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How many different 3-digit numbers are greater than 299 and do not con

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How many different 3-digit numbers are greater than 299 and do not con [#permalink]

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New post 17 Aug 2017, 01:19
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Re: How many different 3-digit numbers are greater than 299 and do not con [#permalink]

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New post 17 Aug 2017, 02:04
Bunuel wrote:
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


3 digits number greater than 299 = 999-299 = 700

Three places to be filled to make desired 3 digit number = - - -

Total ways to fill the left most place = 5 choices {3, 4, 5, 7, 9}
Total ways to fill the Middle place = 7 choices {All digits except 1, 6 and 8}
Total ways to fill the Middle place = 7 choices {All digits except 1, 6 and 8}

Total Desired numbers = 5*7*7 = 245

Answer: Option B
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Re: How many different 3-digit numbers are greater than 299 and do not con [#permalink]

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New post 17 Aug 2017, 02:12
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Bunuel wrote:
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


Total numbers from 299 to 1000 (excluding both) = 999-300+1 = 700
hundred digit = 3,4,5,7 or 9 = 5 options
tenth digit = 7 options (0,2,3,4,5,7,9)
unit digit = 7 options (0,2,3,4,5,7,9)
5*7*7 = 245
B
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How many different 3-digit numbers are greater than 299 and do not con [#permalink]

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New post 17 Aug 2017, 10:50
Bunuel wrote:
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

I didn't calculate total number of three-digit integers between 300 and 1,000.

Using slot method to find three-digit numbers that are > 299 and that do not contain 1, 6, and 8

Integers to use if no other restrictions:

0, 1, 2, 3, 4, 5,6, 7, 8,9:

7 possibilities if no other restrictions

____ * ____ * ____

FIRST SLOT:
1) Numbers must be greater than 299. First is 300. So first slot's smallest number is 3
2) Not allowed: 0 and 2. Strike them from 7 total above, = 5 possibilities: 3, 4, 5, 7, 9

SECOND SLOT: only first restriction applies. Hence 7 possibilities for second slot

THIRD SLOT: same as second slot

__5__ * __7__ * __7__ = 245

Answer B

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Re: How many different 3-digit numbers are greater than 299 and do not con [#permalink]

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New post 17 Aug 2017, 11:35
Luckisnoexcuse wrote:
Bunuel wrote:
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


Total numbers from 299 to 1000 (excluding both) = 999-300+1 = 700
hundred digit = 3,4,5,7 or 9 = 5 options
tenth digit = 7 options (0,2,3,4,5,7,9)
unit digit = 7 options (0,2,3,4,5,7,9)
5*7*7 = 245
B


I dont get it

what if our first digit (hundenredth digit )is 3
it means now we need (0,2,4,5,7,9) on tenth , WHY DID YOU TOOK 3 for tenth digit? Its MENTIONED WE NEED DIFFERENT 3-digit number which means all digit must be different


Please help

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Re: How many different 3-digit numbers are greater than 299 and do not con [#permalink]

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New post 17 Aug 2017, 12:18
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rocko911 wrote:
Luckisnoexcuse wrote:
Bunuel wrote:
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


Total numbers from 299 to 1000 (excluding both) = 999-300+1 = 700
hundred digit = 3,4,5,7 or 9 = 5 options
tenth digit = 7 options (0,2,3,4,5,7,9)
unit digit = 7 options (0,2,3,4,5,7,9)
5*7*7 = 245
B


I dont get it

what if our first digit (hundenredth digit )is 3
it means now we need (0,2,4,5,7,9) on tenth , WHY DID YOU TOOK 3 for tenth digit? Its MENTIONED WE NEED DIFFERENT 3-digit number which means all digit must be different


Please help


Hi rocko911

the question says different three digit number and not different digits. for eg. 333 is different from 444, however the digits in both these numbers are same.

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Re: How many different 3-digit numbers are greater than 299 and do not con   [#permalink] 17 Aug 2017, 12:18
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