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ratios

by [email protected] » Mon Mar 02, 2009 6:58 am
Starting from the same point, a sparrow and a hawk flew in opposite directions. Each traveled at a constant speed until they were 200 feet apart. How far did the sparrow travel?

(1) The ratio of the sparrow’s speed to the hawk’s speed was 3 to 2.
(2) The average speed of the sparrow was 5 feet per second faster than the average speed of the hawk.

A
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Source: — Data Sufficiency |
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by bluementor » Mon Mar 02, 2009 8:16 am
x = Hawk's speed
y = Sparrow's speed
a = distance travelled by Hawk
b = distance travelled by Sparrow
t = flight duration

Time = Distance/Speed


Statement 1: x/y = 2/3

t = a/x = b/y
a/b = x/y
a/b = 2/3 … eqn1

a + b = 200 … eqn2

Using both equations 1 and 2, the distances travelled by the sparrow and hawk can be calculated. Sufficient.

Statement 2: y = x + 5

a/b = x/y
a/b = x/(x+5) … eqn1

a + b = 200 … eqn2

Both these equations will not be sufficient to answer the question. We still need the value of the speed of at least one of the birds. Insuffcient.

Choose A.

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Re: ratios

by sureshbala » Mon Mar 02, 2009 2:30 pm
[email protected] wrote:Starting from the same point, a sparrow and a hawk flew in opposite directions. Each traveled at a constant speed until they were 200 feet apart. How far did the sparrow travel?

(1) The ratio of the sparrow’s speed to the hawk’s speed was 3 to 2.
(2) The average speed of the sparrow was 5 feet per second faster than the average speed of the hawk.

A
Statement I:

Since the sparrow and hawk travelled for the same amount of time, the distance 200 feet will be shared by them in the ratio of their speeds i.e 3:2. So Sparrow covers 120 feet and hawk covers 80 feet

So I is sufficient

Statement II: Given that the ratio of speeds of Hawk and Sparrow is x:x+5. In order to determine the distance traveled by each of them we need to know the value of x which is unknown

So II is not sufficient

Hence A
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