X is proportional to Y. If Y is increased by 30%,

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon Mar 12, 2018 11:52 pm

[GMAT math practice question]

X is proportional to Y. If Y is increased by 30%, by approximately what percent is X^2 increased?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Mar 13, 2018 6:52 am

Max@Math Revolution wrote:[GMAT math practice question]

X is proportional to Y. If Y is increased by 30%, by approximately what percent is X^2 increased?

A. 30%
B. 40%
C. 50%
D. 60%
E. 70%

y becomes 100 to 130

so y^2 becomes y^2 to 1.69y^2 i.e. Increase of 69%

ANswer: OPtion E

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Mar 15, 2018 1:03 am

=>

X = kY for some k.
Since ,
$$(1.3kY)^2=1.69k^2Y^2=1.69(kY)^2=1.69X^2$$
we have
$$\frac{\left(1.69X^2-X^2\right)}{X^2}=0.69$$
which is approximately 70%.

Therefore, the answer is E.

Answer: E

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