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How many different 3-digit . . .

This topic has 1 expert reply and 1 member reply

How many different 3-digit . . .

Post Wed Sep 27, 2017 6:42 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

    The OA is B.

    I tried to make a list but it has so much numbers and I got tired. Is there an easier way to solve this PS question?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Sep 27, 2017 7:41 pm
    Hi Vincen,

    This prompt is essentially just a 'permutation' question, but it does have some minor 'quirks' to it that you have to be careful about to get the correct answer.

    We're asked for the total number of 3-digit numbers that:
    1) Can only use the digits 0, 2, 3, 4, 5, 7, 9
    2) Must be GREATER than 299.

    These restrictions will obviously limit the number of possibilities, but there's one other restriction that we have to remember: a 3-digit number CANNOT begin with a 0 (e.g. 045 is "45", which is a 2-digit number).

    The first digit can be: 3, 4, 5, 7, 9 (5 options)
    The second digit can be: 0, 2, 3, 4, 5, 7, 9 (7 options)
    The third digit can be: 0, 2, 3, 4, 5, 7, 9 (7 options)

    (5)(7)(7) = 245 total options

    Final Answer: B

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: Vincen
    Post Fri Sep 29, 2017 7:19 pm
    Thanks. I really appreciate it.

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