Inequalities Advanced

[miproyecto]

Hi I am currently going through the GMAT Math Prep books (Book 3)

I have a question regarding Problem 1 on page 187 (book 3)

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

My answer would be 7, but I do not know how to get 11 (the answer from the book).

Thanks,
Ed

[StaceyKoprince]

They're looking for a circumstance in which x+y is prime. They do not specify that x and y are integers. (This is REALLY important to notice!)

x < 6, and we're trying to make the "largest" number, so let's make x as big as we can. How about 5.9? Now, y has to be smaller than 5.9, but it could be, say, 5.8.

5.9 + 5.8 is not going to be a prime, obviously (because it won't be an integer), but it should give me an idea of what prime I might be able to create.

5.9 + 5.8 = 11.7. Ah. Okay, so the largest prime that is LESS than 11.7 is 11, so I can definitely create 11. (Say: 5.9 and 5.1!)

Can I create the next prime number, 13? Hmm. No - that would require at least one of the numbers to be bigger than 6, and neither number is bigger than 6, so I can't do that. 11 it is.

So don't make that assumption that x and y are integers!!

[akhp77]

6 > x > y > -3

x < 6 and assume y = 5.9

x + y < 11.9

Largest prime no could be 11

[tim]

That definitely works. Notice how you're adding the same thing to both sides of the inequality, which is always legal.

6 > x > y > -3

x < 6 and assume y = 5.9

x + y < 11.9

Largest prime no could be 11