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# If 2x + 3 = y + 1/y, then x + y = (1) x = –1/4 (2) y = 2

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4118
GPA: 3.39
If 2x + 3 = y + 1/y, then x + y = (1) x = –1/4 (2) y = 2  [#permalink]

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21 Sep 2019, 23:54
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Difficulty:

35% (medium)

Question Stats:

57% (01:54) correct 43% (01:16) wrong based on 20 sessions

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If $$2x + 3 = y + \frac{1}{y,}$$ then $$x + y =$$

(1) $$x = –\frac{1}{4}$$

(2) $$y = 2$$

Source: Nova GMAT

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Math Expert
Joined: 02 Aug 2009
Posts: 7981
If 2x + 3 = y + 1/y, then x + y = (1) x = –1/4 (2) y = 2  [#permalink]

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22 Sep 2019, 19:27
1
If $$2x + 3 = y + \frac{1}{y,}$$ then $$x + y =$$

If you are short of time, we have one equation given, we require one more equation to answer..
If we know the value of y, we can find x, as x does not have any power. However if we know the value of x, there is a likelihood that we do not get the answer, as we will have a quadratic equation with y^2, so y could have two values...
Short of time, mark B without solving

(1) $$x = –\frac{1}{4}$$
$$2x + 3 = y + \frac{1}{y}$$=$$2*-(\frac{1}{4}) + 3 = y + \frac{1}{y}$$=$$\frac{5}{2} = y + \frac{1}{y}$$..
$$2y^2-5y+2=0.....2y(y-2)-(y-2)=0....(2y-1)(y-2)=0$$, so y could be 2 or 1/2
Insuff

(2) $$y = 2$$
$$2x + 3 = y + \frac{1}{y,}$$=$$2x + 3 = 2+ \frac{1}{2}=\frac{5}{2}...2x=\frac{-1}{2}...x=\frac{-1}{4}$$
Thus, $$x+y=2+(\frac{-1}{4})=\frac{7}{4}$$
Suff

B
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If 2x + 3 = y + 1/y, then x + y = (1) x = –1/4 (2) y = 2   [#permalink] 22 Sep 2019, 19:27
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# If 2x + 3 = y + 1/y, then x + y = (1) x = –1/4 (2) y = 2

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