SAT Problems

**Problem 1**

**Problem 2**

If *a – b = 17.*5 and *a + b = 10* , what is the value of *a ^{2 }– b^{2} *?

Answer Help Solution

**Problem 3**

If *x ^{2 }– y^{2 }= 14 *and

*x – y = 7*, what is the value of

*x + y*?

Answer Help Solution

**Problem 4**

**Problem 5**

**Problem 6**

** **For all numbers x and y, let x ♣ y be defined as x ♣ y = x^{2} − 2xy + y^{2} . What is the value of (2♣4)♣8 ?

Answer Help Solution

**Problem 7**

m^{2} − n^{2} < 12

m + n > 10

If m and n are positive integers in the inequalities above and m > n, what is the value of m ?

Answer Help Solution

**Problem 8**

*If a ^{2} – b^{2} = 12*, and

*(a – b*

*) = 4*, then what is the value of

*ab*?

Answer Help Solution

**Problem 9**

**Prob****lem**** 10
**

In the equations above, if *a** 0, *which of the following is equal to *(x – y) (x + y) *?