CAT Practice : Number System - Remainders

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What divides a3 + b3?

Remainder - Large number

    Q.14: If N = (243 + 253 + 263 + 273), then N divided by 102 leaves a remainder of?
    1. 18
    2. 12
    3. 1
    4. 0

 

  • Correct Answer
    Choice D. 0

Detailed Solution

N = 243 + 253 + 263 + 273
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

Correct Answer: Choice D

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When we divide 24 pigeons into 5 groups, 4 are left out or remain. This is the remainder. When there is a question based on this idea in the exam, we have a CAT among the pigeons.