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Bunuel
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Bunuel
6x – 5y + 3z = 23

4x + 8y – 11z = 7

5x – 6y + 2z = 12

Given the equations above, x + y + z = ?

(A) 11
(B) 12
(C) 13
(D) 14
(E) 15

\(6x – 5y + 3z = 23...\) (I)

\(4x + 8y – 11z = 7...\)(II)

\(5x – 6y + 2z = 12...\)(III)

Eqn (I) - Eqn(II)

\(2x -13y + 14z = 16\)...(IV)

Eqn(III) - Eqn (II)

\(x-14y+13z= 5\)...(V)

Eqn.(IV) - Eqn (V)

\(x+y+z= 11\)

Ans A
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PikaB
Equation 1 minus Equation 2 gives us x+y+z that gives us 11

Sorry! it doesn't few more steps are required !
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Hi there,

This problem looks intimidating with 3 equations and 3 unknowns, but there's a beautiful shortcut.

We have:
Equation 1: 6x - 5y + 3z = 23
Equation 3: 5x - 6y + 2z = 12

Now, simply subtract Equation 3 from Equation 1:

(6x - 5y + 3z) - (5x - 6y + 2z) = 23 - 12

Let's expand term by term:
- x terms: 6x - 5x = 1x
- y terms: -5y - (-6y) = -5y + 6y = 1y
- z terms: 3z - 2z = 1z
- Right side: 23 - 12 = 11

So we get: x + y + z = 11

Answer: A

Key Insight: When a GMAT question gives you multiple equations but asks for an expression like x + y + z (not individual values), you almost never need to solve for each variable. Instead, look for ways to add or subtract the equations to directly get the expression you need. Before doing any heavy algebra, always check — can I combine these equations to get what the question is asking for? This saves massive time on test day.
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