If x = 3y = 4z, which of the following must equal 6x ?

VJesus12 wrote:If x = 3y = 4z, which of the following must equal 6x?

I. 18y
II. 3y + 20z
III. (4y + 10z)/3

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only

Let's examine each statement

I. 18y
Given: x = 3y
Multiply both sides by 6 to get: 6x = 18y
Perfect!
Statement I is TRUE
Check the answer choices.....ELIMINATE B and C since they state that statement I is not true.

II. 3y + 20z
Given: x = 3y
Also, since x = 4z, we can multiply both sides by 5 to get: 5x = 20z
Now notice that 6x = x + 5x
= 3y + 20z
Perfect!
Statement II is TRUE
Check the answer choices.....ELIMINATE A and E since they state that statement II is not true.

By the process of elimination, the correct answer is D

Cheers,
Brent

Hi VJesus12,

We're told that X = 3Y = 4Z. We're asked which of the following must equal 6X. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF....
X=12, Y=4, Z=3.....then we're looking for values that equal 6(12) = 72.

I. 18Y

18(4) = 72, so Roman Numeral 1 equals 6X. Eliminate Answers B and C.

II. 3Y + 20Z

3(4) + 20(3) = 12+60 = 72, so Roman Numeral 2 equals 6X. Eliminate Answers A and E. We can technically stop here (since there's only one Answer left). However, we can still disprove Roman Numeral 3....

III. (4Y + 10Z)/3

[4(4) + 10(3)]/3 = 46/3 so Roman Numeral 3 does NOT equal 6X.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich