problem 2 digit integers, same digits, reverse order

Any integer can be written as the sum of terms where each term is the product of the digit and its position. For instance, in the number 25, 2 is the tens digit and 5 is the units digit. So 25 = 2*10 + 5*1. Likewise the integer 734 = 7*100 + 3*10 + 4*1.

If the two digit integer is tu where t is the tens and u is the units, then the integer can be written as 10t + u. Another 2-digit integer that has the same digits in reverse order will be 10u + t.


This is OG12 #182. The answer is A. Two detailed solutions are attached. If you cannot see the attachment, read it here

Hope that clears things up!
-Patrick

It helped indeed, thank you so much!

mepinoargote wrote:It helped indeed, thank you so much!

That's what I do

yea. I got that right also. It has to be a multiple of 11. but again don't you think that its on condition where any of the integer cannot be zero.

thanks.

Asif wrote:yea. I got that right also. It has to be a multiple of 11. but again don't you think that its on condition where any of the integer cannot be zero.

thanks.

The question says M and N are positive. And even if one of the digits is zero, their sum would still be a multiple of 11.
eg:

70 and 07 --> Sum = 77
20 and 02 --> Sum = 22

Hope this answers your question.

vipin85 wrote:70 and 07 --> Sum = 77
20 and 02 --> Sum = 22

Nice, I had not noticed this.

Asif wrote:yea. I got that right also. It has to be a multiple of 11. but again don't you think that its on condition where any of the integer cannot be zero.

thanks.

Hi Asif. The integer 05 is a one-digit integer. The leading zero does not count as a digit whenever a GMAT question says an 'n' digit integer. The question says "If the two-digit integers M and N..." In this case, neither one of the integers can be a multiple of 10 (end with zero) because the other integer would not be a 2-digit integer (because the leading zero would not count towards the number of digits).

-Patrick

Thanks Patrick.

is it me or all the sums for 2 digit numbers in reverse are multiples of 11? might be a shortcut if this is true!

I got this one right, but I was curious is there ever a situation where you can write a two digit number as 10X-Y rather than 10X+Y?