How Many of The 900 Three Digit Numbers have at Least One Even Digit? GMAT Problem Solving

Question: How many of the 900 three digit numbers have at least one even digit?

(A) 100
(B) 101
(C) 102
(D) 775
(E) 875


Correct Answer
:
D

Solution and Explanation 
Approach Solution 1:

This above given sum can be solved by calculating the even digits and the odd digits. So by counting all numbers that are odd digits removing them from 900. The equation becomes 5(odd digits in hundreds place) x 5(odd digits in the tens place) x 5 (odd digits in units place). That makes the required outcome to be 125. Hence, to get the final required digit answer subtracting the original digit from the latter resultant makes:
(900-125) = 775.
Therefore the required option D is appropriate.

Approach Solution 2:

The above given sum can be solved by calculating the even digits and the odd digits.
We will find No. of numbers that have No even digit number.
Odd digits are 1,3,5,7,9
This implies that 5×5×5=125
So, No. of numbers with only the odd digits =125
No. of numbers with at least 1 even digit =900−125
This makes the total equal to 775
Therefore the required option D is appropriate.

Approach Solution 3:
Total 3 digit numbers= 900
There are only 5 odd numbers (1,3,5,7,9)
So 3 digit numbers having containing only odd digits = 5*5*5 = 125
So, 3 digit numbers containing at least one even digit = 900–125 = 775

“How many of the 900 three digit numbers have at least one even digit?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.


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