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# Aptitude - Percentage - Discussion

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"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

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.

Number of such number =14

 Required percentage = 14 x 100 % = 20%. 70

 Karthik said: (Wed, Jun 9, 2010 02:26:29 AM) Any short cut for this?

 Syed said: (Wed, Jun 9, 2010 01:50:45 PM) Ya there is a short cut the concept is : 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.

 Avnish said: (Sun, Jun 24, 2012 01:36:17 PM) In every 10 digits there is 1 or 9 are coming, So we can tell that what is the % of 2 out of 10, That is 20 % only.