If x = 3y = 4z, Which of The Following Must Equal 6x GMAT Problem Solving

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

1. 18y
2. 3y + 20z
3. (4y + 10z)/3

1. I only
2. II only
3. III only
4. I and II only
5. I and III only

“If x = 3y = 4z, which of the following must equal 6x”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Given:
If x = 3y = 4z

Find Out:
The value of 6x

For this problem statement, we will have to follow the process of elimination. All the three statements will be checked so that we can eliminate the incorrect ones.

Statement 1: The first option provided is 18y
From the problem statement, it is given: x = 3y
We will multiply both sides by 6 to get: 6x = 18y
The statement I is TRUE

We will eliminate B and C since they state that statement I is not true.

Statement 2: The second option provided is 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
The statement II is TRUE

We will eliminate A and E since they state that statement II is not true.

Correct Answer: D

Approach Solution 2:

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.
Statement I. 18y = 18*x/3 = 6x, hence TRUE
Statement II. 3y + 20z = 3*x/3 + 20*x/4 = x+5x = 6x, hence TRUE
Statement 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

Correct Answer: D

Approach Solution 3:

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.

Correct Answer: D

Suggested GMAT Problem Solving Questions

• Properties of Circle GMAT Problem Solving 
• If 10, 12 and ‘x’ are sides of an acute angled triangle, how many integer values of ‘x’ are possible? GMAT Problem Solving 
• Assume that all 7-digit numbers that do not begin with 0 or 1 are valid phone numbers GMAT Problem Solving 
• What is the value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Problem Solving 
• The ratio of boys to girls in Class A is 1 to 4, and that in Class B is 2 to 5 GMAT Problem Solving 
• The maximum mark in an examination is 100 and the minimum is 0 GMAT Problem Solving  
• A rectangular box has dimensions 12*10*8 inches GMAT Problem Solving 
• A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving 
• If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day GMAT Problem Solving 
• If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal? GMAT Problem Solving 
• How many terminating zeroes does 200! have? GMAT Problem Solving
• For How Many Values of k is 12^12 the Least Common Multiple of the Positive Integers 6^6, 8^8 and k? GMAT Problem Solving
• Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3 GMAT Problem Solving 
• A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. GMAT Problem Solving
• A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant GMAT Problem Solving 
• What is the value of x? (1) x^2 – 5 x + 6 = 0 (2) x > 0 GMAT Problem Solving 
• How many even divisors of 1600 are not multiples of 16? GMAT Problem Solving 
• How many 5 digit (digit = 0 - 9) zip codes can exist in which at least one digit is repeated? GMAT Problem Solving 
• Is Square Root = Always Positive? GMAT Problem Solving