What is the reminder when X^4 + Y^4 is divided by 5
A. When X-Y is divided by 5 reminder is 1
B. When X+Y is divided by 5 reminder is 2
rate this also
Hey folks, this is again simple if u know a basic concept of numbers.
So it's time again to concentrate..........don't worry i will not eat too much of ur brain as i have done in my earlier posts.
Let's say that when N is divided by D the remiander is R.
Now when k x N is divided by D the remainder will be k x R ,provided k x R is less than D.
If k x R is > D, it is further divided by D and the remainder is given.
Let me take an example here.
92 when divided by 7 gives remainder 1
Now 2x92 when divided by 7 will give 2x1=2 as remainder .
Now 3x92 when divided by 7 will give 3x1=3 as remainder.
Let's look at one more example.
96 when divided by 7 leaves a remainder 5
Now 2x92 when divided by 7 should give 2x5=10 as remainder.
But, since 10 > 7, we further divide it by 7 and hence the remainder will be 3.
Similarly 3x96 /7 the remainder will be 3x5 =15.
This 15/7 leaves 1 as the remainder.
So i think this funda is clear to all of u.
Now let's take our question.
I think it's clear to everyone that each statement alone is not sufficient.
Now combining both...........
From the first statement X-Y = 5p+1
From the second statement X+Y=5q+2
So 2X = 5(p+q)+3
2Y = 5(q-p)+1
Now each term in the expansion of (2X)^4 will contain 5 other than 3^4
So 16(X)^4 when divided by 5 the remainder will be the remainder obtained when 3^4 is divided by 5 ie 1
Similary 16(Y)^4 when divided by 5 the remainder will be the remainder obtained when 1^4 is divided by 5 ie 1.
So the remainder of 16(X^4) +16(Y^4) when divided by 5 is 1+1 =2
So the remainder of 16 (X^4+Y^4) when divided by 5 is 2.
Now apply the above said rule;
(X^4 +Y^4)/5 the possible remainders are 0, 1, 2, 3, 4
16(X^4+Y^4)/5 the possibel remainders are 16x0,16x1,16x2,16x3,16x4
i.e 0, 1, 2, 3, 4
Since we know that the remainder of 16(X^4+Y^4) is 2,
the corresponding remainder of X^4 + Y^4 ie 2 will be the remainder for (X^4+Y^4)/5
So the answer is C.
Is this clear guys,..........
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