Quadratics

Question 1

What is the greatest possible value of integer w?

5^w

(1) is an integer.
(2) w is the smallest single digit prime number greater than or equal to the smallest even positive number.

Answer 1

This falls into the recycled quadratic x^2-y^2 which is the same as (x+y)×(x-y). Just plug in the numbers to get (38+37)(38-37)=75, so statement (1) simplifies to 75/5^w. Since the prime factorization of 75 is 3×5×5, the greatest possible value of w is 2, therefore (1) Sufficient->AD.

Statement (2) is another example of GMAC’s word redundancy.

Question 2

9^4+9^5=?

Answer 2

(9)^4x10

Question 3

If a+b=3, and a^2+b^2=6+a·b, what is the value of a·b?

Answer 3

First square the first equation:

• -> a+b=3
• -> (a+b)^2=9
• -> a^2+2ab+b^2=9

The second equation is:

–> a^2+b^2=6+a·b

Now plug in the second equation in the first - substitute 6+a·b for a^2+b^2

• -> 6+ab+2ab=9
• -> 3ab=3
• -> ab=1