"No one is as deaf as the man who will not listen."
- (Proverb)
4.
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
[A].
1
[B].
14
[C].
20
[D].
21
Answer: Option C
Explanation:
Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Let's look for the no. whose square ends with 1 from 1-10, we will find that there are only two such number that is 1 and 9. That is between 1-70 there will be 14 such number.
Now lets find the percentage. 14 is what percent of 70.
10% of 70 is 7
Therefore 20% of 70 will be 2 * 7 = 14 the answer is 20%.
Chandrakala said:
(Thu, Nov 18, 2010 05:34:41 AM)
What about 4? 4 is also squre, so 4, 24, 34, 44, 54, 64 also have squre that end in the digit 1.
Priya P. said:
(Thu, Dec 2, 2010 09:07:19 AM)
@chandrakala
Its not end in 1 digit, its end with digit 1
as (1)^2=1
(9)^2=81 ;8(1)
got it..
Saranya said:
(Fri, Feb 4, 2011 06:35:58 PM)
Thank you for your short cut syed.
Ross said:
(Wed, Mar 16, 2011 09:04:13 AM)
I see that number 10 is not included into consideration even though it has 1 in its digit unit, why?
Pankaj said:
(Mon, May 2, 2011 12:41:05 PM)
Very good priya.
Pankaj said:
(Mon, May 2, 2011 12:49:21 PM)
@ ROSS
The no 10 after squaring it does not end with 1.......
if u square to 1,11,19,21 it ends with 1
Squaring 10 = 10 x 10 = 100 it ends with 0
Squaring 11 = 11 x 11 = 121 it ends with 1
I think u got it.
Gopal said:
(Sat, Sep 3, 2011 07:32:29 AM)
@pankaj.
It is wrong method unit digit means endshould be 1 or 9.
And 10 will be end in 0 so 10 is not include.
Uttam said:
(Sun, Sep 18, 2011 07:54:54 AM)
Inside the 10 there are 2 digits which ends with 1 and 9.
Number 70 consists 7 tens.
So total no of digits that end with 1 and 9 in 70 are,
7*2=14.
So percentage= (14/70) *100=20.
Joape said:
(Mon, Oct 31, 2011 07:59:50 AM)
It does not count 10, 12, 13, 14, 15, 16, 17, 18.
and they did not state about the square in the question.
Naga said:
(Fri, Dec 2, 2011 10:35:38 PM)
I con't understad this problem
Daniel said:
(Wed, May 30, 2012 01:57:08 PM)
The question doesn't specify that the digits 1 or 9 must be the last digits, so clearly all the number in the teens, would qualitfy as nubers between 1 and 70 that have the digit 1 OR 9.
Required percentage =
% = 20%.