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?