SWAPNILP wrote:

Hi i would like to know why ans is B here...since third digit is missing how can one determine what wud b the reminder? please explain

**Quote:**

\(x\) and \(y\) are positive integers. What is the remainder when \(x\) is divided by \(2^2\)?

(1) \(y = 7\)

(2) \(x = 3^{78y}\)

Hi..

78y is not a 3-digit number but 78*y and you can say this because it is given that y is a positive integer.

so let us see the question..

(1) \(y = 7\)

Nothing about y..

insuff

(2) \(x = 3^{78y}\)

Now, you should check few multiples of 3 and you will find a pattern ..

3^1 divided by 4 leaves 3 as remainder

3^2 =9 leaves 1 as remainder

3^3=27 leaves 3 as remainder and so on.. so pattern is 3,1,3,1...

\(x = 3^{78y}\), and this has an even power 78y, so answer will be that remainder is 1...

sufff

B

Ofcourse other way is binomial expansion.. \(x = 3^{78y}=(4-1)^{78y}\)...

In expansion. all terms except \((-1)^{78y}\) will be multiple of 4, so remainder = \((-1)^{78y}=1\)