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Ted and Rali run one lap on a circular track. Ted runs in a circular

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Math Expert
Joined: 02 Sep 2009
Posts: 60518
Ted and Rali run one lap on a circular track. Ted runs in a circular  [#permalink]

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03 Dec 2019, 01:20
00:00

Difficulty:

35% (medium)

Question Stats:

61% (01:49) correct 39% (01:32) wrong based on 39 sessions

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Ted and Rali run one lap on a circular track. Ted runs in a circular path with a radius of r, and Rali runs in a circular path with a radius of r+q, where r and q are greater than 0. Is r a factor of q?

(1) Ted and Rali finish one lap in the same amount of time.

(2) Rali’s average speed is x times greater than Ted’s, where x is an integer.

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Joined: 10 Dec 2017
Posts: 175
Location: India
Re: Ted and Rali run one lap on a circular track. Ted runs in a circular  [#permalink]

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03 Dec 2019, 04:29
1
Bunuel wrote:
Ted and Rali run one lap on a circular track. Ted runs in a circular path with a radius of r, and Rali runs in a circular path with a radius of r+q, where r and q are greater than 0. Is r a factor of q?

(1) Ted and Rali finish one lap in the same amount of time.

(2) Rali’s average speed is x times greater than Ted’s, where x is an integer.

Are You Up For the Challenge: 700 Level Questions

From 1
1 for TED , 2 for RALI
$$S1*T1=2*pi*r$$
$$T1=(2*pi*r)/S1$$
$$T2=[2*pi*(r+q)]/S2$$
since T1=T2
$$(r+q)/r=S2/S1$$
Not sufficient

From 2
$$(r+q)/r=(T2/T1)*X$$
Not sufficient
From 1 and 2
$$1+q/r=X$$
q/r= integer
C:)
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Joined: 24 Nov 2016
Posts: 1076
Location: United States
Re: Ted and Rali run one lap on a circular track. Ted runs in a circular  [#permalink]

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04 Dec 2019, 08:39
Bunuel wrote:
Ted and Rali run one lap on a circular track. Ted runs in a circular path with a radius of r, and Rali runs in a circular path with a radius of r+q, where r and q are greater than 0. Is r a factor of q?

(1) Ted and Rali finish one lap in the same amount of time.

(2) Rali’s average speed is x times greater than Ted’s, where x is an integer.

rt=d

(1) Ted and Rali finish one lap in the same amount of time. insufic
(2) Rali’s average speed is x times greater than Ted’s, where x is an integer. insufic

(1)&(2) sufic

$$2πr/t=2π(r+q)/xt…xr=r+q…x=r+q/r…x=1+q/r=integer…q/r=integer$$

Ans (C)
Re: Ted and Rali run one lap on a circular track. Ted runs in a circular   [#permalink] 04 Dec 2019, 08:39
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