If x is an integer, what is the value of x?

Hey bunuel,
I got x=-1,2 from the first statement.
But in the second statement, i took positive and negative possibilities and came up with 4 equations.
the 4 equations are
1.(x^2)-x=2
2.(x^2)+x=2
3. -(x^2)+x=2
4. -(x^2)-x=2
Out of these four equations, according to me, only the 1st and the second have real solutions.
So from the 1st equation above i got x=-1,2(Same as the result from our First Statement )
and from the second equation i got x=1,-2.
But everywhere people have written that they got x=-2,2 from the second statement. Can you please explain it to me as to what the issue is.

if x^2 = 4 then isn't x= (2,-2) ?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x is an integer, what is the value of x?

(1) |x - |x^2|| = 2
(2) |x^2 - |x|| = 2


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), it becomes |x^2|=x^2 -> x-x^2=-2, +2. In x-x^2=-2, +2, x^2-x-2=0, (x-2)(x+1)=0 -> x=2, -1, which is not unique and not sufficient.
For 2), in x^2-|x|=-2, 2, x^2=|x|^2 is derived. |x|^2-|x|=2, |x|^2-|x|-2=0, (|x|-2)(|x|+1)=0 -> x|=2, -1. -1 is impossible. |x|=2 -> x=-2,2, which is not unique and not sufficient.
When 1) & 2), x=2 is unique, which is sufficient.
Therefore, the answer is C.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

A slightly different approach:

Statement 1
X is -1 or 2
Insufficient

Statement 2
X is 2 or -2
Insufficient

Combined
2 is the only common root for both equations = hence X must be 2.
Answer = C

Do square and mod cancel each other?

In this circumstance, especially in the test, doing pure algebra may not be your first instinct. By looking at the question, we know that x is an integer and from the statements, it is clear we are dealing with small numbers so draw a table.



Statement 1 alone: both x = -1 and x = 2 gives 2 --> Not sufficient
Statement 2 alone: both x = -2 and x = 2 gives 2 --> Not sufficient

Together, when they overlap, only x = 2 gives 2 - Sufficient.

The table seems tedious but squaring 1's and 2's should come to you instantly and this table can be drawn in <1.5 mins and hence this question can be solved in <2 mins.

This is the correct explanation. Correct answer is E.

VeritasKarishma plz explain

Hi Bunuel!

Can you explain while solving Modulous questions when we have to square ( approach you used to solve the question) and when we have to use method like less than 0 or greater than zero as few people have used this approach?

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