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14 Dec 2020, 15:51
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Bunuel
Hi Bunuel,
Would you suggest using the quadratic equation solver for statement 2 or is there a faster way to do so? Usually, when the value of ax^2 is 2>a, I have trouble eyeballing the solution for X.
Thank you!
16 Dec 2021, 05:27
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If 2 < x < 4, what is the median of the numbers 0, 5, x, 1, 7, and 3?
If you are able to find a unique value of x , then you can find the median. So we can re frame the question stem as Is it possible to find a unique value of x or not?
(1) 2x−5=0
From statement 1, x = 5/2 = 2.5. We will be able to find the median as we know the value of x.
Statement 1 alone is sufficient.
(2) 2x^2−7x+5=0
Solving the quadratic equation, we get two values of x i.e 1 and 2.5.
Since its given that 2 < x < 4, x= 1 will not be possible and only possible value of x is 2.5.
As we got a unique value of x, we can find the median in this case.
Statement 2 alone is sufficient.
Option D is the answer .
If you are able to find a unique value of x , then you can find the median. So we can re frame the question stem as Is it possible to find a unique value of x or not?
(1) 2x−5=0
From statement 1, x = 5/2 = 2.5. We will be able to find the median as we know the value of x.
Statement 1 alone is sufficient.
(2) 2x^2−7x+5=0
Solving the quadratic equation, we get two values of x i.e 1 and 2.5.
Since its given that 2 < x < 4, x= 1 will not be possible and only possible value of x is 2.5.
As we got a unique value of x, we can find the median in this case.
Statement 2 alone is sufficient.
Option D is the answer .
16 Dec 2021, 06:15
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bgribble
This seems not to have been mentioned once in the discussion above: the two statements in a DS question must be consistent. If Statement 1 only gives us one solution for x, that solution will need to work with Statement 2. So if, as Statement 1 tells us, 2x - 5 = 0, then 2x - 5 must be one of the factors of the quadratic in Statement 2. And if we know one of the two factors of 2x^2 - 7x + 5, finding the other factor becomes a lot easier. When we 'FOIL' out, in order to get the "2x^2" and the "+5" in "2x^2 - 7x + 5", we'll need to multiply the 2x from '2x - 5' by x, and we'll similarly need to multiply the -5 from '2x - 5' by -1. So the other factor will need to be x-1, and the other solution for x will be 1, which doesn't satisfy the 2 < x < 4 inequality in the stem, and the answer is D.
