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Director  Joined: 01 May 2007
Posts: 644
If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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14 00:00

Difficulty:   95% (hard)

Question Stats: 27% (01:32) correct 73% (01:37) wrong based on 122 sessions

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

A. 11
B. 13
C. 7
D. 5
E. 2
Intern  Joined: 03 Mar 2007
Posts: 28
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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Im going with 7

X>Y
X<6
Y>-3

Possible X Possible Y
5 2 = 7
5 0

Primes: 3, 5, 7, 11, 13, etc.
Director  Joined: 12 Jul 2007
Posts: 661
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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2
jimmyjamesdonkey wrote:
If x>y, x<6, and y> -3, what is the largest prime number that could be equal to x+y?

Primes: 2, 3, 5, 7, 11, 13, 17, etc

If X is less than 6 and y is less than X, then 6+6 = 12 would be impossible. We know 13 and all the primes > 13 are out. Let's try 11.

5.9 + 5.1 = 11

5.9 < 6
5.1 < 5.9

everything checks out

Only trick is to remember there aren't any restrictions on the numbers, ie they don't have to be integers.
Intern  Joined: 05 Mar 2008
Posts: 12
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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Question:

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

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 ?
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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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1
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 ?

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 ?
Intern  Joined: 30 Jul 2007
Posts: 27
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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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.
Intern  Joined: 24 Jul 2010
Posts: 40
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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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 ?
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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2
whichscore wrote:
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 $$x+y=11=prime$$.

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Intern  Joined: 24 Jul 2010
Posts: 40
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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In fact the answer is 11.
I think that the trap in this question was assuming that x and y are integers.

Thank you bunnel !
Retired Moderator Joined: 20 Dec 2010
Posts: 1546
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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kamalkicks wrote:
Q1. if x>y, x<6, and y>-3
what is the largest prime number that could be equal to x+y

kindly solve... and check what is the answer -- 11 or 7

x=5.6
y=5.4

x>y
5.6>5.4

x<6
5.6<6

y>-3
5.4>-3

x+y=5.6+5.4=11
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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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>>>> if x>y, x<6, and y>-3

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 5007 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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1
If y > -3, then x > -3

So we have -3 < x < 6 and -3 < y < 6

=> x + y < 12

To get the maximum value of x+y we have to maximize both x and y in way that y < x

so x can be max like 5.9 and y = 5.1, and this results in (x+y) becoming a prime number as 11 (11 is the biggest prime number < 12)
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Director  Joined: 01 Feb 2011
Posts: 531
Re: If x > y, x < 6, and y > -3, what is the largest prime number that  [#permalink]

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x,y need not be integers.

Given
x<6
y>-3
x>y => -3<x<6
-3<y<x

sum cannot be greater than 12
maximum value of x+y = maximum of x + maximum of y
=5.9 +5.1

Manager  Joined: 10 Nov 2010
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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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1) If x>y, x<6 and y>-3, what is the largest prime number that could be equal to x+y?

as x<6 max x can be 5

y>-3 to get the largest prime number equal to x+y

y= -2

x+y = 5-2 = 3

Which is not correct. i want to know why?

Second method if we line up
If we line up the inequalities we get -3<y<x<6

But how to proceed further and how we get OA 11

Pls help
Manager  Status: mba here i come!
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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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info given:

-3 < y < 6
-3 < x < 6

-3-3 = -6
-3+6 = +3
+6-3 = +3
+6+6 = +12

-6 < x+y < 12

hence, 11 is the largest prime
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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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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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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.

For better clarity, assume x=5.9, y=11-5.9 = 5.1

or x= 5.8, y = 11-5.8 = 5.2

and so on.

Hope this is clear.
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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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From question stem,

-3<y<x<6

And we have to find out largest prime no. after adding x+y

now first thing is that x+y is an integer because all primes are positive integers.
Second thing is we have maximize the value so take maximum of x and to meet the condition x>y, take value of y just below of x.

lets take x= 5.99
y= 5.98
(Here I am taking two digit after decimal.)
now X+Y = 11.97 ...
but we already know that primes are integers then only possible prime just below this 11.97 is 11.
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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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