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# How many positive integers less than 500 can be formed using

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How many positive integers less than 500 can be formed using [#permalink]  14 Apr 2018, 02:46
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Question Stats:

36% (01:49) correct 63% (01:15) wrong based on 11 sessions
How many positive integers less than 500 can be formed using the numbers 1, 2, 3, and 5 for the digits?

(A) 48
(B) 52
(C) 66
(D) 68
(E) 84
[Reveal] Spoiler: OA

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Kudos [?]: 465 [2] , given: 82

Re: How many positive integers less than 500 can be formed using [#permalink]  20 Apr 2018, 03:35
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$$500$$ is a three digit number so possible numbers below $$500$$ can be $$1$$ digit, $$2$$ digit, and $$3$$ digit numbers above $$100$$ and less than $$500$$
However not all the numbers are included only those numbers that are formed by use of $$1,2,3$$ and $$5$$

Three digit numbers:
There are three places for three digit numbers Hundreds, tens and unit so
for the hundreds place except $$5$$ all given number can be placed so there are $$3$$ possibilities
for the tens place there are $$4$$ possibilities and
for ones place there are $$4$$ possibilities too
in total $$3*4*4 = 48$$

For $$2$$ digits:
there are $$4$$ possibilities for tens place and $$4$$ possibilities for units place
therefore, $$4*4 = 16$$

For $$1$$ digit there is $$4$$ possibility
Therefore total possibility = $$48+ 16 + 4 = 68$$
option D
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern
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Kudos [?]: 30 [2] , given: 22

Re: How many positive integers less than 500 can be formed using [#permalink]  20 Apr 2018, 21:53
2
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Option D : 68

I. All single Digit Numbers = 4

II. All 2 digit Numbers = __ __ for each of the 2 blanks for a possible two digit Numbers we have 4 options ( 1, 2, 3, 5) so 4*4 = 16, in total 16 2 digit numbers can be formed

III. All 3 digit Numbers = __ __ __ except the 1st blank for a possible 3 digit number < 500 , we have 4 options for the other two blanks so 3*4*4 = 48 , in total 48 3 digit numbers < 500 can be formed

Total = 4+16+48 = 68
Manager
Joined: 29 Nov 2017
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Kudos [?]: 77 [1] , given: 99

Re: How many positive integers less than 500 can be formed using [#permalink]  08 May 2018, 03:46
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Oh!! thanks for the explantion, such question should be read quite carefully. Option A is quite tempting. but few ppl would think of single digit and two digit numbers.
Thanks!
Re: How many positive integers less than 500 can be formed using   [#permalink] 08 May 2018, 03:46
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