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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. _________________

Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is [#permalink]
23 Aug 2013, 02:46

Expert's post

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) _________________

Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is [#permalink]
23 Aug 2013, 08:31

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. _________________

Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is [#permalink]
23 Aug 2013, 09:19

Expert's post

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 _________________

Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is [#permalink]
15 Dec 2013, 04:15

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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is [#permalink]
15 Dec 2013, 22:58

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 _________________

“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.”

gmatclubot

Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is
[#permalink]
15 Dec 2013, 22:58