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# Is cone P similar to cone Q?

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Intern
Joined: 26 Feb 2017
Posts: 30
Location: Brazil
GMAT 1: 610 Q45 V28
GPA: 3.11
Is cone P similar to cone Q?  [#permalink]

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04 Oct 2017, 10:27
2
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Difficulty:

75% (hard)

Question Stats:

44% (01:06) correct 56% (00:35) wrong based on 36 sessions

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Is cone P similar to cone Q?
(1) The surface area of P is 9 times the surface area of Q
(2) The volume of P is 9 times the volume of Q
Math Expert
Joined: 02 Aug 2009
Posts: 6542
Is cone P similar to cone Q?  [#permalink]

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06 Oct 2017, 07:55
1
1
vitorpteixeira wrote:
Is cone P similar to cone Q?
(1) The surface area of P is 9 times the surface area of Q
(2) The volume of P is 9 times the volume of Q

HI..

with 100% answering incorrectly, this may help

thing to remember..
Two cones will be similar when the RADIUS and the HEIGHT are in SAME proportion
so $$\frac{R_P}{R_Q}=\frac{H_P}{H_Q}=k$$

let's see the statements

(1) The surface area of P is 9 times the surface area of Q
this means $$9*pi*R_P^2+pi*R_P*\sqrt{H_P^2+R_P^2}=pi*R_Q^2+pi*R_Q*\sqrt{H_Q^2+R_Q^2}$$..
so $$9*=pi*R_P^2+pi*R_P*\sqrt{H_P^2+R_P^2}/pi*R_Q^2+pi*R_Q*\sqrt{H_Q^2+R_Q^2}=(R_P^2+R_P*\sqrt{H_P^2+R_P^2})/(R_Q^2+R_Q*\sqrt{H_Q^2+R_Q^2})$$
two cases..
if similar, the ratio $$k = \sqrt{9}=3$$... Possible
or it can be various combination to get the ratio as 9...Possible
Insuff

(2) The volume of P is 9 times the volume of Q
$$\frac{1}{3}*pi*R_P^2H_P=9*\frac{1}{3}*pi*R_Q^2H_Q............\frac{R_P^2H_P}{R_Q^2H_Q}=9$$..
two cases
1) if $$k^3=9$$ .. similar possible
2) only $$R_P=3*R_Q$$... not similar.. possible
so insuff..

combined..
different values of k in both cases so the cones are NOT similar
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Is cone P similar to cone Q? &nbs [#permalink] 06 Oct 2017, 07:55
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