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# x2 + 1x2 = ?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6212
GMAT 1: 760 Q51 V42
GPA: 3.82
x2 + 1x2 = ?  [#permalink]

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29 Mar 2017, 01:45
00:00

Difficulty:

35% (medium)

Question Stats:

63% (00:45) correct 37% (01:35) wrong based on 126 sessions

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$$x^2 + \frac{1}{x^2}$$ = ?

1) $$x - \frac{1}{x} = 4$$
2) $$x + \frac{1}{x} = 2√5$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Community Reply Senior Manager Joined: 19 Apr 2016 Posts: 274 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) x2 + 1x2 = ? [#permalink] ### Show Tags 29 Mar 2017, 02:12 4 1 MathRevolution wrote: $$x^2 + \frac{1}{x^2}$$ = ? 1) $$x - \frac{1}{x} = 4$$ 2) $$x + \frac{1}{x} = 2√5$$ St I $$x - \frac{1}{x} = 4$$ on squaring both sides, we have $$(x - \frac{1}{x})^2 = 4^2$$ $$x^2 + \frac{1}{x^2} - 2 = 16$$ $$x^2 + \frac{1}{x^2} = 18$$ ----------------Sufficient St II $$x + \frac{1}{x} = 2√5$$ on squaring both sides, we have $$(x + \frac{1}{x})^2 = (2√5)^2$$ $$x^2 + \frac{1}{x^2} + 2 = 20$$ $$x^2 + \frac{1}{x^2} = 18$$ ----------------Sufficient Hence option D is correct Hit Kudos if you liked it ##### General Discussion Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6212 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: x2 + 1x2 = ? [#permalink] ### Show Tags 31 Mar 2017, 01:33 ==> In the original condition, there is 1 variable (x) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. If you actually solve this, you get con 1) = con 2), and thus if you square both sides, from $$x^2 + \frac{1}{x^2} -2=16$$ and $$x^2 + \frac{1}{x^2} +2=20$$, you get $$x^2 + \frac{1}{x^2} =18$$, hence unique and sufficient. Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: x2 + 1x2 = ?  [#permalink]

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22 May 2017, 15:53
MathRevolution wrote:
$$x^2 + \frac{1}{x^2}$$ = ?

1) $$x - \frac{1}{x} = 4$$
2) $$x + \frac{1}{x} = 2√5$$

This question appears to be very simple if you know the properties of foiling; however, this is a question designed to bait the test taker into picking the classic "C" both are sufficient trap. While it knowing (x-y) and (x+y) would be sufficient to solve the question, it is actually not necessary and a skill the GMAT is testing you on... that the GMAT is just testing high school math and algebra is a myth because this clearly this question shows how arithmetic and manual become derelict when calculators are used unnecessarily - well in Singapore it really is but that's another story. Anyways,

Statement 1

$$x - \frac{1}{x} = 4$$ square both sides
$$x - \frac{1}{x} [m]x - \frac{1}{x} = 16 x^2- x(1/x)-x(1/x) + (1/x^2) = 16 x^2-2x(1/x) + (1/x^2) =16 ( pay attention to the reciprocal property) x^2- 2 +(1/x^2) = 16 x^2 + (1/x^2) = 18 Statement 2 [m]x + \frac{1}{x} = 2√5$$
[m]x + \frac{1}{x} [m]x + \frac{1}{x} = 20
x^2 + x(1/x) + x(1/x) + 1/x^2 = 20
x^2 + 2x (1/x) + (1/x^2) = 20 (pay close attention to the reciprocal property- x of any number times its reciprocal is 1 so 2x times the reciprocal of just x is always 2)
x^2 + 2 + (1/x^2) = 20
x^2 + (1/x^2) = 18

Lastly- it is important to note that even though statement 1 and 2 both reduced to a sum of 18- they don't necessarily have to have the same sum. For example, if statement 1 allows you to find x^2 + (1/x^2) and statement 2 also allows you to find x^2 + (1/x^2) but happens to have a different result, say 16 instead of 18, it would still be D.

Thus "D" is the correct answer
Re: x2 + 1x2 = ? &nbs [#permalink] 22 May 2017, 15:53
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