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Founder  Joined: 18 Apr 2015
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Expert's post 00:00

Question Stats: 53% (01:45) correct 46% (01:51) wrong based on 13 sessions
If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$
[Reveal] Spoiler: OA

_________________
Founder  Joined: 18 Apr 2015
Posts: 6901
Followers: 114

Kudos [?]: 1343 , given: 6316

Re: If y^-2 + 2y^-1 [#permalink]
Expert's post
Explanation

$$\frac{1}{y^2} + \frac{1}{2y^1} -\frac{1}{15} = 0$$

This is like to write $$y^2 + 2y - 15 =0$$

Now, this is a quadratic equation, in which the multiplication is 15 and the sum is 2.

Two numbers that give us this are +5 and -3

y + 5 =0

y - 3 =0

OR

y = - 5
y = 3

At this point, the answer could be A and E but we do know that the answer must be one and only. Do not forget that we flipped the entire equation for simplicity. We should turn back because our y was raised to -1.

Which means that our 3 becomes $$\frac{1}{3}$$ and our -5 become $$\frac{- 1}{5}$$.

As you can see, we do have one and only correct solution among the answer choices that is $$\frac{- 1}{5}$$.

C is correct
_________________ GRE Instructor Joined: 10 Apr 2015
Posts: 1981
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Re: If y^-2 + 2y^-1 [#permalink]
1
KUDOS
Expert's post
Carcass wrote:
If $$y^{-2} + 2y^{-1} -15 = 0$$, which of the following could be the value of y?

A. $$3$$

B. $$\frac{1}{5}$$

C $$\frac{-1}{5}$$

D. $$\frac{-1}{3}$$

E. $$-5$$

Let's use some u-substitution!

Notice that we can write $$y^{-2}$$ and $$2y^{-1}$$ as powers of $$\frac{1}{y}$$

Here's what I mean:

$$y^{-2} = \frac{1}{y^2}=(\frac{1}{y})^2$$
and
$$y^{-1} = \frac{1}{y^1}=(\frac{1}{y})^1=\frac{1}{y}$$

So, if we let $$u = \frac{1}{y}$$, we can rewrite the equation as follows: $$u^2 + 2u -15 = 0$$

Factor: $$(u+5)(u-3)=0$$

So, EITHER $$u = -5$$ OR $$u = 3$$

If $$u = -5$$, then $$\frac{1}{u} = -5$$, which means $$u = \frac{-1}{5}$$

If $$u = 3$$, then $$\frac{1}{u} = 3$$, which means $$u = \frac{1}{3}$$

Check the answer choices . . .

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: If y^-2 + 2y^-1   [#permalink] 30 Apr 2019, 16:24
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