Question

if a number x is divided by 17 leaves a remainder 12 while another number y is divided by 34 leaves a remainder 21 then the remainder when (x+y) is divided by 17 is

Answer 1

Step-by-step explanation:

Given: if a number x is divided by 17 leaves a remainder 12 while another number y is divided by 34 leaves a remainder 21.

To find: The remainder when (x+y) is divided by 17 is?

Solution:

As x is divided by 17 leaves a remainder 12,

x can be 29.

As

$17 \: )29 \: (1 \\ 17 \\ - - - \\ 12 \\ - - -$

Accordingly, y is divided by 34 leaves a remainder 21.

y can be 55.

As,

$34 \: ) \: 55 \: ( \: 1 \\ \: \: 34 \\ - - - - \\ 21 \\ - - - -$

Now,

Add both numbers

$x + y = 29 + 55$

or

$x + y = 84$

Divide 84 by 17, to find the remainder

$17) \: 84 \: (4 \\ \: 68 \\ - - - \\ 16 \\ - - -$

Remainder is 16.

Final answer:

The remainder is 16 when (x+y) is divided by 17.

Note*: More possibilities are exist for choosing x and y. Thus, answer can very accordingly.

Hope it helps you.

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