Questions involving Fractions :How to solve them quickly !
here are some questions involving fractions that certainly seem very difficult at first glance. You need a systematic method to solve such questions.
If a is an integer and a^2/12^3 is odd, which of the following must be an odd integer?
A) a/4
B) a/12
C) a/27
D) a/36
E) a/72
Tip: try plugging in a value for ‘a’
One approach to this question is to try to work out a possible value for a and use this as a plugin. There are many things to remember as you do this.
You are told that a^2/12^3 is odd. Therefore, a^2 must be at least as large as 12^3, or is possibly larger than 12^3, since the entire expression must be an integer. How large is 12^3?
Break 12^3 down into its prime factors:
12^3
= (3*4)^3
= (3*2*2)^3
= (3*2^2)^3
= 2^6 *3^3
a is an integer. Therefore, a^2 is the square of an integer, or a perfect square
Is it possible that a^2 = 2^6*3^3? For this to be true, the square root of 2^6*3^3 must be an integer. What is the square root of 2^6*3^3? This is {2^3*3^3}/2, which is not an integer. Therefore, a^2 cannot be 2^6*3^3. The problem lies with the fact that 3 is raised to an odd power. If we raise 3 to an even power, we will obtain an integer as the square root.
Let us test whether it is possible that a^2 = 2^6*3^4. (We are now multiplying by an additional 3.) The square root of 2^6*3^4=2^3*3^2=8*9=72. 72 is an integer. Therefore, it is possible that a = 72.
Plug 72 into each of the answer choices:
A) 72/4 = 18 – an even integer
B) 72/12 = 6 – an even integer
C) 72/27 – a non-integer
D) 72/36 = 2 – an even integer
E) 72/72 = 1 – an odd integer
Therefore, E is our answer.
Note the usefulness of prime factorization in solving this question. Although there are many steps in solving such a question, as long as you know the right method, you will be able to get to the correct answer quickly enough.
ratio and proportion cat level questions
ratio and proportion cat concepts
ratio and proportion for cat pdf
ratio and proportion cat preparation
ratio and proportion difficult questions
ratio and proportion problems with answers
ratio proportion and variation problems with solutions
ratio and proportion aptitude questions with answers pdf