Some question in the GMAT test your ability to reason with numbers. That too, in 30 to 45 seconds.

So while preparing for an exam of this caliber,focus on

**learning math concepts and math reasoning skills.**

One of the math reasoning skills, you must hone, is** Playing with numbers.**

### Tip:

Some of the concepts, you must pay attention to, are

Factors and multiples · Prime and composite numbers · Tests for divisibility · Common factors and common multiples · Prime factorization.....

*Try this sum*

*In an auditorium, 360 chairs are to be set up in a
rectangular arrangement with x rows of exactly y chairs each. If the only other
restriction is that 10 < x < 25, how many different rectangular
arrangements are possible?*

*A. 4 B. 5 C.6 D.8 E.9*

This sum is based on number properties. There are two
methods to solve this problem.

**Method 1 - the conventional way**

You should know the concept of prime factorization.

As per the question

X rows x Y chairs = 360

The product of two numbers = 360

We can say that X and Y are integers.

Now Let's find the prime factorization of 360

360 = 2 x 2 x 2 x 3 x 3 x 5

As per the condition given in the question

The value of x should lie between 10 and 25.

The value of X should be a combination of the prime factors
of 360

360 = 2 x 2 x 2 x 3 x 3 x 5

Pick few of the above numbers and find the product ( the product should lie between 10 and 25)

2 x 2 x 3 = 12

3 x 5 = 15. and so on...

Hence X can have values 12, 15,18, 20,24

The pairs are

x = 12 & y = 30

x = 15 & y = 24

x = 18 & y = 20

x = 20 & y = 18

x = 24 & y = 15

There are five such possibilities

** Answer option: B**

# Method 2: Playing with numbers

Let us say you didn’t know the concept of prime
factorization, then you can play with numbers and arrive at the answer.

X is a number between 10 and 25

Possible values of x

11 12 13 14 15 16 17 18 19 20 21 22 23 24

(Product of one of these numbers) x (a new number) should
give 360

Did you notice that there are prime numbers in the middle.

None
of the prime numbers divide 360 - 13,17,19, 23

Rule out the primes

Whats left.............

12 14 15 16 18 20 21 22 24

(Product of one of these numbers) x (a new number) should give 360

The number should divide 360 and give an
integer.. take one number at a time

360 /12 .. its divisible ... keep it..

360/14 = 360/(7x2) is not an integer ....360 is not divisible
by 7.. rule it out

360/16 = 360/(4x4) is not an integer... 360 is not divisible
by 4 twice.. rule it out

360/21 = 360/(7x3) is not an integer....360 is not divisible
by 7.. rule it out

360/22 = 360/(2x11) is not an integer...360 is not divisible
by 11.. rule it out

Whats left..

12 15 18 20 24

Hence

There are five such possibilities

** Answer option: B**

Hope you understood both the methods. Even if you are out of touch with math .. with logic

you can ace this section...

**If you need any help math help in your GMAT prep... Contact me...**

**My contact details are here:**

**LinkedIn profile : https://www.linkedin.com/in/georgeanand/**

# What next?

# Take a GMAT math diagnostic test