tjerkrintjema wrote:
I do have to say I was puzzled when they stated in terms of the greater x.
But after some thought I was able to come up with this.
so we have X and X-1 as two consecutive positive integers.
X-1 because X is the greater number.
The reciprocals of X and X-1 are.
1/x and 1/(x-1)
The sum is 1/x + 1/(x-1)
To come up with a common denominator we multiply x and (x-1), which is x^2 - x
And the first numerator will be (x-1) times 1, which is x-1, and the other 1 times x, which is x
So the numerator added together (since we have a common denominator this is allowed) will be 2x-1
Therefore our result is (2x-1)/(X^2-X), hence answer E
"in terms of" should also make you think of "number plugging". If I want x in terms of y, I assume a value for y, find out what x should be and then plug in the y value in the options.
So here, I should take x = 2. So two consecutive positive integers such that the greater one is 2 are 1 and 2.
Sum of reciprocal = 1 + 1/2 = 3/2
Put x = 2 in all the options and check. Only (E) gives you 3/2. Hence (E) is the answer.
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Karishma
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