Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #39

1

If x = 2t and y = t/3 what is the value

If x = 2t and y = t/3 what is the value of x^2 ? y^2?

1 Explanation

1

John Robertson

x=2t, y=t/3, x^2-y^2=?

Prompt: quick survey of 1) and 2) show info is given in "t," and I can convert x^2-y^2 into "t" based off what is given, so I did so:
-> x^2-y^2 = (2t)^2 - (t/3)^2 = 4t^2 - (t^2)/9
-> Also, difference of two squares here, so 4t^2 - (t^2)/9 = (2t+t/3)(2t-t/3). Might not be useful but sometimes common factoring shortcuts like that seem to expose answers down the line
->QED: to solve x^2 - y^2= ?, you can do so by solving for t

1) t^2-3=6. Looks like I can solve for t, but solved out a bit just in case
-> t^2=9, t=+/- 3, prompt is solvable, (S)

2) t^3= -27, t= -3, prompt is solvable (S)

Answer: D, both independently sufficient,

Feb 17, 2017 • Comment

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Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.


Section 6.3 Data Sufficiency

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