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Re: Inequalities Question - Request help [#permalink]

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12 Jun 2012, 22:14

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shivanigs wrote:

Hi,

Request your help to understand the concept behind the following question :

If 5 < x < 10 and y = x + 5,what is the greatest possible integer value of x + y?

Hi,

To find the greastest possible integer value of x + y, it is not necessary that both x & y should be integers, x, y should be chosen in such a way that their sum is an integral value.

so, to find, max value of (x + y) x + y = 2x + 5 maximum value of x such that 2x is integer would be 9.5 (given, 5 < x < 10) x + y (maximum) = 19 + 5 =24

Let me know if you need any more assistance on this topic.

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18 B. 20 C. 23 D. 24 E. 25

Since \(y=x+5\) then \(x+y=x+(x+5)=2x+5\). So, we need to find the greatest possible integer value of \(2x+5\).

Multiply \(5 < x < 10\) by 2: \(10<2x<20\). Now add 5 to each part of the inequality: \(15<2x+5<25\). As you can see the greatest possible integer value of \(2x+5\) is 24.

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18 B. 20 C. 23 D. 24 E. 25

Since \(y=x+5\) then \(x+y=x+(x+5)=2x+5\). So, we need to find the greatest possible integer value of \(2x+5\).

Multiply \(5 < x < 10\) by 2: \(10<2x<20\). Now add 5 to each part of the inequality: \(15<2x+5<25\). As you can see the greatest possible integer value of \(2x+5\) is 24.

Answer: D.

Hope it's clear.

Dear Bunuel, 1.)can't understand what is the need to take 2x+5? wont it be easy to calculate with x less than 10.? 2.) when x is not integer but x+y to be integer - we can take x=9.5 and y = 14.5 - giving 24 - is this right?

If 5 < x < 10 and y = x + 5, what is the greatest possible integer value of x + y ?

A. 18 B. 20 C. 23 D. 24 E. 25

Since \(y=x+5\) then \(x+y=x+(x+5)=2x+5\). So, we need to find the greatest possible integer value of \(2x+5\).

Multiply \(5 < x < 10\) by 2: \(10<2x<20\). Now add 5 to each part of the inequality: \(15<2x+5<25\). As you can see the greatest possible integer value of \(2x+5\) is 24.

Answer: D.

Hope it's clear.

Dear Bunuel, 1.)can't understand what is the need to take 2x+5? wont it be easy to calculate with x less than 10.? 2.) when x is not integer but x+y to be integer - we can take x=9.5 and y = 14.5 - giving 24 - is this right?

What do you mean by "need"? One can solve a question with different approaches and you can choose the approach you personally find easier.
_________________

Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]

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23 Sep 2013, 22:26

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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]

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27 Mar 2015, 19:59

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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]

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13 Jun 2016, 04:36

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Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]

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18 Jun 2017, 19:34

Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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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