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the net remainder is the product of above individual remainders. i.e = 21*24*27*30
break them into pairs 21*24/33 gives remainder 9
and 27*30/33 gives remainder 18
the net remainder is the product of above individual remainders. i.e = 21*24*27*30 break them into pairs 21*24/33 gives remainder 9 and 27*30/33 gives remainder 18
so 9*18/33 gives remainder 30.
well - I can only find comfort in the words of Sir Winston Churchill:
"Success is the ability to go from one failure to another with no loss of enthusiasm"
good question! and good official explanation!
actually, after reading umbdude post I had my doubts. But now I know why !!!
I think it's easier: because all of the term divisible by 3 so the remainder of the multiply of them will be the remainder when after dividing by 3 then dividing by 11. This can only be 3 because all other choice is greater than 11
I think it's easier: because all of the term divisible by 3 so the remainder of the multiply of them will be the remainder when after dividing by 3 then dividing by 11. This can only be 3 because all other choice is greater than 11
That's not right:
Consider this 6*6*6 divided by 33. What is remainder?
According to you logic: as all of them are divisible by 3 remainder must be less than 11, but in this case remainder is 18>11.
For the original question the answer IS 30. But my point was that the solution I provided is not easy, so I wonder if there is some easier way to do the same.
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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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23 Aug 2013, 03:46
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rlevochkin wrote:
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
A. 3 B. 27 C. 30 D. 21 E. 18
We can play with the questions the way we like to.... That's the beauty of remainder questions.
When 1044, 1047, 1050, and 1053 divided by 33 individually will give the remainders as 21, 24, 27, and 30 respectively.
Now as per rule, remainders are always non-negative, but still we can consider the negative remainders for the calculation as long as we convert them is positive remainder at the end.
So 21, 24, 27, and 30 when divided by 33 will give the negative remainders as -12, -9, -6, -3
(-12 * -9)(-6 * -3) --------> 108 * 18 ------->Positive Remainder -----> 9 * 18 --------> 162/33 ------Negative Remainder -----> -3 -------> Positive Remainder -----> -3 + 33 = 30 (Always add the divisor in to the negative remainder to obtain positive(correct) remainder)
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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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23 Aug 2013, 09:31
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1
Though I took a while to solve this but I was trying to recollect something which I learnt when I was in love with Remainder theorem.
(1044 x 1047 x 1050 x 1053)/33 (cancelling the common factor 3) =>(1044 x 1047 x 1050 x 351)/11 Denoting remainder using [] [1044/11]= [10] is remainder. Similarly, [1047/11]= [2] [1050/11]= [5] [351/11]= [10] which gives: [(10 x 10 x 10)/11] = [10] as remainder.
Since we initially cancelled the common factor 3. The final remainder will be 10 x 3 =30 i.e. option C.
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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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23 Aug 2013, 10:19
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vabhs192003 wrote:
Though I took a while to solve this but I was trying to recollect something which I learnt when I was in love with Remainder theorem.
(1044 x 1047 x 1050 x 1053)/33 (cancelling the common factor 3) =>(1044 x 1047 x 1050 x 351)/11 Denoting remainder using [] [1044/11]= [10] is remainder. Similarly, [1047/11]= [2] [1050/11]= [5] [351/11]= [10] which gives: [(10 x 10 x 10)/11] = [10] as remainder.
Since we initially cancelled the common factor 3. The final remainder will be 10 x 3 =30 i.e. option C.
Yeah, This is also a fantastic method and, if I remember correctly, has been discussed in Mr. Arun Sharma's CAT QA book
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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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15 Dec 2013, 23:58
vshaunak@gmail.com wrote:
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
A. 3 B. 27 C. 30 D. 21 E. 18
Can somebody suggest a trick to solve this question.
Hi,
Math Experts....need help on this one....
We need to find the remainder in the above case. I started by finding whether any term is divisible by 33 and found the nearest multiple to be 1056 and changed the question to
(1056-12)*(1056-9)*(1056-6)*(1056-3)/33 which can be further reduced to
(-12)(-9)(-6)(-3)/ 33 On simplifying further we get -------> -12*-9*-6*-1/11-------> 648/11 ---Remainder 10.....its not even in the answers choices...
please suggest what's wrong with my approach
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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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16 Dec 2013, 00:05
WoundedTiger wrote:
vshaunak@gmail.com wrote:
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
A. 3 B. 27 C. 30 D. 21 E. 18
Can somebody suggest a trick to solve this question.
Hi,
Math Experts....need help on this one....
We need to find the remainder in the above case. I started by finding whether any term is divisible by 33 and found the nearest multiple to be 1056 and changed the question to
(1056-12)*(1056-9)*(1056-6)*(1056-3)/33 which can be further reduced to
(-12)(-9)(-6)(-3)/ 33 On simplifying further we get -------> -12*-9*-6*-1/11-------> 648/11 ---Remainder 10.....its not even in the answers choices...
please suggest what's wrong with my approach
I will give you a hint, because you really have got it. Just one mistake ;
Remainder of \(\frac{14}{4} = \frac{7}{2} = 1\) Is this correct?
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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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16 Dec 2013, 01:49
mau5 wrote:
WoundedTiger wrote:
vshaunak@gmail.com wrote:
What is the remainder when 1044 * 1047 * 1050 * 1053 is divided by 33?
A. 3 B. 27 C. 30 D. 21 E. 18
Can somebody suggest a trick to solve this question.
Hi,
Math Experts....need help on this one....
We need to find the remainder in the above case. I started by finding whether any term is divisible by 33 and found the nearest multiple to be 1056 and changed the question to
(1056-12)*(1056-9)*(1056-6)*(1056-3)/33 which can be further reduced to
(-12)(-9)(-6)(-3)/ 33 On simplifying further we get -------> -12*-9*-6*-1/11-------> 648/11 ---Remainder 10.....its not even in the answers choices...
please suggest what's wrong with my approach
I will give you a hint, because you really have got it. Just one mistake ;
Remainder of \(\frac{14}{4} = \frac{7}{2} = 1\) Is this correct?
Hmmm...got the point...So do we need to simplify the given expression only till (-12)(-9)(-6)(-3)/ 33 and find out the answer. Basically not touching the denominator.
the answer will be 30.
Is that correct...and can it be generalized for such problems.
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
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16 Dec 2013, 02:59
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WoundedTiger wrote:
Hmmm...got the point...So do we need to simplify the given expression only till (-12)(-9)(-6)(-3)/ 33 and find out the answer. Basically not touching the denominator.
the answer will be 30.
Is that correct...and can it be generalized for such problems.
Actually you just have to multiply the remainder you got by the common factor which you cancelled.
For example, \(\frac{14}{4}\), here you factored out 2. Keep that seperate. Now, remainder of \(\frac{7}{2} = 1\). Thus, the final remainder is 1*2 = 2.
Apply this to your method above and get the same, i.e. 3*10 = 30.
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