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

BTGModeratorVI wrote: ↑

Mon Sep 14, 2020 8:44 am

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

Answer: A
Source: Manhattan prep

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

BTGModeratorVI wrote: ↑

Mon Sep 14, 2020 8:44 am

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

Answer: A

Solution:

Since y > -3 and y < x, then y can be almost as large as 6 (like x). Therefore, x + y < 6 + 6 = 12. Since 11 is the largest prime number less than 12, then x + y could be 11 (for example, x = 5.6 and y = 5.4).

Answer: A