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Is (7+x)/(8+x) ≥ 7/8?

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Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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Thought this was a nice question:

Is (7+x)/(8+x) ≥ 7/8?

(1) x <= 0
(2) x >= 0
[Reveal] Spoiler: OA

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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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New post 21 Jun 2013, 12:29
Is \(\frac{(7+x)}{(8+x)}\) ≥ 7/8?

A complete study of the equation would look like this:

\(\frac{8(7+x)-7(8+x)}{8(8+x)}\geq{0}\)

The N is \(\geq{0}\) if \(x\geq{0}\)
The D is \(>0\) if \(x>-8\)

So overall the equation is \(\geq{0}\) if \(x\geq{0}\) or if \(x<-8\)

(1) x <= 0
Not sufficient

(2) x >= 0
Sufficient
B
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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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New post 21 Jun 2013, 23:24
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mattce wrote:
Thought this was a nice question:

Is (7+x)/(8+x) ≥ 7/8?

(1) x <= 0
(2) x >= 0


From F. S 1, assume x = 0. Thus, the question stem would read as IS 7/8≥ 7/8 ; we get a YES.
Again, assume x = -7, and the question stem would read as IS 0≥ 7/8 ; we get a NO. Insufficient.

From F.S 2, we know that (8+x) will ALWAYS be positive. Thus, we can safely cross multiply and the question stem would read as :

IS 8*(7+x)≥ 7*(8+X) --> IS 8x≥ 7x --> IS x≥ 0 ; This is always true. Sufficient.

B.
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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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New post 22 Jun 2013, 12:32
mau5 wrote:
mattce wrote:
Thought this was a nice question:

Is (7+x)/(8+x) ≥ 7/8?

(1) x <= 0
(2) x >= 0


From F. S 1, assume x = 0. Thus, the question stem would read as IS 7/8≥ 7/8 ; we get a YES.
Again, assume x = -7, and the question stem would read as IS 0≥ 7/8 ; we get a NO. Insufficient.

From F.S 2, we know that (8+x) will ALWAYS be positive. Thus, we can safely cross multiply and the question stem would read as :

IS 8*(7+x)≥ 7*(8+X) --> IS 8x≥ 7x --> IS x≥ 0 ; This is always true. Sufficient.

B.

It's a great explanation
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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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New post 06 Jan 2016, 19:00
Bunuel wrote:
Is (7+x)/(8+x) ≥ 7/8?

The question transforms to: is \(\frac{x}{x+8}\geq{0}\). This equation will hold true for \(x<-8\) and \(x\geq{0}\)

(1) x <= 0. Not sufficient.
(2) x >= 0. Sufficient.

Answer: B.


Hi Bunuel,

When i try to solve this equation, i get:
(7+x)/(8+x) ≥ 7/8
>> (7+x)/(8+x)-7/8 ≥ 7/8-7/8
>> (7+x)/(8+x)-7/8 ≥ 0
>> 8(7+x) - 7(8+x) / 8(8+x) ≥ 0
>> 56 + 8x - 56 - 7x / 8(8+x) ≥ 0
>> x / 8(8+x) ≥ 0

I think i am wrong somewhere. Can you please pinpoint my mistake?
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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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New post 02 Mar 2017, 09:01
Meetup wrote:
Bunuel wrote:
Is (7+x)/(8+x) ≥ 7/8?

The question transforms to: is \(\frac{x}{x+8}\geq{0}\). This equation will hold true for \(x<-8\) and \(x\geq{0}\)

(1) x <= 0. Not sufficient.
(2) x >= 0. Sufficient.

Answer: B.


Hi Bunuel,

When i try to solve this equation, i get:
(7+x)/(8+x) ≥ 7/8
>> (7+x)/(8+x)-7/8 ≥ 7/8-7/8
>> (7+x)/(8+x)-7/8 ≥ 0
>> 8(7+x) - 7(8+x) / 8(8+x) ≥ 0
>> 56 + 8x - 56 - 7x / 8(8+x) ≥ 0
>> x / 8(8+x) ≥ 0

I think i am wrong somewhere. Can you please pinpoint my mistake?


Absolutely there.
Just remove 8 from denominator. Its not needed to find the values of x.
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Re: Is (7+x)/(8+x) ≥ 7/8? [#permalink]

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New post 02 Mar 2017, 09:47
Bunuel wrote:
Is (7+x)/(8+x) ≥ 7/8?

The question transforms to: is \(\frac{x}{x+8}\geq{0}\). This equation will hold true for \(x<-8\) and \(x\geq{0}\)

(1) x <= 0. Not sufficient.
(2) x >= 0. Sufficient.

Answer: B.


short and nice explanation
Re: Is (7+x)/(8+x) ≥ 7/8?   [#permalink] 02 Mar 2017, 09:47
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