the possibility of eight and seven random possibilities;

with that said, if we multiply the various options together we get the total outcomes possible.

4*5*3*8*7 = 3360

Answer is C!

I agree with the 4*5*3 (forgot about 1 not being prime) but what about after that? don't you have to take into account that under some circumstances you won't have 8 choices left? what if the first digits are 235...this leaves us with only 7 choices for the 4th digit and 5 for the 5th. don't we have to take this into account at all?

I am getting 2688 4*3*8*7+4*12*7*6 there are 3 combinations when 2nd and 3rd digit are same and 12 combinations when they are different, accordingly available choices for 4th digit are 8 and 7 respectively, similarly for 5th digit, they are 7 and 6 respectively.

Just perfect.. It took time for me to before the bulb could lighten up !

For the benefit of those who could not understand, let me try and explain:

1st digit can be chosen in 4 ways : 2,4,6, 8
2nd digit can be choosen in 5 ways : 1 3 5 7 9
3rd digit can be choosen in 3 ways 3 5 7
4th in 7
5th in 6
But as per question 4th and 5th digit should have been used at 1st, 2nd and 3rd place. But there are no such restriction for 2nd and 3rd digit.
And depending on whether 2nd and 3rd digits are same or different, it can be how many digits we have for 4th and 5th digit.
2 and 3rd digit can be as follows ;
13 15 17
33 35 37
53 55 57
73 75 77
93 95 97
So, we have 3 combinations of same number and 12 combination for different number.
When we have same numbers, number of digits available is 1 more for 4th and 5th places.

How many 5 digit numbers can be created if the following terms apply: the leftmost digit is even, the second is odd, the third is a non even prime and the fourth and fifth are two random digits not used before in the number?

a) 2520 b) 3150 c) 3360 d) 6000 e) 7500

In my way:C(4,1)C(5,1)C(3,1)A(7,2)+C(4,1)C(5,1)C(3,1)A(8,2)

But there is no correct answer in my way...

I got D, but not really sure.

Say the number is ABCDE
Possible A = 2,4,6,8 => Total = 4
Possible B = 1,3,5,7,9 => Total = 5
Possible C = 3,5,7 => Total =3
Possible D & E = Anything hasn't used before, say x and x
Together, we have total possibility of 4*5*3*x*x = 60*x^2

Since we know the answer must be divisible 60, B is out.
We also know that the answer must be divisible by x^2
So for A, 252/6 = 42
for C, 336 / 6 = 56
for D, 600/6 = 100
For E, 750/6 = 125

Looks like on D is possible answer since it is in term of 10*10 square. However, 10 is too high to use here, I think, so I am not sure.
I need to point out that it is unclear to me fron the question if we can use the same number for the last two digits.

1st digit is an even integer hence 5 choices
2nd digit is an odd integer hence 5 choices
3rd digit is non-even prime hence 3 choices
4th digit should be a random number which is not one of the other 3 hence 7 choices
5th digit should be a random number which is not one of the other 4 hence 6 choices

Therefore no. of choices =5*5*3*7*6=3150
_________________

This is the first time I've ever posted on this site before so bear with me if I do something retarded. Anyway... here is how I see the problem:

There are 3 cases:

1) The 2nd and 3rd digit are equal.
2) The 2nd and 3rd digit are different and the 2nd digit is prime.
3) The 2nd and 3rd digit are different and the 2nd digit is prime.

In the first case you have 5*3*1*8*7 = 840 choices because if the 2nd and third digit are equal then the second digit must be chosen from the same set as the third and the third digit must be the same as the second.

In the second case you have 5*3*2*7*6 = 1260 choices because if the 2nd digit is prime you only can choose 3, 5, or 7 and since the third digit must be different you only get 2 choices.

In the 3rd case you have 5*2*3*7*6 = 1260 choices because if the 2nd digit is not prime you can only choose 1 or 9. But you still can choose any of the three for the third digit.

So, 840 + 1260 + 1260 = 3360, which is C.

I'm not positive about this answer but I think it is correct. Does anyone know what the official guide says? What problem number from what book is it?

This is the first time I've ever posted on this site before so bear with me if I do something retarded. Anyway... here is how I see the problem:

There are 3 cases:

1) The 2nd and 3rd digit are equal.
2) The 2nd and 3rd digit are different and the 2nd digit is prime.
3) The 2nd and 3rd digit are different and the 2nd digit is NOT prime.

In the first case you have 5*3*1*8*7 = 840 choices because if the 2nd and third digit are equal then the second digit must be chosen from the same set as the third and the third digit must be the same as the second.

In the second case you have 5*3*2*7*6 = 1260 choices because if the 2nd digit is prime you only can choose 3, 5, or 7 and since the third digit must be different you only get 2 choices.

In the 3rd case you have 5*2*3*7*6 = 1260 choices because if the 2nd digit is not prime you can only choose 1 or 9. But you still can choose any of the three for the third digit.

So, 840 + 1260 + 1260 = 3360, which is C.

I'm not positive about this answer but I think it is correct. Does anyone know what the official guide says? What problem number from what book is it?

Well, the problem states that the first digit must be even.

According to the arithmetic review of the official guide as well as wikipedia, 0 is an even number, which makes sense based upon the definition of an even number.

So, the choices for the first number are { 0, 2, 4, 6, 8 }

Well, the problem states that the first digit must be even.

According to the arithmetic review of the official guide as well as wikipedia, 0 is an even number, which makes sense based upon the definition of an even number.

So, the choices for the first number are { 0, 2, 4, 6, 8 }

If the first digit were 0, it would not be a five-digit number

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...