x + y = 120 ....... (i)

Correct Option: C

x + y = 120 ....... (i)

Here, the first divisor (91) is a multiple of second divisor (13).
∴  Required remainder = Remainder obtained on dividing 17 by 13 = 4

Correct Option: B

Here, the first divisor (91) is a multiple of second divisor (13).
∴  Required remainder = Remainder obtained on dividing 17 by 13 = 4

Of the given alternatives,
When 64 is divided by 3, remainder = 1
When 65 is divided by 5, remainder = 0

Correct Option: C

Of the given alternatives,
When 64 is divided by 3, remainder = 1
When 65 is divided by 5, remainder = 0

Let the unknown number be x.
∴  71   x + 47 = 98 × 7
⇒  71x = 686 – 47 = 639

Correct Option: D

Let the unknown number be x.
∴  71   x + 47 = 98 × 7
⇒  71x = 686 – 47 = 639

4⁶¹ + 4⁶² + 4⁶³
= 4⁶¹ (1 + 4 + 4²)
= 4⁶¹ × 21 which is divisible by 3.

Correct Option: A

4⁶¹ + 4⁶² + 4⁶³
= 4⁶¹ (1 + 4 + 4²)
= 4⁶¹ × 21 which is divisible by 3.