How many numbers greater than 4000 can be formed from the figures 3,5,7,8,9 ?
256
215
216
220
217
4 digit numbers
This topic has expert replies
The correct answer should be 216.
First we deal with the 4 digit numbers: [] [] [] []
As for the first digit, only 5, 7 ,8 and 9 can be used, as utilizing 3 will lead to the number being smaller than 4000 thus does not satisfy the condition of >4000.
In order to find out how many 4 digit numbers that are >4000, we use 4P1x4P1x3P1x2P1=96 numbers.
(We pick one number from 5,7,8,9 for 1st digit, and at the 2nd digit, 3 can now be used hence there will still be 4 numbers to pick on for the 2nd digit, we have used 2 numbers so far, thus the 3rd digit having 3 to pick from, the last digit having 2 numbers to pick from. That explains for the eqn above)
Now we move on to five digit numbers. It is fairly straight forward since all five digit numbers are >4000, thus we can just use 5P5=120
120+96=216
note that when dealing with situations where the ORDER does matter eg. numbers and letters, we use nPr instead of nCr
hope this helps!
First we deal with the 4 digit numbers: [] [] [] []
As for the first digit, only 5, 7 ,8 and 9 can be used, as utilizing 3 will lead to the number being smaller than 4000 thus does not satisfy the condition of >4000.
In order to find out how many 4 digit numbers that are >4000, we use 4P1x4P1x3P1x2P1=96 numbers.
(We pick one number from 5,7,8,9 for 1st digit, and at the 2nd digit, 3 can now be used hence there will still be 4 numbers to pick on for the 2nd digit, we have used 2 numbers so far, thus the 3rd digit having 3 to pick from, the last digit having 2 numbers to pick from. That explains for the eqn above)
Now we move on to five digit numbers. It is fairly straight forward since all five digit numbers are >4000, thus we can just use 5P5=120
120+96=216
note that when dealing with situations where the ORDER does matter eg. numbers and letters, we use nPr instead of nCr
hope this helps!
-
- Senior | Next Rank: 100 Posts
- Posts: 46
- Joined: Sat Feb 27, 2010 2:58 am
- Location: GMAT
This is not a GMAT type question ! Please post only GMAT type question.
GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT, GMAT
What's life without GMAT !!!!!!!!
What's life without GMAT !!!!!!!!
- gmatboost
- Master | Next Rank: 500 Posts
- Posts: 312
- Joined: Tue Aug 02, 2011 3:16 pm
- Location: New York City
- Thanked: 130 times
- Followed by:33 members
- GMAT Score:780
I am definitely I proponent of calling out non-GMAT questions here, but I think this one is totally reasonable.
Greg Michnikov, Founder of GMAT Boost
GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.
Also, check out the most useful GMAT Math blog on the internet here.
GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.
Also, check out the most useful GMAT Math blog on the internet here.
Hi - I think GMAT Sucker may have also meant the language or wording of the question is not clear or GMAT like.
So if repetition of the digits is NOT ALLOWED, then the explanation above is perfect, and nicely done.
But if the repetition of digits is allowed, (which is not specified in question above) then we have a different answer naturally.
Thanks
Kaps
So if repetition of the digits is NOT ALLOWED, then the explanation above is perfect, and nicely done.
But if the repetition of digits is allowed, (which is not specified in question above) then we have a different answer naturally.
Thanks
Kaps