Value of s

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vrn2vw: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Mon Sep 28, 2015 7:22 am

by vrn2vw » Mon Dec 07, 2015 6:14 pm

In the figure above, points P and Q lie on the circle with center O. What is the value of s?

A) 1/2
B) 1
C) sqrt(2)
D) sqrt(3)
E) sqrt(2)/2

OA is B

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Source: Beat The GMAT — Problem Solving | Mon Dec 07, 2015 6:14 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Dec 07, 2015 6:16 pm

In the figure above, points P and Q lie on the circle with center O. What is the value of S?

a) 1/2
b) 1
c) âˆš2
d) âˆš3
e) (âˆš2)/2

Here's one approach:

So, s = 1
Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Mon Dec 07, 2015 6:55 pm

vrn2vw wrote:

In the figure above, points P and Q lie on the circle with center O. What is the value of s?

a) 1/2
b) 1
c) âˆš2
d) âˆš3
e) (âˆš2)/2

The slopes of perpendicular lines are the negative reciprocals of each other.

So the slope of segment OQ is the negative reciprocal of the slope of segment OP.

Since point O is the origin, and has coordinates (0, 0), we can easily calculate the slope of OP, which is -1/âˆš3. So the slope of OQ is âˆš3/1.

Since OP and OQ are both radii of a circle, they are the same length.

So, if OP goes across -âˆš3 and up 1 in that length, then OQ, which lies in the first quadrant and has a slope the negative reciprocal of the slope of OP, must go across 1 and up âˆš3.

So the correct answer is B.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

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ararjun: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sat Nov 14, 2015 12:56 am

by ararjun » Tue Dec 08, 2015 7:31 pm

I took the long road using the distance formula

Since OPQ is a right triangle

OP^2 + OQ^2 = PQ^2
(âˆš3^2 + 1^2) + (s^2 + t^2) = (s + âˆš3)^2 + (t - 1)^2
4 + s^2 + t^2 = (s^2 + 3 + 2sâˆš3) + (t^2 + 1 - 2t)
0 = 2sâˆš3 - 2t
sâˆš3 = t
s/t = 1/âˆš3
s = 1

Answer B

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Dec 08, 2015 10:31 pm

Hi vrn2vw,

Brent's approach to solving this question is exactly how I would have done it, so I won't rehash that explanation. Instead I'll point out the patterns and "hints" that were in the original drawing (and that you should be on the lookout for when dealing with similar questions).

1) Any time you see a diagonal line segment on a graph, you can draw a right triangle using that line as the hypoteneuse.

2) Right triangles on the GMAT are almost always pattern-based (angles or sides; at the very least, the Pythagorean Theorem). Here, we have a 1 and a âˆš3, so we should be thinking 30/60/90.

3) Radii have the same length no matter what direction they go in.

4) Lines "add up" to 180 degrees.

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Wed Dec 09, 2015 10:00 am, edited 1 time in total.

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 09, 2015 7:44 am

[email protected] wrote:
Brent's approach to solving this question is exactly how I wouldn't have done it, so I .....

I think/hope you mean "would"

Brent Hanneson - Creator of GMATPrepNow.com

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Dec 09, 2015 10:04 am

Hi Brent,

HA. Yes, I did mean 'would' - I was clearly typing too fast!

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Dec 11, 2015 2:47 pm

If I had a nickel for every time I've done that ...

You haven't lived until you've written 2 + 2 = 22 on a board in front of 20+ talented students who've paid over $1000 to take your class! ._.

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