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

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Manager
Joined: 04 Dec 2011
Posts: 80

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Schools: Smith '16 (I)
If 5 < x < 10 and y = x + 5, what is the greatest possible integer [#permalink]

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19 Dec 2011, 07:28
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Difficulty:

45% (medium)

Question Stats:

42% (00:30) correct 58% (00:37) wrong based on 38 sessions

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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

I just want to know what is the flaw in my logic..? if i take maximum value of x to be 9 as per eq1 and from 2nd equation its 9+5=14.. i read the solution but somehow still not convinced with the answer..can someone help..??

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-5-x-10-an ... 34434.html
[Reveal] Spoiler: OA

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Nikhil

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

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19 Dec 2011, 07:50
nikhil007 wrote:
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

I just want to know what is the flaw in my logic..? if i take maximum value of x to be 9 as per eq1 and from 2nd equation its 9+5=14.. i read the solution but somehow still not convinced with the answer..can someone help..??

Multiply 2 for the inequality 10<2x<20

Add x on both sides : x+y= 2x+5

Max int value for 2x will be 19

so Max (x+y)=19+5=24

So ,D .....
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Rajesh
Helping hands are anytime better than praying hearts

Kudos ???!@#$$!!! I just love them Kudos [?]: 16 [0], given: 11 Manager Joined: 04 Dec 2011 Posts: 80 Kudos [?]: 27 [0], given: 13 Schools: Smith '16 (I) Re: If 5 < x < 10 and y = x + 5, what is the greatest possible integer [#permalink] ### Show Tags 19 Dec 2011, 08:40 I got the point..but i just want to know what was wrong with my logic..?? _________________ Life is very similar to a boxing ring. Defeat is not final when you fall down… It is final when you refuse to get up and fight back! 1 Kudos = 1 thanks Nikhil Kudos [?]: 27 [0], given: 13 Intern Joined: 31 Oct 2011 Posts: 44 Kudos [?]: 16 [0], given: 11 Location: India Re: If 5 < x < 10 and y = x + 5, what is the greatest possible integer [#permalink] ### Show Tags 19 Dec 2011, 08:57 nikhil007 wrote: I got the point..but i just want to know what was wrong with my logic..?? 5<x<10; max x =9 10<2x<20;max 2x =19(not 9*2=18)==> x=9.5 20<4x<40;max 4x=39 (not 19*2=38)==> x=19.5 Since this an inequality, we can take the value of x directly for y=x+5 . find the value of x+y means he is asking you to find: x+y=(max value of 2x)+5. The max value of 2x is 19 ...not 18 ... _________________ Regards, Rajesh Helping hands are anytime better than praying hearts Kudos ???!@#$$ !!! I just love them

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

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19 Dec 2011, 10:28
The maximum Integer value for 2x is 19, since x is can be fraction and and is less than 10.
2x+5= 2*Less Than 10+ 5= Less than 25= 24

Kudos [?]: 286 [0], given: 11

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

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19 Dec 2011, 10:30
also your equation is X+5 NOT X+Y that the question have asked for.

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

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19 Dec 2011, 10:47
silly me..i got the point now..well in that case max value for x =9 and y=9+5 =14 so x+Y should be 14+9=23...confused...???
_________________

Life is very similar to a boxing ring.
Defeat is not final when you fall down…
It is final when you refuse to get up and fight back!

1 Kudos = 1 thanks
Nikhil

Kudos [?]: 27 [0], given: 13

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Joined: 26 Apr 2011
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible integer [#permalink]

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20 Dec 2011, 05:55
x can take a fraction value so if i take x=9.5 then 2x =19
so x+y=x+x+5=19+5=24
Ans is D

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

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20 Dec 2011, 05:56
x can take a fraction value so if i take x=9.5 then 2x =19
so x+y=x+x+5=19+5=24
Ans is D

Kudos [?]: 21 [0], given: 14

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124653 [2], given: 12079

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

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18 Jun 2017, 01:49
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nikhil007 wrote:
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

I just want to know what is the flaw in my logic..? if i take maximum value of x to be 9 as per eq1 and from 2nd equation its 9+5=14.. i read the solution but somehow still not convinced with the answer..can someone help..??

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-5-x-10-an ... 34434.html
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Kudos [?]: 124653 [2], given: 12079

Re: If 5 < x < 10 and y = x + 5, what is the greatest possible integer   [#permalink] 18 Jun 2017, 01:49
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