Equation solving - If x + 3y + 5z = 31 . . .

[Brent@GMATPrepNow]

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.

[truplayer256]

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

[Brent@GMATPrepNow]

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

[sureshbala]

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

[x2suresh]

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