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What is the remainder when a is divided by 4?

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What is the remainder when a is divided by 4? [#permalink] New post 19 Dec 2010, 14:22
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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.
[Reveal] Spoiler: OA
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Re: MGMAT's Number Properties Data Sufficiency Question [#permalink] New post 19 Dec 2010, 14:44
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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.

Answer: A.

Questions on remainders:

PS:
remainder-101074.html
remainder-problem-92629.html
number-properties-question-from-qr-2nd-edition-ps-96030.html
remainder-when-k-96127.html
ps-0-to-50-inclusive-remainder-76984.html
good-problem-90442.html
remainder-of-89470.html
number-system-60282.html
remainder-problem-88102.html

DS:
remainder-problem-101740.html
remainder-101663.html
ds-gcd-of-numbers-101360.html
data-sufficiency-with-remainder-98529.html
sum-of-remainders-99943.html
ds8-93971.html
need-solution-98567.html
gmat-prep-ds-remainder-96366.html
gmat-prep-ds-93364.html
ds-from-gmatprep-96712.html
remainder-problem-divisible-by-86839.html
gmat-prep-2-remainder-86155.html
remainder-94472.html
remainder-problem-84967.html

Hope it helps.
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Re: MGMAT's Number Properties Data Sufficiency Question [#permalink] New post 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.
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Re: MGMAT's Number Properties Data Sufficiency Question [#permalink] New post 19 Dec 2010, 14:52
It does help. Thanks.
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What is the remainder when a is divided by 4? [#permalink] New post 07 Aug 2013, 23:02
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What is the remainder when a is divided by 4?
(1) a is the square of a odd integer.
(2)a is a multiple of 3.

Last edited by Zarrolou on 07 Aug 2013, 23:10, edited 1 time in total.
Edited the question, added OA.
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Re: What is the remainder when a is divided by 4? [#permalink] New post 07 Aug 2013, 23:10
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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)+1 a 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] New post 09 Aug 2013, 02:57
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Re: What is the remainder when a is divided by 4? [#permalink] New post 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
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