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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] New post 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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Re: How many positive integers less than 500 can be formed using [#permalink] New post 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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Re: How many positive integers less than 500 can be formed using [#permalink] New post 20 Apr 2018, 21:53
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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
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Re: How many positive integers less than 500 can be formed using [#permalink] New post 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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