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

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

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New post 19 Dec 2011, 07:28
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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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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible integer [#permalink]

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

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New post 19 Dec 2011, 08:40
I got the point..but i just want to know what was wrong with my logic..??
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Re: If 5 < x < 10 and y = x + 5, what is the greatest possible integer [#permalink]

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

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New post 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

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

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

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

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

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New post 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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New post 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

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

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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.

Answer: D.

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