is x > 3?
1) (x-3)(x-2)(x-1) > 0
2) x > 1
OA: E
the OE was complicated. could someone simplify it?
1) (x-3)(x-2)(x-1) > 0
2) x > 1
OA: E
the OE was complicated. could someone simplify it?
First thing about DS questions, I love solving them by trying to show that the statement can give yes & no answers to the question and thereby eliminating them,
Lets take 2) first, since it is easier
Statement (2): x>1
We can easily eliminate since x can be 1.5 or 2 or 10, we can't say whether x is greater than 3 or not. So, there goes Statement 2) and answer choices (B) and (D)
Statement (1): (x-3)(x-2)(x-1) > 0
take x as 1.5 -> (1.5-3)(1.5-2)(1.5-1) -> (-ve)(-ve)(+ve) -> so the answer is positive, since two neagtives make a prositive and therefore we have proved that x can be less than 3
now, let us prove that x can be greater than 3
-> take x as 4 -> (4-3)(4-2)(4-1) -> which is obviously greater than zero.
So, statement 1 alone is also not sufficient and so there goes answer choice (A) as well
Combining both statements
X> 1 and (x-3)(x-2)(x-1) > 0
from our calculations for statement 2, we already showed that taking x=1.5 and x=4, we are able to satisfy the inequality and since these two values of x are greater than 1, we are thus unable to determine whether x>3.
Hope this helps.
