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In the equation above, x =

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Math Expert
Joined: 02 Sep 2009
Posts: 62456
In the equation above, x =  [#permalink]

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29 Mar 2017, 01:42
1
5
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Difficulty:

25% (medium)

Question Stats:

77% (01:36) correct 23% (01:40) wrong based on 268 sessions

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$$x(5+\sqrt{7})=90$$
In the equation above, x =

A. $$5(5-\sqrt{7})$$

B. 15/2

C. 45

D. $$90(5-\sqrt{7})$$

E. $$90(5+\sqrt{7})$$

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Re: In the equation above, x =  [#permalink]

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29 Mar 2017, 02:20
5
2
Bunuel wrote:
$$x(5+\sqrt{7})=90$$
In the equation above, x =

A. $$5(5-\sqrt{7})$$

B. 15/2

C. 45

D. $$90(5-\sqrt{7})$$

E. $$90(5+\sqrt{7})$$

$$x(5+\sqrt{7}) = 90$$

$$x = 90/(5+\sqrt{7})$$

$$x = (90*(5-\sqrt{7}))/((5+\sqrt{7})*(5-\sqrt{7}))$$

$$x = (90*(5-\sqrt{7}))/(25-7)$$

$$x = (90*(5-\sqrt{7}))/18$$

$$x = 5*(5-\sqrt{7})$$

Hence option A is correct
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Re: In the equation above, x =  [#permalink]

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16 Oct 2018, 17:14
Bunuel wrote:
$$x(5+\sqrt{7})=90$$
In the equation above, x =

A. $$5(5-\sqrt{7})$$

B. 15/2

C. 45

D. $$90(5-\sqrt{7})$$

E. $$90(5+\sqrt{7})$$

Simplifying we have:

x = 90/(5 + √7)

We must rationalize the denominator by multiplying numerator and denominator of the right side of the equation by the conjugate of (5 + √7). The conjugate of (5 + √7) is (5 - √7). Multiplying the rightside by (5 - √7)/(5 - √7), we have:

90(5 - √7)/(25 - 7) = 90(5 - √7)/18 = 5(5 - √7)

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Re: In the equation above, x =  [#permalink]

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16 Oct 2018, 18:59
1
The best approach for solving this question is to simply put the answer choices one by one in place of x
By inputing answer choices in value of x, we get Option B as the answer where L.H.S=R.H.S.
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Joined: 12 Sep 2017
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Re: In the equation above, x =  [#permalink]

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13 Jan 2019, 15:44
ScottTargetTestPrep wrote:
Bunuel wrote:
$$x(5+\sqrt{7})=90$$
In the equation above, x =

A. $$5(5-\sqrt{7})$$

B. 15/2

C. 45

D. $$90(5-\sqrt{7})$$

E. $$90(5+\sqrt{7})$$

Simplifying we have:

x = 90/(5 + √7)

We must rationalize the denominator by multiplying numerator and denominator of the right side of the equation by the conjugate of (5 + √7). The conjugate of (5 + √7) is (5 - √7). Multiplying the rightside by (5 - √7)/(5 - √7), we have:

90(5 - √7)/(25 - 7) = 90(5 - √7)/18 = 5(5 - √7)

Hello ScottTargetTestPrep !

Why usually when we rationalize the denominator it ends up being 1 but in this case is not?

I have seen a lot of examples here that people automatically put a 1 after this kind of terms:

(5 + √7)(5 - √7) = 1 (Now I know is not 1)

Should we have to solve it in all cases?

Kind regards!
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Re: In the equation above, x =  [#permalink]

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14 Jan 2019, 18:08
1
Hi jfranciscocuencag,

It sometimes ends up as 1; for example, (4 + √15) x (4 - √15) = 16 - 15 = 1; however in other examples the outcome is not 1.

For example, (4 + √14) x (4 - √14) = 16 - 14 = 2. More often, it is the latter case rather than the former, so never expect for the result to be 1 until you carry out the multiplication.
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Scott Woodbury-Stewart

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Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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Director
Joined: 16 Jan 2019
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Re: In the equation above, x =  [#permalink]

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31 Jan 2019, 03:36
I had considered that x must be between 90/(5+√9) & 90/(5+√4) [Since working with perfect squares is a lot easier].

Which roughly means 11<x<12

So A is the only option that is even remotely close to this range.

*Is this approach correct?*
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3338
Re: In the equation above, x =  [#permalink]

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28 Feb 2020, 14:08

Solution

Given
• x(5+√7)=90

To find
• Value of x

Approach and Working out
• x(5+√7)=90
• x = 90 / (5+√7)
• Multiplying by (5-√7) in both numerator and denominator, we get:
o x =90(5-√7)/ (25-7)
o x =90(5-√7)/ 18
o x =5(5-√7)

Hence, option A is the correct answer.

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Re: In the equation above, x =   [#permalink] 28 Feb 2020, 14:08
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