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Math Expert V
Joined: 02 Sep 2009
Posts: 56272
If P and Q are sectors in two different circles such that the area of  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 40% (02:02) correct 60% (01:30) wrong based on 50 sessions

### HideShow timer Statistics If P and Q are sectors in two different circles such that the area of P is greater than the area of Q, is the perimeter of P greater than that of Q?

(1) The radius of P is twice that of Q.
(2) The angles in both sectors are equal.

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If P and Q are sectors in two different circles such that the area of  [#permalink]

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Bunuel wrote:
If P and Q are sectors in two different circles such that the area of P is greater than the area of Q, is the perimeter of P greater than that of Q?

(1) The radius of P is twice that of Q.
(2) The angles in both sectors are equal.

Question : Is $$(Angle_1/360)*2πp > (Angle_2/360)*2πq$$?

Statement 1: The radius of P is twice that of Q.
i.e. angles are unknown for the two sectors hence the comparison can't be established

NOT SUFFICIENT

Statement 2: The angles in both sectors are equal.
i.e. area of P is greater than the area of Q
i.e. $$(Angle/360)πp^2 > (Angle/360)πq^2$$
i.e. $$p^2 > q^2$$ where p and q are the radius of circle P and Q respectively
i.e. p > q
SUFFICIENT

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Originally posted by GMATinsight on 18 Sep 2018, 01:53.
Last edited by GMATinsight on 25 Sep 2018, 23:08, edited 1 time in total.
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Re: If P and Q are sectors in two different circles such that the area of  [#permalink]

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GMATinsight OA is B
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Re: If P and Q are sectors in two different circles such that the area of  [#permalink]

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Bunuel wrote:
If P and Q are sectors in two different circles such that the area of P is greater than the area of Q, is the perimeter of P greater than that of Q?

(1) The radius of P is twice that of Q.
(2) The angles in both sectors are equal.

Let angle sector P be A and sector Q be B
radius sector P= P and sector Q =Q
Given: p^2/Q^2> B/A
Statement 1: P=2Q
This gives : 4A>B
Insufficient
Statement 2: A=B
This tells us directly P=Q
Sufficient
B Re: If P and Q are sectors in two different circles such that the area of   [#permalink] 25 Sep 2018, 22:51
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# If P and Q are sectors in two different circles such that the area of  