If xy : yz : zx = 1:2:3, then what is x : y : z ? GMAT Problem Solving

Question: If xy : yz : zx = 1 : 2 : 3, then what is x : y : z?

1. 2 : 3 : 6
2. 3 : 2 : 6
3. 6 : 2 : 3
4. 6 : 3 : 2
5. 3 : 6 : 2

Correct Answer: B

Approach Solution (1):

The quickest way is to plug the numbers from the answer choices.
In case of option A: 2 : 3 : 6. See if xy : yz : zx is equal to 1 : 2 : 3
Answer comes out as 6 : 18 : 12- incorrect
Check with the option B: 3 : 2 : 6
Answer: 6 : 12 : 18 = correct
You can keep going on, but just seeing xy you can tell that it won’t be equal to 1 in the ratios.

Approach Solution (2):

xy : yz : zx = 1 : 2 : 3, so,

\(\frac{xy}{yz}=\frac{1}{2}or\frac{x}{z}=\frac{1}{2}orx:z=1:2\)

\(\frac{yz}{zx}=\frac{2}{3}or\frac{y}{x}=\frac{2}{3}ory:x=2:3orx:y=3:2orx:y=1:\frac{2}{3}\)

So, x : y : z =  \(1:\frac{2}{3}\):2, now multiply all by 3 to get,

x : y : z = 3 : 2 : 6

“If xy : yz : zx = 1 : 2 : 3, then what is x : y : z?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills.

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