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O is the circle’s center and ∠POR is a right angle.
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30 Jan 2019, 08:08
30 Jan 2019, 08:08
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Question Stats:
55% (01:13) correct
44% (00:57) wrong based on 74 sessions
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Attachment:
circle dotted.png [ 3.69 KiB | Viewed 5429 times ]
O is the circle’s center and ∠POR is a right angle.
Quantity A |
Quantity B |
OR |
QR |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
O is the circle’s center and ∠POR is a right angle.
[#permalink]
30 Jan 2019, 09:11
30 Jan 2019, 09:11
1
amorphous wrote:
Attachment:
circle dotted.png
O is the circle’s center and ∠POR is a right angle.
Quantity A |
Quantity B |
OR |
QR |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Useful property: In a triangle, the side OPPOSITE a larger angle is longer than the side OPPOSITE the smaller angle
Opposite angles are equal, so ∠POQ is also 43°
Since we're told ∠POR = 90°, we can conclude that ∠QOR = 47°
Since angles in a triangle add to 180°, we can conclude that ∠OQR = 43°
∠QOR is greater than ∠OQR
So, the side OPPOSITE ∠QOR (QR) must be greater than the side OPPOSITE ∠OQR (OR)
In other words, QR > OR
Answer: B
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Re: O is the circle’s center and ∠POR is a right angle.
[#permalink]
03 Feb 2019, 20:27
03 Feb 2019, 20:27
The answer is wrong but the concept is correct
Opposite angles are equal so <POQ = 43
<QOR = 90 - 43 = 47
Also <OQR = 180 - (90+47) = 43
Hence, from the scenario opposite side of the greater angle has greatest length
QR > OR
The answer is B
Opposite angles are equal so <POQ = 43
<QOR = 90 - 43 = 47
Also <OQR = 180 - (90+47) = 43
Hence, from the scenario opposite side of the greater angle has greatest length
QR > OR
The answer is B
Re: O is the circle’s center and ∠POR is a right angle.
[#permalink]
03 Feb 2019, 23:06
03 Feb 2019, 23:06
Expert Reply
amorphous wrote:
Attachment:
The attachment circle dotted.png is no longer available
O is the circle’s center and ∠POR is a right angle.
Quantity A |
Quantity B |
OR |
QR |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
See the attached figure..
Rule : Side opposite larger angle with in the same triangle is larger than the side opposite smaller angles.
Take triangle OQR, which is a right angled triangle..
angle QOR = 180-(angle TOS + angle SOR)=180-(43+90)=47.
angle OQR=180-(90+angle QOR)=180-(90+47)=43.
thus angle QOR>angle OQR, therefore (side opposite angle QOR)>(side opposite angle OQR).. or QR>OR, that is B>A
B
Attachments
circle dotted.png [ 5.38 KiB | Viewed 5261 times ]
_________________
Some useful Theory.
1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
1. Arithmetic and Geometric progressions : https://gre.myprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://gre.myprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://gre.myprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://gre.myprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://gre.myprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html
Re: O is the circles center and POR is a right angle.
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10 Jun 2023, 07:47
10 Jun 2023, 07:47
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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