Can you play with numbers - GMAT math tip

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/

Facebook learning group: https://www.facebook.com/groups/semanticsGMAT/

What next? 

Take a GMAT math diagnostic test