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Inequalities-Integer constraints

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rishisbook
 Post subject: Inequalities-Integer constraints
 Post Posted: Sun Aug 28, 2011 3:28 am 
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Students


Posts: 28
There are some problems wherein you are not given whether the variables are integers or not. How do you decide whether we actually have to select integers or decimals as plug-in values to find the answer.

For example, a question in inequality strategy guide is as follows:

Given : x>y, x<6 and y>-3.

Find the max. prime number value for x+y?

What i selected as the answer was 5+2 or 4+3 =7 as the max prime value.But the actual answer is 5.6+5.4=11. Isn't that a little difficult to figure out in two minutes. Will the GMAT test questions where you have to consider awkward decimals to come down to the final answer?
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mithunsam
 Post subject: Re: Inequalities-Integer constraints
 Post Posted: Sun Aug 28, 2011 3:40 pm 
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Course Students


Posts: 76
If the question doesn't say that the variables are integer, then you need to consider both integers and decimals.

For this particular question, we can write y<x<6. Since we have to identify the greatest prime number, we have to take max of x and y within the constraints mentioned in the question.

So, x could be 5.9, y could be 5.8.

x+y = 5.9 + 5.8 = 11.7

This is not a prime, but we got the range. The biggest prime < 11.7 is 11. (We can stop the calculation here).

But, if you want to calculate ->
Since y is always < x, we can reduce value of y by .7. This gives y = 5.1

Now x + y = 5.9 + 5.1 = 11
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JohnHarris
 Post subject: Re: Inequalities-Integer constraints
 Post Posted: Tue Sep 06, 2011 12:23 pm 
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Forum Guests


Posts: 38
rishisbook wrote:
....But the actual answer is 5.6+5.4=11. ...


I'm a little confused here. The actual answer is 11 and has nothing to do with the exact values of x and y other than, for the answer, their sum is a prime and ...

So why does the answer give 5.6 and 5.4 as the values for x and y. As pointed out by mithunsam, another set of x and y (5.9 and 5.1) also works.

In fact, let y be any number between 5 and 6, i.e. 5 < y < 6, and x = 11 - y. Then x is also between 5 and 6 satisfying the conditions of the problem as well as their sum being the answer 11.
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jnelson0612
 Post subject: Re: Inequalities-Integer constraints
 Post Posted: Sat Sep 17, 2011 11:20 pm 
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ManhattanGMAT Staff


Posts: 1857
Hey all, the answer is indeed 11, which can be reached through a variety of values for x and y. The numbers given in the Strategy Guide are just examples of what could work as values for x and y. They are definitely not the only possible values for x and y.

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Jamie Nelson
ManhattanGMAT Instructor
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