Going through the whole Manhattan / Economist Courses and still...

Thank you. Yes indeed Stat. 1 is Sufficient. Could you explain me how you did that so easily in your head > why do i need the ten's digit to be 2 and the one's digit to be 1? What's the reason behind it? So far i got just a algebraic explanation from a certain user, which i find too time consumming on the gmat:

This rule is just based on how we multily, there is nothing more to it.

X = abc = a*100 + b*10 + c
Y = cba = c*100 + b*10 + a

XY = (a*100 + b*10 + c)*(c*100 + b*10 + a)
=>XY = 10000*ac + 1000*ab + 100a^2 + 1000bc + 100b^2 + 10ab + 100c^2 + 10*bc + ac
=> XY = 10000*ac + 1000*(ab + bc) + 100*(a^2 + b^2 + c^2) + 10*(ab + bc) + ac


If it can be proved that ac, (ab+bc) and (a^2 + b^2 + c^2) are single digits then the unit digit will be ac, 10th place will be (ab+bc) and 100th place will be (a^2 + b^2 + c^2)

thanks

Hello reto.

I can't say about other people. But my experience shows that finishing courses and reading books is like one-third of math way.

I listen Veritas course, read Manhattan books, complete Magoosh course and after all this I start doing Gmat club tests.
This was terrible sensation. It was like completely new math. I think this is because books and courses give you the ways to solving tasks, but don't give you direct instructions about solving.
When I have done GMAT club eighth CAT it became much easier.

I did 18 math cats from different sources and during last two weeks start Manhattans' tests.
This is even more terrible than GMAT Club tests )
A lot of tasks that I completely not understand. It's really scary and unpleasant but when I reread my old drafts I understand that it's ok.

It's ok because you grow and GMAT give to you harder tasks, this is why it is so difficult all the time. The key moment is that you are grow.
If you will not stop, you will beat GMAT. I am assured that this is only matter of time and your wilfulness.

First off, I'm guessing this is a "hard" math question so I wouldn't worry too much right now...

Anyway, think of the multiplication. A three digit number means that you will be adding together 3 "lines" of numbers. Each line is shifted over one... and you only have to worry about the hundreds digit. Don't bother multiplying all the numbers. Since the hundreds digit is said to be 6, that will be made by adding together (1+4+1=6). The 1's and the 4 come from multiplying 1X1 and 2X2. The only way that can happen is if the 2 is in the middle, and the other digits are 1's.

Let's look at the multiplication.

121
121
121
+2420
+12100
14641

(Hundreds digit is in bold so you can see how to visualize that place in the final answer).

Again, you do NOT have to do this out, but if you get an intuition for the numbers you can get the right answer without the work.

Note that the other combinations of multiplying digits of 1 and 2 will give you (1+1+1=3), (1+4+4=9), and (4+4+4=12)-->2 in the hundreds place. Only (1+4+1=6), and the only way to get that is (1^2)+(2^2)+(1^2), i.e. 121*121.

I did this question by thinking of all the possibilities first. I started with (Stat. 2) because it looked easier. That was easy to show it was not suff. Playing with (Stat 1) which looked more difficult eventually made it clear that only 121 for both X and Y worked, so it was sufficient.

I've a question for u guys, can we consider X=112, if X=112 and Y=211 then XY=23632. Hundred's digit is 6 and the remainder when X divided by 3 is 1

You're right, I forgot to check that possibility... you still end up with (1+4+1) to make the hundreds digit... but thankfully (112*211) and (121*121) have the same remainder. Like I said, I'm sure this wasn't an easy question.