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

Question

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

Source:   Nova GMAT  
Difficulty Level:   600

BrentGMATPrepNow · Accepted Answer

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

pushpitkc · Answer

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

Evaluating the options available
I. 18y = 6x(Because x = 3y)
II. 3y + 20z = x + 5x = 6x
(Here, x=3y and x=4z)
III. (4y + 10z)/3
This option doesn't give us 6x for sure, because 4y is a little more than x 
and 10z is 2,5x (added they give 4x(approximately), which divided by 3 gives us around 1.3x)

Hence  (D) I and II only   is our answer choice

sashiim20 · Answer

Checking the options.
I. 18y
Given ; x = 3y
  \frac{18y}{3y}  * x = 6x (Must be True)

II. 3y + 20z
Given 3y = x; 4z = x
 \frac{20z}{4z}  * x = 5x
3y + 20z = x + 5x = 6x (Must be True)

III.  \frac{(4y + 10z )}{3} 
 (\frac{4}{3}x + \frac{10}{4}x )/3  =  (\frac{4}{3}x + \frac{5}{2}x)/3  =  (\frac{8x + 15x}{6})/3  =  \frac{23x}{18} (Not True) 
 Answer (D) I and II only ...

generis · Answer

Test values. Because x is the greatest number, use LCM of 3, 4, and 6 (because x gets multiplied by 6) for x.

Let x = 12, y = 4, z = 3

6x = 72

I. 18 y?

Yes. 18*4 = 72. Eliminate (B) and (C)

II. 3y + 20z?

3y = 12, and 20z = 60. (12 + 60) = 72. Correct. And you're done -- eliminate answers A and E because they do not include II. I am not that brave. Checking III.

III.  \frac{(4y + 10z)}{3} ?

4y = 16, and 10z = 30.  \frac{(16 + 30)}{3} =\frac{46}{3}  -- and is nowhere near 72. Reject.

Answer D

amanvermagmat · Answer

Given x=3y=4z or y = x/3 and z = x/4

Since we have a clear relation of x with both y and z, its easy to test each statement by converting in terms of x.

I. 18y = 18*x/3 = 6x, hence TRUE

II. 3y + 20z = 3*x/3 + 20*x/4 = x+5x = 6x, hence TRUE

III. (4y + 10z)/3 = (4*x/3 + 10*x/4)/3 = 4x/9 + 5x/6 = 23x/18, so NOT TRUE

Only I and II are true, hence  D answer

Abhishek009 · Answer

x = 3y = 4z = 12

Or, x = 12 ; y = 4 & z = 3

So, 6x = 72

Now, check the options -

I. 18y = 18*4 = 72 
 II. 3y + 20z = 3*4 + 20*3 = 72 
 III. (4y + 10z)/3 = (4*4 + 10*3)/3 = 46/3

Hence, the correct answer must be (D) I and II only

ScottTargetTestPrep · Answer

We are given that x = 3y = 4z and need to determine what must equal 6x. From the given information, we see that 6x = 18y = 24z. Let’s analyze each Roman numeral:
 
I. 18y
 
Since 6x = 18y, Roman numeral I is true.
 
II. 3y + 20z 
 
Since 3y = x and 20z = 5(4z) = 5x, 3y + 20z = x + 5x = 6x; Roman numeral II is also true.
 
III. (4y + 10z)/3
 
Let’s express 4y and 10z in terms of x. 
 
4y = (4/3)3y = (4/3)x
 
10z = (10/4)4z = (5/2)x
 
Now, we have: 
 
(4y + 10z)/3 = ((4/3)x + (5/2)x)/3 =  /3 = (23/18)x. 
 
Clearly, this expression is not equal to 6x.
 
Thus, only Roman numerals I and II are true.
 
Answer: D

akadiyan · Answer

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

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

Option 1: 18Y
Since we know that X=3Y
18Y=6X

This is valid.

Option 2:3Y+20Z
X=3y
X=4Z , 20Z=5X
3Y+20Z = X+5X = 6X

This is valid

Option 3:(4Y+10z)/3
You get X less than 6. Not valid

Only 1 and 2 are correct

Ans:   D

KSBGC · Answer

it's given,

x=3y=4z

we know that the value of z , 3y and 4z must be equal. Now to make the value equal, we can find out the LCM of x, 3y and 4z. LCM is 12
So,

x=12
y=4
z=3

The value of 6x = 6*12=72

Now scan the answer choice that fits.

Option A: 18y=18*4=72

option B: 3y+20z = 3*4 + 20*4 = 72

option c: (4y+10z)/3 = (4*3 + 10*4)/3 = (12+40)/3 = Fractional value and less than the value of 6x. Eliminate it.

Thus Option D is the best answer.

rakeshmishra5690 · Answer

x = 3y = 4z
y = x/3 and z = x/4

1) 18y = 18*x/3 = 6x
2) 3y +20z = 3*x/3 + 20*x/4 = 6x
3) (4y + 10z)/3 =4*x/9 + 10*x/12 = 46x/36

Ans D

GMATINSECT · Answer

X=3Y=4Z

X=3y
X/3=Y ,

X=4Z
X/4=z

Try to insert above values in the option , you will find only I & II works !

CrackverbalGMAT · Answer

lets assume x = 3y = 4z =  12  
we choose 12 as it is the LCM of 3 and 4

then we can say that x= 12 , y = 4 , z = 3.
question here is which of the following must equal 6x?
6 x = 6 * 12 = 72

So after substituting values of y and z in the options ,we should get 72 
I. 18y = 18* 4= 72 Hence True
II. 3y + 20z = 3*4 + 20*3= 72 So its true
III. (4y + 10z)/3 = (4*4 + 10* 3)/3 = 46 /3 So its NOT TRUE

Option D ( I and II only) is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards