What is the value of 10y + 17z ?

Either (1) or (2) alone is not sufficient, because each has additional variable x.

(1)+(2)
By operation -2*(1)+(2), we can eliminate x and obtain the value of 10y + 17z.
SUFFICIENT

FINAL ANSWER IS (C)

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This is a fairly easy question on solving simultaneous linear equations. Since the question does not give us any additional constraints for x, y and z (for example, it doesn’t tell us if the variables are integers, positive only etc.,) the individual statements are insufficient.

Therefore, we can eliminate answer options A, B and D straight away. Answer options C and E are the possible answers at this stage.

Combining both the statements, we have the following:
Let’s multiply the equation in the first statement by -2. The equation becomes,
-2x -4y-14z = -80.
Adding the above equation with the equation given in statement II, i.e. 2x – 6y – 3z =30, we have,
-10y – 17z = -50 or 10y + 17z = 50.
The combination of statements is sufficient to answer the question. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!