exam Maths Puzzle Numerical Ability

Prove that among any 39 consecutive natural numbers
it is always possible to find one whose sum of digits
is divisible by 11.

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exam Other Question

Richard drove his rig at �x� mph for 3 hours, then increased his speed to (x + 15) mph and drove 2 more hours. Write a polynomial that represents the total distance that he traveled. How much distance he covered if x = 45 Mph? ABCD is a square (ie all sides are equal and all angles and rightangles). CX is made to equal CY (using compasses from the centre C.) Prove that AX = AY.