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by das.ashmita » Tue Jun 12, 2012 9:25 pm
Hi shivanigs

5<x<10 (given)
IMO
For x+y to be an integer,
take x= 9.5 and hence y = 9.5 + 5 = 14.5 (Since only 0.5 + 0.5 will fetch an integer)

Therefore, max (x+y) = 9.5 + 14.5 = 24.
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by shivanigs » Wed Jun 13, 2012 1:40 am
That was a very simple and clear explanation Asmita.it really helped.Thanks a lot!
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by GMATGuruNY » Wed Jun 13, 2012 3:13 am
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?
Another approach is to determine the range of y and then add it to the range of x.

Substituting x = y-5 into 5 < x < 10, we get:
5 < y-5 < 10
10 < y < 15.

Adding 5 < x < 10 to 10 < y < 15, we get:
5+10 < x+y < 10+15
15 < x+y < 25.

Thus, the greatest integer value of x+y is 24.

The solution above employs a very helpful technique: substituting an EQUATION into an INEQUALITY.
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