Logic Nightmare
Mistake in Logic Nightmare 1
Sorry!
There are 8 statements made in Mrs. George's class about the values of integers a and b from 4 students:
Student A: x is a prime number, while y is not what Student B says it is.
Student B: y is a number that is an even amount greater than x, while x has 8 factors.
Student C: (x - y)(x + y) is greater than the positive difference of the squares of x and y, and xy = y^2 + 5y.
Student D: B's first statement was true, and the sum of x and y is not two less than the square of one more than the number of factors x has.
All students told a true statement and a false statement.
What is the value of (x + 2y)(y + 3x)?
The answer is 7770.
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1 solution
I have no idea how you solved this if you did. If not, look at the first statement of C. He says that (a-b)(a+b)< aa-bb. However, (a-b)(a+b) can be proven to equal aa-bb. Therefore, Student C's first statement is false, and his second is true. After that, it is pretty simple. After all, I don't want to ruin all the fun... (aa=a squared).