What is the best way to tackle this kind of problems?

[smodak]

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

[pemdas]

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

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

[sourabh33]

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.

[GMATGuruNY]

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.