Question

If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?
18
12
1
0

Answer 1

Answer:

Choice D is the correct answer.

Step-by-step explanation:

Unit digits of N = 4 + 5 + 6 + 3 = 18  

N is divisible by 2  

We know that, a3 + b3 = (a + b)(a2 – ab + b2)

=> (a + b) always divides a3 + b3  

Therefore, 243 + 273 is divisible by 51 (24 + 27)  

Also, 253 + 263 is divisible by 51 (25 + 26)  

The given divisor 102 can be expressed as 51 * 2  

Hence, N is completely divisible by 102  

Remainder = 0

The question is "If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?"

Hence the answer is 0.

Choice D is the correct answer.