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Question 298192: Maurice wants to multiply together two numbers composed of two digits each. Unfortunately, he reverses the digits of one of the numbers and obtains a result which is greater than the exact result by 3015. Which of the following could be one of the numbers?
(A) 23 (B) 38 (C) 45 (D) 62 (E) 81
Answer by amoati(11)   (Show Source):
You can put this solution on YOUR website! Let's assume that the numbers are A & B and it was B that Maurice reverses.
Since B is 2 digits number we can say that B = W + 10 Y
So the exact result would be A * (W + 10 Y) and when he reserves the digits of the B number, the result would be A * (Y + 10 W)
So the difference would be A * (Y + 10 W) - A * (W + 10 Y) = 3015
So A * (Y + 10 W - W -10 Y) = 3015
A * (9 W - 9 Y) = 3015
dividing by 9
A * (W - Y) = 335
335 is the multiplication of 5 * 67 (67 is a prime number)
So the difference between the two digits of the B number is 5
then the correct answer would be (B) 38
In fact we can verify our answer since now we know both numbers A = 67, B = 38
So A * B = 67 * 38 = 2546 and when B is reserved 67 * 83 = 5561 and the difference 5561 - 2546 = 3015 :)
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