CAT Exam Model Paper 8 with solutions for free online practice

Question : 1 of 60

Marks: +1, -0

SECTION - 1

If x and y are positive integers, then the last digit of which of the following is same as the last digit of the sum of x and y?

$x^{7}+y^{7}$
$x^{13}+y^{13}$
$x^{20}+y^{20}$
None of these

Validate

Solution:

The cyclicity of each digit from 0 to 9 is a factor of 4.
Hence any digit raised to a power of the type 4k + 1 will always end in the same digit. Hence the answer is

x^{13}+y^{13}

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