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How many numbers are there between 100 and 1000 in which all digits 14 Oct 2015, 21:20
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35% (medium)

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67% (01:35) correct 33% (01:54) wrong based on 330 sessions

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How many numbers are there between 100 and 1000 in which all digits are distinct.

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: https://www.GMATinsight.com
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How many numbers are there between 100 and 1000 in which all digits 15 Oct 2015, 04:45
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GMATinsight
How many numbers are there between 100 and 1000 in which all digits are distinct.

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: https://www.GMATinsight.com
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We know that numbers between 100 and 1000 will be 3 digit integers.

Let the arrangement be ABC where A,B,C represent distinct digits.

We have 9 options for A (as 0 can not start a 3 digit number), 9 options again for B and 8 for C, giving a total of 9*9*8 = 648 options.

B is the correct answer.
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How many numbers are there between 100 and 1000 in which all digits 02 Aug 2020, 02:52
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ENGRTOMBA2018
GMATinsight
How many numbers are there between 100 and 1000 in which all digits are distinct.

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: https://www.GMATinsight.com

We know that numbers between 100 and 1000 will be 3 digit integers.

Let the arrangement be ABC where A,B,C represent distinct digits.

We have 9 options for A (as 0 can not start a 3 digit number), 9 options again for B and 8 for C, giving a total of 9*9*8 = 648 options.

B is the correct answer.
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Hi,

9 options for B because of zero right?

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How many numbers are there between 100 and 1000 in which all digits 02 Aug 2020, 07:01
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Nups1324

9 options for B because of zero right?
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Yes, the first digit of the number must be nonzero, so we have only 9 choices for it, but when we consider the tens digit, zero becomes a possible value, and we again have 9 choices. That leaves 8 choices for the ones digit, so the answer is (9)(9)(8), which must end in '8' (multiplying units digits), so 648 is the only plausible answer.
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How many numbers are there between 100 and 1000 in which all digits 02 Aug 2020, 22:33
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IanStewart
Nups1324

9 options for B because of zero right?

Yes, the first digit of the number must be nonzero, so we have only 9 choices for it, but when we consider the tens digit, zero becomes a possible value, and we again have 9 choices. That leaves 8 choices for the ones digit, so the answer is (9)(9)(8), which must end in '8' (multiplying units digits), so 648 is the only plausible answer.
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Thank you so much Ian. :)

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How many numbers are there between 100 and 1000 in which all digits 26 Nov 2024, 06:51
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