Hi All,

This question is perfect for TESTing VALUES.

We're told to take the sum of the reciprocals of two CONSECUTIVE POSITIVE INTEGERS....

Let's TEST 2 and 3....

The sum of the reciprocals would be...

1/2 + 1/3 =
3/6 + 2/6 =
5/6

We're asked how this sum relates to the greater integer X. In simple terms, we're looking for an answer that equals 5/6 when X = 3...

Answer A: X/3 = 3/3 = 1 NOT a match
Answer B: X^2 - X = 3^2 - 3 = 6 NOT a match
Answer C: 2X - 1 = 6 - 1= 5 NOT a match
Answer D: (2X - 1)/(X^2 + X) = 5/12 NOT a match
Answer E: (2X - 1)/(X^2 - X) = 5/6 This IS a MATCH

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Let two consecutive positive integers be x and x-1 (Greater integer is x)
So,
(1/x) + [1/(x-1)]
= (2x-1)/x(x-1)
=(2x-1)/(x^2- x)


Answer E

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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Option E
The greater integer is x and therefore the lesser integer is x-1.
Plug numbers or solve algebraically...
1/x+1/(x-1)
2x-1/x^2 -x


Sent from my iPhone using Tapatalk

E
If greater integer is x then smaller one is x-1
Thus,
1/x + 1/(x-1)
= (2x-1)/x(x-1)
=(2x-1)/(x^2- x)
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MANHATTAN GMAT OFFICIAL SOLUTION:

If the greater of the two integers is x, then the two integers can be expressed as x – 1 and x. The sum of the reciprocals would therefore be:

\(\frac{1}{x-1} + \frac{1}{x} = \frac{x+(x-1)}{(x-1)x}=\frac{2x-1}{x^2-x}\).

The correct answer is E.
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Hi!
I tried using x nd x+1
kindly help me with this solution as using this i am unable to reach to the correct answer choice.
thanks

You won't be able because the question says that the greater integer is x. So to get correct answer you have to use x-1 and x.
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Hi Celestial09,

From your post, it's not clear what work you did when attempting to answer this question. However, if you look a few posts 'up', you'll see how it's relatively easy to answer this question by TESTing VALUES.

GMAT assassins aren't born, they're made,
Rich
_________________

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