algebraic translation works the best as a general plan, then you could look into certain no-s property concepts
st(1) i/(d+2)=q1+r, i/d=q2+r; i/(d+2)-q1=i/d-q2 not sufficient
st(2) i/(d+2)=d+r not sufficient;
combined st(1&2): i/(d+2)-d=i/d-q2 <> id-d^2(d+2)=id+2i-q2*d(d+2) <> 2i=d(d+2)(d+q2)
it looks like none of solution is present

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

Nice question!

IMO, the best and simple way to solve these question is to aim for identifying more than 1 solutions for each statement.


Given I & D are Integers

Evaluating Statement 1

Remainder when I is divided by D or D+2 is same.

The goal here should be to identify at least two where the condition is true

D = 2, I = 8 -> Remainder is 0 for both 8/2 & 8/4
D = 3, I = 15 -> Remainder is 0 for both 15/3 & 15/5

Therefore Insufficient
Evaluating Statement 2

The quotient when I is divided by (D+2) is D

D = 2, I = 8 -> quotient is 2 when 8/2+2
D = 3, I = 15 -> quotient is 3 when 15/3+2

Therefore insufficient



Evaluating Statement 1 & 2 together

Both of the following cases are in sufficient even if apply both st 1 & st 2

D=2, I =8
D=3, I =15

Therefore insufficient


It is imperative to recognize that in question like this the author will definitely provide you with subtle hints and will make sure the questions are solvable.

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.