GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the coordinate plane, points (a, b) and (c, d) are equidi
[#permalink]
30 Sep 2018, 15:58
30 Sep 2018, 15:58
Expert Reply
5
Bookmarks
00:00
Question Stats:
68% (01:01) correct
31% (01:34) wrong based on 141 sessions
Hide Show timer Statistics
In the coordinate plane, points (a, b) and (c, d) are equidistant from the origin.
\(|a| > |c|\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
\(|a| > |c|\)
Quantity A |
Quantity B |
|b| |
|d| |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: In the coordinate plane, points (a, b) and (c, d) are equidi
[#permalink]
10 Dec 2018, 17:41
10 Dec 2018, 17:41
5
Answer: B
What we have:
Distance from (a,b) to origin (0,0) = √((a-0)^2 + (b-0)^2) = √(a^2 + b^2)
Distance from (c,d) to origin (0,0) = √((c-0)^2 + (d-0)^2) = √(c^2 + d^2)
It is said that points (a, b) and (c, d) are equidistant from the origin. It means their distances from origin are equal, so:
√(a^2 + b^2) = √(c^2 + d^2) , both sides to power2:
a^2 + b^2 = c^2 + d^2
As it is said that |a| > |c| so we can conclude that |a|^2 > |c|^2 [They are both positive, thus when they are in the same power, their comparison result will be just the same as when the power is 1.]
Now that we know a^2 > c^2 and a^2 + b^2 = c^2 + d^2, so we can construe that b^2 is less than d^2 and so |b| is less than |d| (b and d don’t necessarily have the same relation) B is bigger than A
What we have:
Distance from (a,b) to origin (0,0) = √((a-0)^2 + (b-0)^2) = √(a^2 + b^2)
Distance from (c,d) to origin (0,0) = √((c-0)^2 + (d-0)^2) = √(c^2 + d^2)
It is said that points (a, b) and (c, d) are equidistant from the origin. It means their distances from origin are equal, so:
√(a^2 + b^2) = √(c^2 + d^2) , both sides to power2:
a^2 + b^2 = c^2 + d^2
As it is said that |a| > |c| so we can conclude that |a|^2 > |c|^2 [They are both positive, thus when they are in the same power, their comparison result will be just the same as when the power is 1.]
Now that we know a^2 > c^2 and a^2 + b^2 = c^2 + d^2, so we can construe that b^2 is less than d^2 and so |b| is less than |d| (b and d don’t necessarily have the same relation) B is bigger than A
General Discussion
Re: In the coordinate plane, points (a, b) and (c, d) are equidi
[#permalink]
28 Oct 2018, 11:48
28 Oct 2018, 11:48
The answer is B
