How many even 4 digit number can be made using all the digits from 2, 4, 5 and 8, without repetition?
A) 4*4*4*4
B) 3*4*4*4
C) 3*3*3*3
D) 3*3*2*1
E) 3*2*2*1
The OA is D.
Experts, how can I get the correct answer here?
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
How many even four digit number can be made using all . . .
This topic has expert replies
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi M7MBA,
We're asked to find the total number of EVEN 4-digit integers using the digits 2, 4, 5 and 8, but WITHOUT repetition. This question is a permutation question with one specific 'restriction' that we have to deal with first:
Since the 4-digit integer must be EVEN, it MUST end with 2, 4 or 8. There are 3 options for the 4th digit. Once we place one of those digits....
There will be 3 options for the first digit. Once we place one of those digits...
There will be 2 options for the second digit. Once we place one of those digits...
There will be 1 option for the third digit.
Total options = (3)(3)(2)(1) = 18
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're asked to find the total number of EVEN 4-digit integers using the digits 2, 4, 5 and 8, but WITHOUT repetition. This question is a permutation question with one specific 'restriction' that we have to deal with first:
Since the 4-digit integer must be EVEN, it MUST end with 2, 4 or 8. There are 3 options for the 4th digit. Once we place one of those digits....
There will be 3 options for the first digit. Once we place one of those digits...
There will be 2 options for the second digit. Once we place one of those digits...
There will be 1 option for the third digit.
Total options = (3)(3)(2)(1) = 18
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7271
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
M7MBA wrote:How many even 4 digit number can be made using all the digits from 2, 4, 5 and 8, without repetition?
A) 4*4*4*4
B) 3*4*4*4
C) 3*3*3*3
D) 3*3*2*1
E) 3*2*2*1
The OA is D.
Experts, how can I get the correct answer here?
Since the 4-digit number has to be even, the units digit must be either 2, 4 or 8. Therefore, the units digit has 3 choices. Since the digit can't be repeated, the thousands digit now has 3 choices, the hundreds 2 choices and the tens 1 choice. So there are 3 x 2 x 1 x 3 = 3 x 3 x 2 x 1 such 4-digit even numbers.
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
