GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
How many positive integers less than 500 can be formed using
[#permalink]
14 Apr 2018, 02:46
14 Apr 2018, 02:46
2
Expert Reply
4
Bookmarks
00:00
Question Stats:
40% (01:27) correct
59% (01:37) wrong based on 62 sessions
Hide Show timer Statistics
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
(A) 48
(B) 52
(C) 66
(D) 68
(E) 84
Re: How many positive integers less than 500 can be formed using
[#permalink]
20 Apr 2018, 03:35
20 Apr 2018, 03:35
3
\(500\) 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
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
Re: How many positive integers less than 500 can be formed using
[#permalink]
20 Apr 2018, 21:53
20 Apr 2018, 21:53
2
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
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
