Japanese Multiplication Trick, and What It Has to Do With the GRE
//www.youtube.com/watch?v=e-P5RGdjICo
Watch this silent video for a new (to most of us) visual way to multiply!
What does this have to do with the GRE? Note that the 3 at right (which ended up in the ones place) was completed before any of the “big” numbers at left. That is, we didn’t need to know what our answer started with to know what our answer ended with.
Regardless of the method of multiplication you use (even if that “method” is a calculator), you will want to remember this very important principle for the GRE:
If you only need the units digit (ones place) of the answer, you only need the units digits of the numbers being multiplied.
Here is a GRE problem where that principle is essential to solving:
If m is the units digit of (456,789)(13,457,668) and n is the units digit of (13,456,789)(457,668), what is the units digit of the product of n and m?
This problem seems simple enough — until you realize that 456,789 x 13,457,668 is too big for the GRE’s calculator. Fortunately, though, if you only need the units digit of the answer, you only need the units digits of the numbers being multiplied. Since 9 x 8 = 72, which ends in 2, 456,789 x 13,457,668 also ends in 2. So, m = 2.
Similarly, 13,456,789 x 457,668 also ends in 2, since 9 x 8 = 72, which ends in 2. So, n = 2 as well.
Since nm = 2 x 2 = 4, the answer is 4.
If you’re still skeptical, get a calculator and try with some slightly smaller numbers. What should 999 x 556 end in? Well, 9 x 6 = 54, so it should end in 4. Sure, enough, 999 x 556 = 555,444. It works!