kanusha
First thought: Terminatieng and non terminating
My concept after reading the question: Terinating – non repeating, Non terminating – Repeating numbers after decimal
My Strategy : 1.All numbers are squares or cubes 2. Simply these 3. Then divide
I have learned – Denominator having 2^m5^n are terminating numbers
Dear
kanusha,
I am responding to your private message.
First of all, you may find this blog helpful.
https://magoosh.com/gmat/2012/gmat-math- ... -decimals/What you say in the last line is correct and is key to understanding this problem. My only caution would be: use proper mathematical grouping symbols. You are not thinking like a mathematician when you write
2^m5^n
That is precisely the way it is written by someone who isn't thinking carefully about the mathematical symbols. What you meant is:
(2^m)(5^n)
Those parenthesis are not garnish, not extra decorative elements --- they are absolute essential pieces of mathematical equipment, and you are setting yourself up for mistake if you casually ignore their tremendous importance. See:
https://magoosh.com/gmat/2013/gmat-quant ... g-symbols/In this problem, all of the denominators happen to be squares and other powers.
289 = 17^2
196 = 14^2
225 = 15^2
144 = 12^2
128 = 2^7
I think it's good to know the perfect squares up to 20^2 = 400. It's also good to know the first eight powers of 2. It just saves time, and helps to deepen number sense.
Nevertheless, the fact that most of these are squares is not particularly relevant. All you have to do is find the prime factorization of the denominator. As soon as you find a prime factor other than 2 or 5, then you know the decimal would be repeating & non-terminating.
If the denominator an odd number not ending in a 5, then it can't be divisible by 2 or 5: it must have other prime factors and must lead to a repeating & non-terminating decimal. If the denominator is divisible by 3, a very easy check, then it lead to a repeating & non-terminating decimal.
The easy way to handle these, even without knowing they are perfect squares ----
(A) 289 --- an odd number, so not divisible by 2, and clearly not divisible by 5, so it must have other prime factors. No good.
(B) 196 --- divide by 2 = 98 --- divide by 4 = 49 --- other odd factors. No good.
(C) 225 --- 2 + 2 + 5 = 9, which is divisible by 3, so that means 225 is divisible by 3. No good.
(D) 144--- 1 + 4 + 4 = 9, which is divisible by 3, so that means 144 is divisible by 3. No good.
(E) only one left
Does all this make sense?
Mike