Re: Math question from the GRE General Test
- From: "Jay Petrulis" <jpetrulis@xxxxxxxx>
- Date: 23 Nov 2005 07:09:31 -0800
panayiotismanola...@xxxxxxxxx wrote:
> Hi,
>
> The following question appears in the math section of a 'retired' GRE
> General Test. My claim is that the official answer is incorrect. Can
> someone provide feedback?
>
> It is given that y = x + (1/x) and 0 < x < 10. Is it true that (A) y >
> 100, (B) y < 100, (C) y = 100, or (D) there is not enough information
> to answer this question?
>
> My contention is that (B) is true while ETS contends that (D) is the
> case.
>
> Thanks.
>
> Peter
(i) Trial and error. Test at x = 5, for instance, to confirm that (B)
is a possible answer. Test at x = 0.01 to confirm that (A) is
possible.
(ii) Solve for x, f(x) = x + 1/x = 100, determine if x exists in the
range in question. This will be a quadratic. Determine if there is a
solution in the range for (C) to be possible,
(iii) Also, I don't know if calculus knowledge is presumed for the
test (don't think so for the general test), but take the derivative and
determine if there is a local min or max (min at x = 1 ==> f(1) = 2).
Take the second derivative and determine that f(x) is concave up
throughout the range in question. Check the values at the endpoints
(or near). Check close to zero. 1/x is rising faster than x is
falling.
ETS is correct. Values can be chosen that make (A), (B), or (C) true.
.
- References:
- Math question from the GRE General Test
- From: panayiotismanolakos
- Math question from the GRE General Test
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