Note: If the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.
[(Sum of digits at odd places) - (Sum of digits at even places)]/11
=> [(3+4+6+2) - (2+5+8)]/11 => (15 - 15)/11 = 0/11 = 0
similarly others number are divisible by 11
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The product of two positive numbers is p. If each of the numbers is increased by 2, the new product is how much greater twice the sum of the two original numbers?
Lets assume number are x,y
So, there product = xy
Given number increased by 2
so, now number are x+2,y+2.
Given product is twice the sum of two original No.
=> product = (x+2)(y+2) = 2(x+y)
=> xy+2x+2y+4 =2(x+y)
=> xy+4
so it increase by 4
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A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?
Note: If the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11. [(Sum of digits at odd places) - (Sum of digits at even places)]/11.
4+5+2 = 11 and 1+6+4 = 11 . Then 11-11 =0.
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What should be multiplied to 2880 to make it a perfect square?
Note: To make perfect square, all the powers of prime factors should be even.
2880 = 2^6 * 3^2 * 5
So, In 2880 powers of prime factors 2 and 3 are even.
But power of prime factor 5 is 1, which is odd.
So, to make it a perfect square we need to multiply number by 5.
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