Question 1169939
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Let's look at some examples of what is being done here.  Divide one number y by some even integer x and look at the quotient and remainder; and then divide y by x/2 and look at the quotient and remainder.<br>
(1)<br>
13/4 = 3 remainder 1
13/2 = 6 remainder 1<br>
19/6 = 3 remainder 1
19/3 = 6 remainder 1<br>
50/12 = 4 remainder 2
50/6 = 8 remainder 2<br>
In all of these examples, the remainder when divided by the larger divisor is less than half the divisor.  The result is that the quotient doubles and the remainder stays the same.<br>
(2)<br>
29/6 = 4 remainder 5
29/3 = 9 remainder 2<br>
29/8 = 3 remainder 5
29/4 = 7 remainder 1<br>
37/10 = 3 remainder 7
37/5 = 7 remainder 2<br>
In these examples, the remainder when divided by the larger divisor is greater than half the divisor.  The result is that the quotient is 1 more than doubled, and the remainder is reduced by the smaller divisor.<br>
Those are the only two possible results.<br>
In the given example, the remainder decreases by 16 when divided by the smaller number, x/2.<br>
So x/2 = 16, and x = 2*16 = 32.<br>
ANSWER: x = 32<br>
CHECK (examples)<br>
61/32 = 1 remainder 29
61/16 = 3 remainder 13<br>
157/32 = 4 remainder 29
157/16 = 9 remainder 13<br>