If x > y, x < 6, and y > -3, what is the largest prime number that

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 ?

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.

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 \(x+y=11=prime\).

Answer: 11.

>>>> 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:



>>>>>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)

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)

The key here is to recognize that the question does NOT state that x and y are integers

Given: -3 < y < x < 6

B) 13
Let's first see if there is a way for x + y to equal 13, the greatest answer choice
Since we are told that x and y are each less than 6, there is no way for their sum to equal 13
Eliminate answer choice B

A) 11
Now let's try the second greatest answer choice, 11
Is there a way for x + y to equal 11?
You bet.
If x =5.9 and y = 5.1, then x + y = 11

Answer: A

Cheers,
Brent

We have, -3<y<x<6 and x & y can be any real number integer or non-integer.
max (x+y) should be < 6+6<12
so largest prime number equal to x+y = 11
i.e. x = 5.9 and y = 5.1, x+y = 11

Answer: A

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

x < 6
=> Largest value of x can be very close to 6
Lets say x = 5.9

Now x > y and y > -3
=> y can be maximum equal to 5.8999

To make x + y largest prime number we can start by making x + y integer
=> y = 5.1
=> x + y = 5.9 + 5.1 = 11

We cannot get a bigger integer value of x and y as x < 6 and x > y

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Inequalities