What is the remainder when 233^4 - 233^3 + 233^2 - 233, is divided by

Question

What is the remainder when  233^4 - 233^3 + 233^2 - 233 , is divided by 232?

A. 0
B. 1
C. 229
D. 230
E. 231

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gmatophobia · Answer

Remainder when 233 is divided by 232 = 1

We can use the remainder theorem to find the net remainder.

Concept : The net remainder is the sum / difference of individual remainder.

Remainder when ( 233^4 - 233^3 + 233^2 - 233 ) is divided by 232 =  1^4 - 1^3 + 1^2 - 1  = 0

Option A

Mattia73 · Answer

233^4-233^3 + 233^2-233
(233^4-3) + (233^2-1)= 233+233= 466/233= 2 with 0 of remainder

OPTION A

wadhwakaran · Answer

Remainder is zero.
Option A

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wadhwakaran · Answer

Remainder is zero.
Option A

Take 233 common in the first two and then the other two

Posted from my mobile device

sumit99kr · Answer

The above expression can be written as below-

(232+1)^4− (232+1)^3+ (232+1)^2− (232+1).

When divided by 232, each term would leave remainder as below-

1 - 1 + 1 -1 = 0.

Hence A is the correct option.

chetan2u · Answer

233^4 - 233^3 + 233^2 - 233 
 233^3(233-1) + 233(233-1)=(233^3+233)(232) …Divisible by 232
So, remainder is 0.

Also, as shown by  gmatophobia , the remainders can be added or subtracted or multiplied.

233 would leave a remainder of 1. 
So,  233^4 - 233^3 + 233^2 - 233  would leave a remainder of  1^4-1^3+1^2-1=1-1+1-1=0

A

What is the remainder when 233^4 - 233^3 + 233^2 - 233, is divided by

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GMAT Problem Solving (PS) Questions

What is the remainder when 233^4 - 233^3 + 233^2 - 233, is divided by

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