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What is the remainder when a is divided by 4? [#permalink]
19 Dec 2010, 14:22

1

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00:00

A

B

C

D

E

Difficulty:

25% (low)

Question Stats:

76% (01:42) correct
23% (01:13) wrong based on 47 sessions

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.

Re: MGMAT's Number Properties Data Sufficiency Question [#permalink]
19 Dec 2010, 14:44

1

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Expert's post

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.

Positive integer a divided by positive integer d yields a reminder of r can always be expressed as a=qd+r, where q is called a quotient and r is called a remainder, note here that 0\leq{r}<d (remainder is non-negative integer and always less than divisor).

So according to above, when positive integer a is less than divisor d then remainder upon division a by d is always equals to a, for example 5 divided by 10 yields reminder of 5. So when 1 is divided by 4 remainder is 1.

Or algebraically: 1 divided by 4 can be expressed as 1=0*4+1, so r=1.

Back to the original question:

What is the remainder when a is divided by 4?

(1) a is the square of an odd integer --> a=(2k+1)^2=4k^2+4k+1, first two terms (4k^2 and 4k) are divisible by 4 and the third term (1) when divided by 4 yields the remainder of 1. Sufficient.

Or you can try several numbers for a: a=1^1=1 --> 1 divided by 4 yields remainder of 1; a=3^1=9 --> 9 divided by 4 yields remainder of 1; a=5^1=25 --> 25 divided by 4 yields remainder of 1; ...

(2) a is a multiple of 3 --> clearly insufficient as a can as well be a multiple of 4, 12 for example, and in this case the remainder will be 0, and it also can not be a multiple of 4, 3 for example, and in this case the remainder will be 3. Not sufficient.

Re: MGMAT's Number Properties Data Sufficiency Question [#permalink]
19 Dec 2010, 14:50

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.

To answer your specific question, if you divide 1 by 4, the reminder is 1. So the answer is valid.

Re: What is the remainder when a is divided by 4? [#permalink]
07 Aug 2013, 23:10

2

This post received KUDOS

What is the remainder when a is divided by 4?

(1) a is the square of a odd integer. Method #1: a=1 reminder=1; a=9 reminder=1, a=25 reminder=1; a=49 reminder=1... I see a pattern, I am convinced that this is sufficient. Method #2:a=(2k+1)^2 (where k is an integer) a=4k^2+4k+1, a=4(k^2+k)+1a is a multiple of four plus one, hence the reminder will be one. Sufficient

(2)a is a multiple of 3. a=3 reminder=3, a=9 reminder=1. Not sufficient.
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Re: What is the remainder when a is divided by 4? [#permalink]
10 Aug 2013, 03:32

ksear wrote:

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.

1^2/4 = (4-3)^2/4 = (4^2 - 2.4.3 + 9)/4 = 4 + 6 + 9/4 = 10 + 9/4 so the remainder from 9/4 we have is 1 . That's how we can realize why 1 appears as the remainder when 1^2 is divided by 4.

Thus the answer is (A)
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Re: What is the remainder when a is divided by 4?
[#permalink]
10 Aug 2013, 03:32