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If the circumference of circle P is 15.174 and the circumfer

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If the circumference of circle P is 15.174 and the circumfer

by BTGmoderatorAT » Wed Nov 15, 2017 1:50 am
If the circumference of circle P is 15.174 and the circumference of circle Q is 6.28, then the diameter of circle P minus the diameter of circle Q is approximately equal to

(A) 1.5
(B) 3.0
(C) 5.5
(D) 9.0
(E) 9.4

Is there a strategic approach to this question? Please I need any experts help.
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by GMATGuruNY » Wed Nov 15, 2017 4:16 am
ardz24 wrote:If the circumference of circle P is 15.174 and the circumference of circle Q is 6.28, then the diameter of circle P minus the diameter of circle Q is approximately equal to

(A) 1.5
(B) 3.0
(C) 5.5
(D) 9.0
(E) 9.4

Is there a strategic approach to this question? Please I need any experts help.
C = πd ≈ 3d.

Circle P:
3d ≈ 15.174
3d ≈ 15
d ≈ 5.

Circle Q:
3d ≈ 6.28
3d ≈ 6
d ≈ 2.

Thus:
Approximate difference between the diameters = 5-2 = 3.

The correct answer is B.
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by EconomistGMATTutor » Wed Nov 15, 2017 6:38 am
If the circumference of circle P is 15.174 and the circumference of circle Q is 6.28, then the diameter of circle P minus the diameter of circle Q is approximately equal to

(A) 1.5
(B) 3.0
(C) 5.5
(D) 9.0
(E) 9.4

Is there a strategic approach to this question? Please I need any experts help.
Hi ardz24,
Let's take a look at your question.

Let's find the diameter of circle P using circumference formula:

$$Circumference=2\pi r$$
$$15.174=2\pi r$$
$$2r=\frac{15.174}{\pi}$$
$$\pi=3.14\approx3$$
$$2r=\frac{15.174}{3}$$
$$2r\approx5$$
$$Diameter\approx5$$

Diameter of Circle P is 5.

Let's now find the diameter of circle Q using circumference formula:

$$Circumference=2\pi r$$
$$6.28=2\pi r$$
$$2r=\frac{6.28}{\pi}$$
$$2r=\frac{6.28}{3}$$
$$2r\approx2$$
$$Diameter\approx2$$

Diameter of Circle Q is 2.

Diameter of Circle P - Diameter of Circle Q
$$=5-2$$
$$=3$$

Therefore, Option B is correct.

Hope it helps.
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