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
The OA is the option D.
How can I prove that the correct option is the option D? Could anyone clarify this question to me? Thanks in advance.
If x = 3y = 4z, which of the following must equal 6x ?
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Let's examine each statementVJesus12 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
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
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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
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
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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 analyze each Roman numeral choices.
I. 18y
18y = 6(3y) = 6x
Yes, I is true.
II. 3y + 20z
3y + 20z = 3y + 5(4z) = x + 5x = 6x
Yes, II is true.
At this point, since there is only one answer choice which includes I and II, we know the answer is D. However, let's also analyze Roman numeral III as an exercise:
III. (4y + 10z)/3
Since x = 3y, y = x/3. Likewise, since x = 4z, z = x/4. Thus we have:
(4y + 10z)/3 = (4(x/3) + 10(x/4))/3 = (4x/3 + 5x/2)/3 = 4x/9 + 5x/6 = 8x/18 + 15x/18 = 23x/18
We see that III is not true.
Answer: D
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