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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..??

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 .....
_________________

Regards, Rajesh Helping hands are anytime better than praying hearts

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

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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

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.

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