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Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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24 Jun 2008, 09:47

Question:

If x>y, x<6 and y > -3, what is the largest prime number that could be equal to x+y ?

My answer:

sorting out inequalities here, simplified form is -3 < y < x < 6

So as per this x not equals y and is less greater than x. As x is <6, largest possible value is 5. Hence largest possible value for y is 4 (as it should be < x). Maximum SUM (x+y) =10 and largest prime possible is 7

As per MGMAT explanation answer is 11. Here is the explanation from the book which doesn't make sense to me:

"The upper extreme for x is less than 6. The upper extreme for y is also < 6 as long as it is less than x. Therefor, x+y must be less than 12.The larget prime number less than 12 is 11".

The part I am not clear here is "The upper extreme for y is also < 6 as long as it is less than x". How it can be ever > 4 as it should be always less than x which in turn should be < 6 ?

Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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24 Jun 2008, 09:54

1

This post received KUDOS

The question does not state that x and y are integers. So x must be less than 6

Make x = 5.999999 Make y = 5.111111

Now x + y = 11.

pbvmba wrote:

Question:

If x>y, x<6 and y > -3, what is the largest prime number that could be equal to x+y ?

My answer:

sorting out inequalities here, simplified form is -3 < y < x < 6

So as per this x not equals y and is less greater than x. As x is <6, largest possible value is 5. Hence largest possible value for y is 4 (as it should be < x). Maximum SUM (x+y) =10 and largest prime possible is 7

As per MGMAT explanation answer is 11. Here is the explanation from the book which doesn't make sense to me:

"The upper extreme for x is less than 6. The upper extreme for y is also < 6 as long as it is less than x. Therefor, x+y must be less than 12.The larget prime number less than 12 is 11".

The part I am not clear here is "The upper extreme for y is also < 6 as long as it is less than x". How it can be ever > 4 as it should be always less than x which in turn should be < 6 ?

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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24 Jun 2008, 10:03

Rewrite -3 < y < x < 6. We know that if x > y, then you can assign the highest possible value for x, and the next highest value possible value for y. It didn't say y or x had to be a negative number, so I allowed y and x to be positive.

I plugged in 5.99 for x and 5.98 for y = 11.97. Since that's not a prime, the next possible number down is 11.

Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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21 Nov 2010, 08:45

Guys, i have a question here from the MGMAT but I can't understand the answer to the following question : If x>y, x<6, and y>-3, what is the largest prime number that could be equal to x + y ? could someone help ?

Guys, i have a question here from the MGMAT but I can't understand the answer to the following question : If x>y, x<6, and y>-3, what is the largest prime number that could be equal to x + y ? could someone help ?

So we have: \(-3<y<x<6\).

Note that we are not told that \(x\) and \(y\) are integers. Obviously as \(x<6\) and \(y<x\) then \(x+y\) must be less than 6+6=12. Let's check whether \(x+y\) could be equal to the first prime less then 12, so to 11. Now, if \(y=5.1<5.9=x<6\) then \(x+y=11=prime\).

These conditions just tell you that on the number line, both x and y lie between -3 and 6 and that x is to the right of y:

Attachment:

Ques2.jpg [ 2.86 KiB | Viewed 3900 times ]

>>>>>what is the largest prime number that could be equal to x+y

The maximum value x and y can take is a little less than 6 so their sum must be a little less than 12. The largest prime less than 12 is 11. You can make 11 in a number of ways: (5.6 = x, 5.4 = y), (5.8 = x, 5.2 = y) etc.

They don't say that x and y must be integers. Had they said that, then the greatest sum would have been 7 (4 = x, 3 = y)
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Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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04 Sep 2011, 09:04

excellent question.... my answer was 7 i did reach till -3<y<x<6, then i "assumed" that to get a prime number(which is an integer) , we need to add two integers :O
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Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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22 Sep 2013, 21:42

atewari wrote:

If x>y, x<6 and y>-3, what is the largest prime number that could be equal to x+y?

I solve the question to have the result as 7 with the inequality expression being -3<y<x<6. Whereas, the Manhattan guide gives a solution as 11 with the same inequality expression. Am I missing something?

Yes, you are missing something.

Firstly, both x & y are not necessarily integers. Again, y>-3, thus, y can take any value as long as y<x and x<6. Had x=6, then y could be any value between {-3,6}[not including both the end points]. Thus, Max value of (x+y) <12. The nearest prime =11.

Re: If x > y, x < 6, and y > -3, what is the largest prime number that [#permalink]

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03 Sep 2017, 06:51

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