What is the remainder when a is divided by 4?

Question

(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.

Bunuel · Answer

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} 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.

whiplash2411 · Answer

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

ksear · Answer

It does help. Thanks.

domfrancondumas · Answer

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.

Zarrolou · Answer

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.

Asifpirlo · Answer

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)

shashankism · Answer

What is the remainder when p is divided by 4 ?
(1) p is the square of an odd integer.
(2) p is a multiple of 3.

sashiim20 · Answer

(1) p is the square of an odd integer.

Lets try  3^2, 7^2

3^2 = 9. 
9 divided by 4 gives remainder 1.

7^2 = 49 
49 divided by 4 gives remainder 1.

Any square of odd integer divided by 4 will give remainder 1. --------  (I is Sufficient)

(2) p is a multiple of 3.

12 is multiple of 4 hence will give remainder 0.
3 divided by 4 will give remainder 3.
6 divided by 4 will give remainder 2. etc... 
Therefore multiple values. --------  (II is Not Sufficient)

Answer (A).. .

Bunuel · Answer

Merging topics. Please refer to the discussion above.

shashankism · Answer

(1) Let a = (2k+1)^2 as it is square of an odd integer = 4k^2 + 4k +1 . So when it is divided by 4, remainder =1.  Sufficient 
(2) a is a multiple of 3, i.e. 3,6,9,12,15,........ So when it is divided by 4, remainder = 3 , 2, 1, 0, So  Not sufficient

Answer A.

davidbeckham · Answer

Thanks,  Bunuel . I was wondering how do we solve this question using the first method if the question says that a is divided by, say, 5 instead of 4?

AKAV46 · Answer

1) if a is 1, 9, 25, 49 ... a/4 remainder is 1 sufficient
2) if a is 3, 6, 9, 12 .... remainder is 3, 2, 1, 0 no unique answer. Insufficient

A

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What is the remainder when a is divided by 4?

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