How many different 3digit 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
How many different 3digit numbers are greater than 299 and do not contain the digits 1, 6, or 8?
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The 3digit numbers are greater than 299 are from 300 to 999, i.e. a total of 700 numbers.BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:39 pmHow many different 3digit 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
*# 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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Take the task of creating the 3digit numbers and break it into stages.BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:39 pmHow many different 3digit 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
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 3digit 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:
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Cheers,
Brent
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Solution:BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:39 pmHow many different 3digit 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
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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