Math Is Fun Forum

gulfkaran

Member

Registered: 2017-06-24

Posts: 2

What are the steps involved in solving these questions ?

I do not understand how they have reached that answer .

I was looking at a book of quantitative aptitude and found these questions in it .

Can somebody explain the steps involved in finding the answer .

Thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,357

Re: What are the steps involved in solving these questions ?

hi gulfkaran

Welcome to the forum.

Example 23:  Lets say that when you divide 12284 by something (x) the remainder is r.  We can write this equation for that process

12284 = nx + r.  That means you divide by x, it goes n times with remainder r.

In the same way for the other number we can write

8655 = mx + r.  m is the number of times x goes into 8655 with the same remainder r.

We can eliminate r from these equations by subtracting one from the other:

3629 = nx - mx = (n-m)x

So find the factors of 3629.  Turns out it is the product of two primes, so there's only one answer **

3629 = 19 x 191 so that tells us that x = 19 and n-m = 191.

example 24 is done similarly.

The hcf (highest common factor) is 16.  That means that 16 is the largest number that goes into both numbers exactly so you can write each as a product where 16 is one factor.

So if we call the numbers 16a and 16b, when we multiply them we get 256ab = 5376, which simplifies to ab = 21.

Once again the only factorisation is 3 x 7 so a = 3 and b = 7.

Have a look at this page: https://www.mathsisfun.com/greatest-common-factor.html

This page calls it the greatest common factor but that's the same as 'highest'.

Bob

** Strictly there's two answers as 3629 = 1 x 3629.  But fairly obviously x = 1 doesn't work in this problem.

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gulfkaran

Member

Registered: 2017-06-24

Posts: 2

Re: What are the steps involved in solving these questions ?

Thanks a lot for explaining it Bob ,

It takes a lot of time to study for questions like that , its all very twisted

I found a good book here , i will try to learn from this when i get free time