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.....
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
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
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
360/21 = 360/(7x3) is not an integer....360 is not divisible
by 7
360/22 = 360/(2x11) is not an integer...360 is not divisible
by 11
Whats left..
12 15 18 20 24
Hence
There are five such possibilities
you can ace this section...
If you need any help math help in your GMAT prep... Contact me...
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What next?
Take a GMAT math diagnostic test
