How many positive integers less than 500 can be formed using the digit

Question

How many positive integers less than 500 can be formed using the digits 1, 2, 3, 4, 5, assuming that repetitions are allowed?

A. 73
B. 100
C. 125
D. 130
E. 155

gmatophobia · Answer

The number can be a single-digit number, a two-digit number, or a three-digit number

Single Digit Number  :

The number of possible combinations = 5

Two Digit Number  :

_ _

The number of ways each of the tens and units places can be filled = 5 * 5 = 25

Three Digit Number  :

_ _ _

The number of ways the hundreds place can be filled = 4 
 The number of ways each of the tens and units places can be filled = 5 * 5 = 25

Total number of combinations possible = 5 + 25 + (25*4) = 130

Option D

princevora · Answer

please explain the extra 5 + 25. we dont have 0 as a digit.

gmatophobia · Answer

princevora  - Could you elaborate on your question?

We have added 5 because the number can have a single digit, and 25 because the number can have two digits.

zywx · Answer

Take 3 Places  a   b   c

For 2 digit numbers, we can have 5 possibilities for b and 5 for c - 5*5 = 25
For 1 digit numbers, 5 possibilities for c - 5

total 100 + 25 + 5 = 130

DanTheGMATMan · Answer

Straightforward permutation- have to split into scenarios with different numbers of digits:

https://www.youtube.com/watch?v=jpiyoMwn40U

user34745792203 · Answer

Hi,

in my opinion the answer has to be 100.

Three digit number given as:

XYZ

X:  {1,2,3,4}
 Y:  {1,2,3,4,5}
 Z:  {1,2,3,4,5}

# of integers  = 4*5*5 = 100

We cannot have single and double digit units because X and Y cannot be equal to 0.

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