How many different 3-digit . . .

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

How many different 3-digit . . .

by Vincen » Wed Sep 27, 2017 6:42 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

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?

Quote

Source: Beat The GMAT — Problem Solving | Wed Sep 27, 2017 6:42 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » 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 [email protected]