If x + 3y + 5z = 31, and x + 5y + 9z = 59, then x + y + z = A) 3 B) 5 C) 7 D) 9 E) 11 Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

x+3y+5z=31 Equation 1 x+5y+9z=59 Equation 2 Equation 2- Equation 1= 2y+4z=28 y+2z=14--->y=14-2z x+3(14-2z)+5z=31 Equation 3 x+5(14-2z)+9z=59 Equation 4 Equation 4- Equation 3=28-2z=28 z=0 Substituting z=0 into y=14-2z, we get y=14 x+3(14)=31 x=-11 x+y+z=0+14-11=3 A

Nice, work - the answer is A Here's another way to tackle this question: For convenience, we’ll label the two equations: (a) x + 3y + 5z = 31 (b) x + 5y + 9z = 59 If we subtract (equation b) – (equation a) we get: 2y + 4z = 28 The next part is tricky. We need to recognize that “x + y + z” and “2y + 4z” are both “hiding” in equation (a) We can rewrite equation (a) as: x + y + z + 2y + 4z = 31 It’s even clearer if we rewrite equation (a) as: (x + y + z ) + (2y + 4z ) = 31 We then replace 2y + 4z with 28, we get (x + y + z ) + (28) = 31 From this, we can conclude that x + y + z = 3 The correct answer is A

Brent Hanneson wrote:Nice, work - the answer is A Here's another way to tackle this question: For convenience, we’ll label the two equations: (a) x + 3y + 5z = 31 (b) x + 5y + 9z = 59 If we subtract (equation b) – (equation a) we get: 2y + 4z = 28 The next part is tricky. We need to recognize that “x + y + z” and “2y + 4z” are both “hiding” in equation (a) We can rewrite equation (a) as: x + y + z + 2y + 4z = 31 It’s even clearer if we rewrite equation (a) as: (x + y + z ) + (2y + 4z ) = 31 We then replace 2y + 4z with 28, we get (x + y + z ) + (28) = 31 From this, we can conclude that x + y + z = 3 The correct answer is A This can also be answered quickly this way... x+3y+5z = 31-----------(a) x+5y+9z = 59-----------(b) [2x(a)] - (b) gives us straightaway x+y+z=3

Brent Hanneson wrote:If x + 3y + 5z = 31, and x + 5y + 9z = 59, then x + y + z = A) 3 B) 5 C) 7 D) 9 E) 11 Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum. 2*(eqn1) - eqn2 = x+y+z = 3