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19 Dec 2010, 15:22
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
76% (01:07) correct
24%
(01:28)
wrong
based on 495
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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.
(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.
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.
19 Dec 2010, 15:44
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ksear
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.
General Discussion
whiplash2411
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19 Dec 2010, 15:50
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ksear
To answer your specific question, if you divide 1 by 4, the reminder is 1. So the answer is valid.
