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If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the
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20 Nov 2017, 11:26

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Question Stats:

If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

Kudos for correct solution.

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

Show: :: OA

A, C, D, and F

Kudos for correct solution.

Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the
[#permalink]
28 Nov 2017, 03:26

Need either a closer look or discerning eye to get solution on the fly otherwise its would literally waste much time

Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the
[#permalink]
29 Nov 2017, 05:46

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1

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Bunuel wrote:

If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

Show: :: OA

A, C, D, and F

Here the equation can be written as-

\(\frac{5(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{5(x + 1)}{(x - 2)}\)

or \(\frac{(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{(x + 1)}{(x - 2)}\)

or \(\frac{(x + 12)(x+1)}{(x + 12)(x-2)} = \frac{(x + 1)}{(x - 2)}\)

Now looking at the values we notice only when x=2 & x =-12, the equation is not possible, rest all are the possible values.

_________________

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then which of the following are possible values of x?
[#permalink]
06 Nov 2018, 06:02

Expert Reply

3

Bookmarks

If \(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}\) then which of the following are possible values of x?

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5

_________________

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5

_________________

Re: then which of the following are possible values of x?
[#permalink]
09 Nov 2018, 11:05

3

Quick Approach to these type of Questions Solve for the Denominator = 0 and REJECT those values for 'x' as the Denominator can't be 0.

In this question x not equal to 2 & -12 AS IT WILL MAKE THE Denominator 0.

In this question x not equal to 2 & -12 AS IT WILL MAKE THE Denominator 0.

Re: then which of the following are possible values of x?
[#permalink]
11 Nov 2018, 00:40

1

Expert Reply

Carcass wrote:

If \(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}\) then which of the following are possible values of x?

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5

Indicate all such values.

A. − 60

B. − 12

C. − 1

D. 1

E. 2

F. 5

\(\frac{5x^2 + 65x + 60}{x^2 + 10x -24} = \frac{5x+5}{x-2}.......(5x^2 + 65x + 60)*(x-2)=(x^2 + 10x -24)*(5x+5).........5(x^2+13x+12)*(x-2)=(x^2 + 10x -24)*5(x+1).........(x+12)(x+1)*(x-2)=(x + 12)(x -2)*(x+1)\)

so LHS=RHS therefore all values of x are possible except when the denominator becomes 0....

1) x-2=0 means x=2

2) \(x^2 + 10x -24=0........x^2+12x-2x-24=0....(x+12)(x-2)=0\) so x can be 2 or -12

combined x should not be 2 and -12 and rest of the values are possible.

Thus A, C, D and F

_________________

Some useful Theory.

1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048

2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825

3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html

4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html

5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the
[#permalink]
14 Jun 2019, 08:14

1

pranab01 wrote:

Bunuel wrote:

If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

Show: :: OA

A, C, D, and F

Here the equation can be written as-

\(\frac{5(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{5(x + 1)}{(x - 2)}\)

or \(\frac{(x^2 + 13x + 12)}{(x^2 +10x - 24)} = \frac{(x + 1)}{(x - 2)}\)

or \(\frac{(x + 12)(x+1)}{(x + 12)(x-2)} = \frac{(x + 1)}{(x - 2)}\)

or \(\frac{(x+1)}{(x-2)} = \frac{(x + 1)}{(x - 2)}\).

Now looking at the values we notice only when x=2, the equation is not possible, reset all are the possible values.

also, x=-12 gives undefined value, so this is also not possible

Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the
[#permalink]
14 Jun 2019, 22:18

jelal123 wrote:

also, x=-12 gives undefined value, so this is also not possible

Thanks. might be an oversight

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Re: then which of the following are possible values of x?
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30 Jul 2021, 09:20

Carcass , can you please explain the answer of the question. Thanks in advance.

_________________

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Life is 10% what happens to you and 90% how you react to it. ...

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Re: then which of the following are possible values of x?
[#permalink]
30 Jul 2021, 11:07

Expert Reply

Ahasunhabib999 wrote:

Carcass , can you please explain the answer of the question. Thanks in advance.

Dear Sir the two explanations above (the short and the longest one ) are both perfect.

There is not a real shortcut

_________________

Re: If (5x^2 + 65x + 60)/(x^2 +10x - 24) = (5x + 5)/(x - 2), the
[#permalink]
24 Oct 2021, 21:28

Bunuel wrote:

If \(\frac{(5x^2 + 65x + 60)}{(x^2 +10x - 24)} = \frac{(5x + 5)}{(x - 2)}\), then which of the following are possible values of x?

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

Kudos for correct solution.

A. −60

B. −12

C. −1

D. 1

E. 2

F. 5

Show: :: OA

A, C, D, and F

Kudos for correct solution.

This problem makes no sense for me

_________________

PhD in Applied Physics

Re: then which of the following are possible values of x?
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11 Aug 2022, 02:22

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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