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What is the remainder when 1044*1047*1050*1053 is divided by

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Re: Remainders  [#permalink]

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New post 05 Mar 2014, 11:37
Bunuel wrote:
ngoctraiden1905 wrote:
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.


There is a *slightly* easier solution. If we factor out a 3 from each number, we come up with:

\(3*3*3*3*(348*349*310*311)/33\) = \(3*3*3*(348*349*310*311)/11\)

Now our task is to reduce each number to its remainder when divided by 11.

We notice that 352 is the closest multiple of 11 to the numbers inside the parentheses, and thus the remainders are (-1 * -2 * -3 * -4)* 3 * 3 * 3.

-4*-3 = 12; remainder 1
-1*2 = 2, remainder 2
3*3*3 = 27; remainder 5

Now 5*2*1 = 10, which is the remainder when divided by 11. Multiplying this by 3 (because the question asks the remainder when divided by 33), we get 10*3 = 30.

Answer: C
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Re: What is the remainder when 1044*1047*1050*1053 is divided by  [#permalink]

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New post 04 Jun 2014, 18:58
Lets use the remainder theorem.

33 = 3*11
first divide any number that is divisible by 3 lets say 1053/3 = 351
so (1044*1047*1050*351)/11

1044/11 = r10
1047/11 = r2
1050/11 = r5
351/11 = r10
multiply all the r and we get 100
now 100 is greater than 11 so again divide by 11
100/11 = r10
since we divide the orginal multiplication my 3 so we have to multiply the final remainder by 3
hence 30 is the remainder and answer is C
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Re: What is the remainder when 1044 * 1047 * 1050 * 1053 is  [#permalink]

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New post 05 Jun 2014, 22:56
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


You are changing the divisor. Divisor should not be changed in such problems. If changed, revert back later

Here the divisor is 33; as soon as we "attempt to simplify", it changed to 11.

Now, if 11 is the divisor, all the options in the OA except 3 are invalid as remainder would always be less than divisor

As far as the problem is concerned; just multiply 10 with 3 = 30 & there comes the answer (As 3 was simplified earlier)
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Re: What is the remainder when 1044*1047*1050*1053 is divided by  [#permalink]

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New post 01 Sep 2014, 13:07
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


Because you reduced you fraction by 3. That's the reason you are getting 10. Multiply 10 by 3 and you will get correct remainder 30.
If one reduce fraction by some factor to simplify the calculation then one must not forget to multiply answer by same factor in the end.
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Re: What is the remainder when 1044*1047*1050*1053 is divided by  [#permalink]

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New post 10 Sep 2016, 09:31
Answer should be 3. Here is my analysis:

Since all the numbers in the numerator are divisible by 3, the fraction can be reduced to a number with a denominator 11. The remainder should always be less than the divisor. So dividing a number with 11 should leave a remainder less than 11. Looking at the answer choices 3 is the only one that is less than 11.

I tried computing in a calculator (( 1044 * 1047 * 1050 * 1053) + 3) / 33 did not leave any remainder.

Please someone update the OA. It is (A)
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What is the remainder when 1044*1047*1050*1053 is divided by  [#permalink]

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New post 03 Sep 2017, 05:39
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


Bunuel, Is it the correct approach?

1044*1047*1050*1053 = n*(n + 3)*(n + 6)*(n + 9)

3*6*9 = 162

162/33, remainder = 30
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Re: What is the remainder when 1044*1047*1050*1053 is divided by  [#permalink]

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New post 03 Sep 2017, 06:08
manhasnoname wrote:
Answer should be 3. Here is my analysis:

Since all the numbers in the numerator are divisible by 3, the fraction can be reduced to a number with a denominator 11. The remainder should always be less than the divisor. So dividing a number with 11 should leave a remainder less than 11. Looking at the answer choices 3 is the only one that is less than 11.

I tried computing in a calculator (( 1044 * 1047 * 1050 * 1053) + 3) / 33 did not leave any remainder.

Please someone update the OA. It is (A)



Just a comment on your logic :
If you are saying :
"I tried computing in a calculator (( 1044 * 1047 * 1050 * 1053) + 3) / 33 did not leave any remainder. "
than here remainder will be 33-3=30 .. not 3...

example.... 16/10 = 1 quotient and 6 remainder....
in your terms : (16+4)/10 does not leave a remainder so 16/10 doesn't have a remainder of 4.. instead remainder is 10-4 =6

so if on calculator you see after adding 3.. number gets properly divided means original remainder is 33-3 ie 30. which is the correct answer.

Hope m clear.
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Re: What is the remainder when 1044*1047*1050*1053 is divided by  [#permalink]

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New post 01 May 2019, 12:06
What is the remainder when 30 is divided by 4?

One approach:
1. Break the dividend 30 into factors: 30 = 5*6
2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2
3. Multiple the resulting remainders: 1*2 = 2

Step 3 indicates that 30 divided by 4 will yield a remainder of 2.
This approach can be applied to any problem that asks for the remainder when a large integer is divided by a divisor.
Repeat the 3 steps until the value yielded by Step 3 is less than the divisor.

Quote:
What is the remainder when 1044*1047*1050*1053 is divided by 33?

A. 3
B. 27
C. 30
D. 21
E. 18


Since 1044 has a digit sum that is a multiple of 3 (1+0+4+4=9), 1044 is divisible by 3:
1044 = 3*348
Since 1047 is 3 more than 1044, 1047 = 3*348 + 3 = 3(348+1) = 3*349
By extension:
1050 = 3*350
1053 = 3*351
Thus:
1044*1047*1050*1053 = (3*348)(3*349)(3*350)(3*351) = 81*348*349*350*351

Dividing 33 into each of the five factors in blue and multiplying the resulting remainders, we get:
15*18*19*20*21

18*20 = 360
19*21 = (20-1)(20+1) = 20²-1² = 400-1 = 399
Thus:
15*18*19*20*21 = 15*360*399

Dividing 33 into each of the 3 factors in red and multiplying the resulting remainders, we get:
15*30*3

15*30*3 = 1350
Dividing 33 into 1350, we get:
40 R30
The value in green is less than the divisor (33) and thus is the desired remainder.

.
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Re: What is the remainder when 1044*1047*1050*1053 is divided by   [#permalink] 01 May 2019, 12:06

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