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MGMAT's Number Properties Data Sufficiency Question

Expert replies
by ksear » Sun Dec 19, 2010 2:25 pm
Hi everyone,

I'm a little confused regarding the correct answer for the below mentioned question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer.
(2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder?
When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

Thanks.
Kash.
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Source: — Data Sufficiency |

by anshumishra » Sun Dec 19, 2010 3:01 pm
ksear wrote:Hi everyone,

I'm a little confused regarding the correct answer for the below mentioned question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer.
(2) a is a multiple of 3.

According to the book, the answer is A.

But according to me, the answer should be C since if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder?
When we use 3 for a, the square of a will give us 9 which when divided by 4, gives us remainder of 1.

Thanks.
Kash.
Statement 1 :

Any odd number is of the form 2n+1
So, a = (2n+1)^2 = 4n^2+4n+1

Hence, clearly when divided by 4, the remainder is 1 ---> Sufficient

Statement 2 :

Remainder of 3n/4 = ?

If n= 1, r = 3
If n= 2, r = 2

Hence Not sufficient.

Answer is A.
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by ksear » Sun Dec 19, 2010 3:02 pm
Thanks.
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by Whitney Garner » Sun Dec 19, 2010 7:22 pm
ksear wrote:Hi everyone,
... if we take the first statement and use the value 1 for a, it gives us 1 for the square of 1, what would be the remainder?
...[/i]
Very nice explanation anshumishra - to answer the original poster's question above:

If you divide any number by a number larger than itself, the original number is its own remainder. Examples:

1/4 = 0 R1
3/5 = 0 R3
13/14 = 0 R13

:)
Whit
Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
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Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated :heart-eyes:
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