joondez wrote:

Abhishek009 wrote:

I. 143 = 13*11

II. 147 = 21*7

How did you find this out?

Dear

joondez,

I'm happy to help.

My friend, one of the most important skills on the GMAT Quant is developing

number sense.

For example, when I look at 147, I notice that 147 = 140 + 7. Well, 140 is divisible by 7--it's equal to 20*7. Of course 7 is divisible by 7. Therefore:

147 = 140 + 7 = 20*7 + 7 = (20 + 1)*7 = 21*7

Part of number sense is being able to "chop up" numbers to see what is divisible by what. Here's a video that explains more.

Multiples For 143, we use another trick. You may be familiar with the algebraic formula know as "

Difference of Two Squares."

\(P^2 - Q^2 = (P + Q)(P - Q)\)

Well, we can use this for algebra, but we also can use this for numbers. See:

Advanced (Non-Calculator!) Factoring on the GMATWe know that \(12^2 = 144\), and \(143 = 144 - 1\). Therefore

\(143 = 144 - 1 = 12^2 - 1^2 = (12 + 1)(12 - 1) = 13*11\)

BTW, another trick we can use: suppose we have a three-digit number

abc, where those are the three digits. If it's true that

b = a + c, then it has to be true that the number is divisible by 11. For example, consider the number 473. Any number of this kind we can write in the form (10*N) + N for some positive integer N. For this number,

473 = 430 + 43 = 43*10 + 43 = 43(10 + 1) = 43*11

Don't just memorize these patterns: really make sure you understand them.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep