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# If the radius of a circle is positive integer less than 50, what is

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
If the radius of a circle is positive integer less than 50, what is  [#permalink]

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Updated on: 29 Nov 2017, 20:12
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65% (hard)

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44% (01:21) correct 56% (01:18) wrong based on 70 sessions

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If the radius of a circle is positive integer less than 50, what is the probability that the area of circle is an integer?

(A) $$0$$
(B) $$\frac{7}{50}$$
(C) $$\frac{1}{7}$$
(D) $$\frac{1}{3}$$
(E) $$\frac{7}{22}$$

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Originally posted by chetan2u on 29 Nov 2017, 19:52.
Last edited by chetan2u on 29 Nov 2017, 20:12, edited 2 times in total.
updated the choices
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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 20:07
1
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7.
So area will be an integer when radii are 7,14,21,28,35,42,49.

Now the sample set is 49 as the radius is less than 50. 50 cannot be included.

So probability has to be 7/49=1/7.

Am I right?

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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 20:10
1
Sasindran wrote:
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7.
So area will be an integer when radii are 7,14,21,28,35,42,49.

Now the sample set is 49 as the radius is less than 50. 50 cannot be included.

So probability has to be 7/49=1/7.

Am I right?

Sent from my iPhone using GMAT Club Forum

Yes, you are absolutely correct. typo in 50, it was supposed to be 51.
But since you have already answered it as 50, will edit the choices accordingly
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 20:11
chetan2u wrote:
Sasindran wrote:
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7.
So area will be an integer when radii are 7,14,21,28,35,42,49.

Now the sample set is 49 as the radius is less than 50. 50 cannot be included.

So probability has to be 7/49=1/7.

Am I right?

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Yes, you are absolutely correct. typo in 50, it was supposed to be 51.
But since you have already answered it as 50, will edit the choices accordingly

Ok. Good question though. It tests the basic concept of pi=22/7 rather than 3.14.

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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 20:12
chetan2u wrote:
If the radius of a circle is positive integer less than 50, what is the probability that the area of circle is an integer?

(A) 0
(B) 1/50
(C) 7/50
(D) 22/50
(E) 1

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As Radius of Circle is +ve Integer it can take values from - 7,14,21,35,42,49

P = 7/49.. Am I Missing something here??
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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 21:29
rahul16singh28 wrote:
chetan2u wrote:
If the radius of a circle is positive integer less than 50, what is the probability that the area of circle is an integer?

(A) 0
(B) 1/50
(C) 7/50
(D) 22/50
(E) 1

Self made

As Radius of Circle is +ve Integer it can take values from - 7,14,21,35,42,49

P = 7/49.. Am I Missing something here??

You're missing 28. That gives you 7/49 = 1/7
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If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 22:29
chetan2u wrote:
Sasindran wrote:
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7.
So area will be an integer when radii are 7,14,21,28,35,42,49.

Now the sample set is 49 as the radius is less than 50. 50 cannot be included.

So probability has to be 7/49=1/7.

Am I right?

Sent from my iPhone using GMAT Club Forum

Yes, you are absolutely correct. typo in 50, it was supposed to be 51.
But since you have already answered it as 50, will edit the choices accordingly

The question does not say assume pi as 22/7, so what if we were to assume pi as 3.14?
The only way to get an integer area would be if the radius had 2x5, at the least, as this would give us "100" as r^2 and 100 x 3.14= integer.
Possible cases:
2 x 5, 2 x 5 x 3, 2 x 2 x 5, 2 x 2 x 2 x 5, and 2 x 5 x 5 ( if we are to assume less than 51), which is only 5 cases.
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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 22:32
rahulkashyap wrote:
chetan2u wrote:
Sasindran wrote:
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7.
So area will be an integer when radii are 7,14,21,28,35,42,49.

Now the sample set is 49 as the radius is less than 50. 50 cannot be included.

So probability has to be 7/49=1/7.

Am I right?

Sent from my iPhone using GMAT Club Forum

Yes, you are absolutely correct. typo in 50, it was supposed to be 51.
But since you have already answered it as 50, will edit the choices accordingly

The question does not say assume pi as 22/7, so what if we were to assume pi as 3.14?
The only way to get an integer area would be if the radius had 2x5, at the least, as this would give us "100" as r^2 and 100 x 3.14= integer.
Besides 2 x 5, we could also have 2 x 2 x 5, 2 x 2 x 2 x 5, and 2 x 5 x 5 ( if we are to assume less than 51), which is only 4 cases.

Please note that value of pi is 22/7 which is rounded off to 3.14. In fact the non rounded of value will be 3.14285714285714.....

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Re: If the radius of a circle is positive integer less than 50, what is  [#permalink]

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29 Nov 2017, 22:33
rahulkashyap wrote:
chetan2u wrote:
Sasindran wrote:
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7.
So area will be an integer when radii are 7,14,21,28,35,42,49.

Now the sample set is 49 as the radius is less than 50. 50 cannot be included.

So probability has to be 7/49=1/7.

Am I right?

Sent from my iPhone using GMAT Club Forum

Yes, you are absolutely correct. typo in 50, it was supposed to be 51.
But since you have already answered it as 50, will edit the choices accordingly

The question does not say assume pi as 22/7, so what if we were to assume pi as 3.14?
The only way to get an integer area would be if the radius had 2x5, at the least, as this would give us "100" as r^2 and 100 x 3.14= integer.
Besides 2 x 5, we could also have 2 x 2 x 5, 2 x 2 x 2 x 5, and 2 x 5 x 5 ( if we are to assume less than 51), which is only 4 cases.

The exact decimal value of pi isn't 3.14. It has 2.7 trillion decimal digits. 3.14 is only an approximation. Taking 22/7 as the value of pi is a better option.
Re: If the radius of a circle is positive integer less than 50, what is   [#permalink] 29 Nov 2017, 22:33
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# If the radius of a circle is positive integer less than 50, what is

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