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saruba
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it is 15 and not 14 because we r not told x and y r integers themselves therefore their value can be 6.9 and 8.9 also.... ie x+y<9+7
i hope it helped
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If the x and y can be 6.9 and 8.9, then the sum would 15.8, which would round up to 16? Or are we assumed to round down?
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risys82
If the x and y can be 6.9 and 8.9, then the sum would 15.8, which would round up to 16? Or are we assumed to round down? Or am I missing the point?

We can do round off if we are asked the approximate value in the question. But in this case, we are asked to find the "greatest integer value" and there is no mention of approximation in the question.
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x = 6.5 and y = 8.5.
x + y = 15
Hence , 15 it is.
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Solution:

1+2<x+y<7+9;

3<x+y<15

x+y has to be an integer that is less than 15, the next largest to 15 is 14.
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Interesting question.
If you put the possible answers, probably we could have fallen for the trap more easily.
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cano
Interesting question.
If you put the possible answers, probably we could have fallen for the trap more easily.

Also don't put tricky in the subject of the thread. :wink: This is the type of question everyone needs to practice on so they understand there can be questions where there is a distinct difference between available inputs and outputs.
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15 should be answer
x= 6.99999999999999999
y = 8.9999999999999999
when adding up integer value should be 15
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Since they've asked for the largest integer value hence it would be, 6.5+8.5= 15
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If you add both the inequalities you will get the largest possible integer value as 15 only.

1<x<7
+ 2<y<9
----------
3<x+y<16
----------

Hence, the largest possible integer value is 15
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