smodak wrote:If i and d are integers, what is the value of i?
(1) The remainder when i is divided by (d+2) is the same as when i is divided by d
(2) The quotient when i is divided by (d+2) is d
E
Sometimes it's easier to start with statement 2.
Statement 2: The quotient when i is divided by (d+2) is d.
i/(d+2) = d
i = d(d+2)
If d=1, i=1*(1+2) = 3.
If d=2, i=2*(2+2) = 8.
Since in the first case i=3 and in the second case i=8, insufficient.
Statement 1: The remainder when i is divided by (d+2) is the same as when i is divided by d.
The combinations of values that satisfied statement 2 also satisfy statement 1.
Let i=3, d=1.
i/d = 3/1 = 3 R0.
i/(d+2) = 3/(1+2) = 3/3 = 1 R0.
When the divisor is d+2, the remainder is the same as when the divisor is d.
Let i=8, d=2.
i/d = 8/2 =4 R0.
i/(d+2)/ = 8/(2+2) = 8/4 = 2 R0.
When the divisor is d+2, the remainder is the same as when the divisor is d.
Since in the first case i=3 and in the second case i=8, insufficient.
Statements 1 and 2 together:
Since the combinations of values used above satisfy both statements, and in the first case i=3 and in the second case i=8, insufficient.
The correct answer is
E.
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