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

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by Max@Math Revolution » Thu Nov 15, 2018 1:37 am

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[Math Revolution GMAT math practice question]

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

A. 2 : 3 : 6
B. 3 : 2 : 6
C. 6 : 2 : 3
D. 6 : 3 : 2
E. 3 : 6 : 2
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by Brent@GMATPrepNow » Thu Nov 15, 2018 6:29 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

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

A. 2 : 3 : 6
B. 3 : 2 : 6
C. 6 : 2 : 3
D. 6 : 3 : 2
E. 3 : 6 : 2
Let's focus on pairs of values

If xy : yz : zx = 1:2:3, then we know that xy : yz = 1:2
Take xy : yz and divide both sides by y to get the EQUIVALENT ratio x:z
This means x:z = 1:2

Check the answer choices...
A. 2 : 3 : 6 this answer choice says x:z = 2:6. We need x:z = 1:2 ELIMINATE A
B. 3 : 2 : 6 this answer choice says x:z = 3:6 (which equals 1:2) KEEP B
C. 6 : 2 : 3 this answer choice says x:z = 6:3. We need x:z = 1:2 ELIMINATE
D. 6 : 3 : 2 this answer choice says x:z = 6:2. We need x:z = 1:2 ELIMINATE
E. 3 : 6 : 2 this answer choice says x:z = 3:2. We need x:z = 1:2 ELIMINATE

By the process of elimination, the correct answer is B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Thu Nov 15, 2018 8:23 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

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

A. 2 : 3 : 6
B. 3 : 2 : 6
C. 6 : 2 : 3
D. 6 : 3 : 2
E. 3 : 6 : 2
\[?\,\, = \,\,\,x:y:z\]
$$xy:yz:zx = 1:2:3\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{
\,\,xy:yz\,\,\mathop = \limits^{y\, \ne \,0} \,\,x\,:\,z\,\,\, = \,\,\,1:2\,\,\,\mathop = \limits^{{\rm{bridge}}\,{\rm{!}}} \,\,\,3:6 \hfill \cr
\,\,yz:zx\,\,\mathop = \limits^{z\, \ne \,0} \,\,y\,:\,x\,\,\, = \,\,\,2:3 \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,?\,\,\,:\,\,\,\,x:y:z = 3:2:6$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Max@Math Revolution » Sun Nov 18, 2018 5:07 pm
=>

xy : yz : zx = xyz/z : xyz/x: xyz/ y = 1/z : 1/x : 1/y = 1:2:3
=> z : x : y = 1 : 1/2 : 1/3 = 6 : 3 : 2
=> x : y : z = 3 : 2 : 6

Therefore, the answer is B.
Answer: B
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