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How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

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by BTGModeratorVI » Sun Jul 19, 2020 1:39 pm

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How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

(A) 222
(B) 245
(C) 291
(D) 315
(E) 343

Answer: B
Source: Magoosh
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Re: How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

by Jay@ManhattanReview » Tue Jul 21, 2020 5:40 am
BTGModeratorVI wrote: ↑
Sun Jul 19, 2020 1:39 pm
 How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

(A) 222
(B) 245
(C) 291
(D) 315
(E) 343

Answer: B
Source: Magoosh
The 3-digit numbers are greater than 299 are from 300 to 999, i.e. a total of 700 numbers.

*# of ways to fill hundreds digit = 5; only digits 3, 4, 5, 7 or 9 can work;
*# of ways to fill tens digit = 7; only digits 0, 2, 3, 4, 5, 7 or 9 can work;
*# of ways to fill units digit = 7; only digits 0, 2, 3, 4, 5, 7 or 9 can work;

Total such numbers = 5*7*7 = 245

Correct answer: B

Hope this helps!

-Jay
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Re: How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

by Brent@GMATPrepNow » Tue Jul 21, 2020 7:46 am
BTGModeratorVI wrote: ↑
Sun Jul 19, 2020 1:39 pm
 How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

(A) 222
(B) 245
(C) 291
(D) 315
(E) 343

Answer: B
Source: Magoosh
Take the task of creating the 3-digit numbers and break it into stages.

Stage 1: Select the first digit (hundreds digit)
Since the first digit can be 3, 4, 5, 7 or 9, we can complete stage 1 in 5 ways

Stage 2: Select the second digit (tens digit)
Since the second digit can be 0, 2, 3, 4, 5, 7 or 9, we can complete stage 2 in 7 ways

Stage 3: Select the third digit (units digit)
Since the third digit can be 0, 2, 3, 4, 5, 7 or 9, we can complete stage 3 in 7 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a 3-digit number) in (5)(7)(7) ways (= 2445 ways)

Answer: B

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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Re: How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

by Scott@TargetTestPrep » Sat Jul 24, 2021 3:40 am
BTGModeratorVI wrote: ↑
Sun Jul 19, 2020 1:39 pm
 How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?

(A) 222
(B) 245
(C) 291
(D) 315
(E) 343

Answer: B
Solution:

We have 5 choices (3, 4, 5, 7, and 9) for the hundreds digit, 7 choices (all 10 digits except the 3 mentioned ones) for each of the tens and the units digits. Therefore, we have 5 x 7 x 7 = 245 such numbers.

Answer: B

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