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# If 5 < x < 10 and y = x + 5, what is the greatest possible

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Manager
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If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  12 Jun 2012, 21:05
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Question Stats:

39% (01:48) correct 61% (00:36) wrong based on 231 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jun 2012, 02:04, edited 1 time in total.
Senior Manager
Joined: 28 Mar 2012
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Concentration: Entrepreneurship
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Kudos [?]: 204 [1] , given: 23

Re: Inequalities Question - Request help [#permalink]  12 Jun 2012, 22:14
1
KUDOS
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.

Regards,
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My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

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Kudos [?]: 41114 [7] , given: 5667

Re: Inequalities Question - Request help [#permalink]  13 Jun 2012, 02:03
7
KUDOS
Expert's post
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?

Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8.

Original question is below:

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.

Hope it's clear.
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Manager
Joined: 02 Jun 2011
Posts: 160
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Kudos [?]: 34 [0], given: 11

Re: Inequalities Question - Request help [#permalink]  13 Jun 2012, 03:52
Bunuel wrote:
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?

Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8.

Original question is below:

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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 27227
Followers: 4232

Kudos [?]: 41114 [0], given: 5667

Re: Inequalities Question - Request help [#permalink]  13 Jun 2012, 03:59
Expert's post
kashishh wrote:
Bunuel wrote:
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?

Please read and follow: 11-rules-for-posting-133935.html Pay attention to the points #3, 7 and 8.

Original question is below:

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.

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.
_________________
Manager
Joined: 27 Apr 2012
Posts: 61
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
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Kudos [?]: 20 [0], given: 19

Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  13 Jun 2012, 04:09
Dear Bunuel,

Apologies for the wrongful post..did not know the rules.Have gone thru the same,will not happen again.Thanks for your help!

Regards
Manager
Joined: 02 Jun 2011
Posts: 160
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Kudos [?]: 34 [0], given: 11

Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  13 Jun 2012, 08:29
Dear Bunuel,
sorry for the word 'need'. i just only wanted to know whether the way i did is right.
Math Expert
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  13 Jun 2012, 08:43
Expert's post
kashishh wrote:
Dear Bunuel,
sorry for the word 'need'. i just only wanted to know whether the way i did is right.

Yes, the way you solved is totally OK.
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  23 Sep 2013, 22:26
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  14 Oct 2013, 09:36
The question asks what is the greatest integer value of 2X+5, where 5<X<10, the greatest value of 2X which is integer will be achieved if X=9.5

Hence the greatest integer value of X+Y = 2x9.5+5=24, answer - D
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible [#permalink]  27 Mar 2015, 19:59
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] 27 Mar 2015, 19:59
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