# Math Reasoning Skill – playing with numbers Some question, in the GMAT /GRE,  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 concepts
• reasoning skills.

## One of the math reasoning skills, you must focus on, is Playing with numbers.

Focus on:

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 integers = 360.

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

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.  The Possible values of x are

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

(one of these numbers) x (a unknown number) = 360

Did you notice that there are prime numbers in the middle.( 11,13….23)

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

(one of these numbers) x (a new number) = 360

This means 360 is perfectly divisible by either of these two numbers.

Take one number at a time

360 /12 .. its divisible … keep it..

360/14 = 360/(7×2) is not an integer ….360 is not divisible by 7.. rule it out

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

360/21 = 360/(7×3) is not an integer….360 is not divisible by 7.. rule it out

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

Whats left.. 12 15 18 20 24

There are five such possibilities ## What next? Master this skills with a small test. click here

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

With logic you can ace this section…

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