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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Is the area of circle X greater than the area of circle Y?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 86% (00:52) correct 14% (00:47) wrong based on 94 sessions

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Is the area of circle X greater than the area of circle Y?

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.

(2) The radius of circle X is greater than the radius of circle Y.

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Manager  Joined: 11 Sep 2013
Posts: 105
Re: Is the area of circle X greater than the area of circle Y?  [#permalink]

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Bunuel wrote:
Is the area of circle X greater than the area of circle Y?

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.
(2) The radius of circle X is greater than the radius of circle Y.

Kudos for a correct solution.

To determine whether the area of circule X is greater than that of circle Y => To determine whether R of X is greater than that of circle Y
(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.
=> R of X > R of Z, R of Z < R of Y
=> Do not know whether R of X > R of Y
=> INSUFFICIENT
(2) The radius of circle X is greater than the radius of circle Y
=> SUFFICIENT
=> Ans: B
VP  D
Joined: 05 Mar 2015
Posts: 1000
Re: Is the area of circle X greater than the area of circle Y?  [#permalink]

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1
[quote="Bunuel"]Is the area of circle X greater than the area of circle Y?

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.
(2) The radius of circle X is greater than the radius of circle Y

(1)says X>Z & Y>Z
one possiblity is that X>Y>Z then also statements were correct but one cannot infer whether X>Y or Y>X
Hence insuff.

(2) Area=pi* r^2
So, X>Y

Suffficient Intern  Joined: 19 Dec 2014
Posts: 35
Re: Is the area of circle X greater than the area of circle Y?  [#permalink]

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1
Let X = radius of circle x
Let Y = radius of circle y
Let Z = radius of circle z

Statement 1

2*$$\pi$$*X > 2*$$\pi$$*Z --> X > Z

2*$$\pi$$*Z < 2*$$\pi$$*Y --> Y > Z

But we don't know if X > Y

ex: X = 4, Y=5, Z = 2 or
X = 5, Y=4, Z = 2

Insufficient

Statement 2

X > Y
we can answer this by squaring both sides and multiplying by $$\pi$$

Sufficient

Manager  S
Joined: 13 Mar 2013
Posts: 158
Location: United States
GPA: 3.5
WE: Engineering (Telecommunications)
Re: Is the area of circle X greater than the area of circle Y?  [#permalink]

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1
Is the area of circle X greater than the area of circle Y?

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.
(2) The radius of circle X is greater than the radius of circle Y.

Kudos for a correct solution.

I have seen a similar question in number format --- whether the underlying concept is similar --- only here they have changed it into geometry .This how Gmat works i guess .

St . 1 is not sufficient .
radius of X = x
radius of Y =y
radius of Z =z

2pie x > 2pie z
and
2pie z < 2pie y

There is no relation between x and y . Hence not sufficient .

St 2.
radius of X = x
radius of Y =y
radius of Z =z

x > y

If radius of x is more than y . Then area of x will definitely more than y .

B ans .
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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: Is the area of circle X greater than the area of circle Y?  [#permalink]

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Bunuel wrote:
Is the area of circle X greater than the area of circle Y?

(1) The circumference of circle X is greater than the circumference of circle Z, and the circumference of circle Z is less than the circumference of circle Y.
(2) The radius of circle X is greater than the radius of circle Y.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question asks whether the area of circle X is greater than the area of circle Y.

Given information from the question stem: This question asks you to determine whether circular region x has a larger area than does circular region y.

Statement 2 seems easier to evaluate so you can start there.

Statement 2: This statement gives you the relationship between the radius of circle x and that of circle y. Circle x has the larger radius. Since the formula for the area of a circle is πr^2 and π is a constant, it is true that a larger radius definitely means a larger area of the circle. This statement is sufficient. The answer is either B or D.

Statement 1: This statement compares the circumference of circles x and y with that of circle z. The statement can be rewritten as “circumference x > circumference z” and “circumference y > circumference z.” This does not allow for a comparison of circles x and y; it simply indicates that each is larger than circle z. This information is not sufficient.

The correct answer is B.
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Posts: 46
Re: Is the area of circle X greater than the area of circle Y?  [#permalink]

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Statement 1. X > Z & Y > Z.
Since we don’t have any relation between X and Y, we cannot answer this question using statement 1. Hence, Insufficient.
Statement 2. X > Y. Since area of a circle is directly proportional to the radius of the circle, greater radius means greater area. Hence, Sufficient. Re: Is the area of circle X greater than the area of circle Y?   [#permalink] 18 Dec 2018, 23:26
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