DS Geometry

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prachi18oct: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 27, 2014 10:33 pmFollowed by: 5 members; Thanked: 8 times

by prachi18oct » Sun Jul 19, 2015 4:20 pm

In the quadrilateral above, what is the measure of angle x?

(1) y = 75
(2) The quadrilateral MNQR is a reflection of quadrilateral QOPR around line QR.

Shouldn't the OA be
C ?

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Mon Jul 20, 2015 1:20 am

B?

Since its a reflection, we can say that quadrilateral is a trapezium with NO parallel to MP. Now, its possible to get X.

Regards,

Pranay

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jul 20, 2015 2:18 am

prachi18oct wrote:In the quadrilateral above, what is the measure of angle x?

(1) y = 75
(2) The quadrilateral MNQR is a reflection of quadrilateral QOPR around line QR.

Statement 2:
When a figure is reflected about a line, the result is SYMMETRY about the line.
Thus, the following figure is implied:

As shown in the figure above, x=75.
SUFFICIENT.

Statement 1:
The figure could look like this:

In this case, x=75.

The figure could look like this:

In this case, x=90.

Since x can be different values, INSUFFICIENT.

The correct answer is B.

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prachi18oct: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 27, 2014 10:33 pmFollowed by: 5 members; Thanked: 8 times

by prachi18oct » Mon Jul 20, 2015 6:26 am

GMATGuruNY wrote:
prachi18oct wrote:In the quadrilateral above, what is the measure of angle x?

(1) y = 75
(2) The quadrilateral MNQR is a reflection of quadrilateral QOPR around line QR.

Statement 2:
When a figure is reflected about a line, the result is SYMMETRY about the line.
Thus, the following figure is implied:

As shown in the figure above, x=75.
SUFFICIENT.

Statement 1:
The figure could look like this:

In this case, x=75.

The figure could look like this:

In this case, x=90.

Since x can be different values, INSUFFICIENT.

The correct answer is B.

Hi GMATGuruNY,

Is it necessary that the QR be perpedicular to NO and MP? OG says "Lines shown as straight can be assumed to be straight" so we can safely assume that QR and NO are perpendicular and so are Qr and MP ?

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 21, 2015 4:26 am

prachi18oct wrote:Hi GMATGuruNY,

Is it necessary that the QR be perpedicular to NO and MP? OG says "Lines shown as straight can be assumed to be straight" so we can safely assume that QR and NO are perpendicular and so are Qr and MP?

We can safely assume that NO, OP, MP, NM and QR are straight lines.
We CANNOT assume that any of these straight lines are parallel or of equal length.
The third figure in my post above illustrates a case in which NO is not parallel to MP:

Statement 2, however, requires that NO be parallel to MP.
Proof:
Since statement 2 implies symmetry about QR, âˆ NQR = âˆ OQR.
Since âˆ NQR + âˆ OQR = 180, âˆ NQR = âˆ OQR = 90.
The same line of reasoning can be used to show that âˆ MRQ = âˆ PRQ = 90.
The following figure is yielded:

Since NO and MP are both perpendicular to the same line -- QR -- NO and MP must be PARALLEL.

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Tue Jul 21, 2015 10:02 am

prachi18oct wrote:In the quadrilateral above, what is the measure of angle x?

(1) y = 75
(2) The quadrilateral MNQR is a reflection of quadrilateral QOPR around line QR.

Let us take the Statement 1:
It just gives us y = 75. But we are not sure if this is a trapezoid (although it may look like, but no where it is mentioned that PM is || to ON) or not, hence we cannot conclude anything for the angle x

Statement2:
The quadrilateral MNQR is a reflection of quadrilateral QOPR around line QR.
This means angle RMP = angle RPO = 105
And angle MNQ = angle POQ

We also know that the sum of 4 angles of a quadrilateral = 360.
So 105 + 105 + x + y = 360
=> x+x = 150
Hence x = 75.

So, the correct option is B

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Wed Jul 22, 2015 3:47 am

Not able to see diagram

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Satya.Achanta: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Fri Jul 10, 2015 3:52 am; Location: Ann Arbor, Michigan,USA

by Satya.Achanta » Thu Jul 23, 2015 6:56 am

I though, since in 1st option given y=75, x would also be 75 because they look like same in the diagram.and the lines MN and PO are parallel. Can you let me know how to interpret these kinda problems ?, here why cant't be y=x ?

-Satya Achanta

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 23, 2015 7:44 am

Satya.Achanta wrote:I though, since in 1st option given y=75, x would also be 75 because they look like same in the diagram.and the lines MN and PO are parallel. Can you let me know how to interpret these kinda problems ?, here why cant't be y=x ?

Figures for PS problems are generally drawn to scale.
The same CANNOT be said for DS figures, which are often NOT drawn to scale.
In many cases, figures in DS problems are provided not to help us but to FOOL us.
Here, the provided figure LOOKS symmetrical about QR in order to FOOL us into assuming that x=y.
But -- illustrated in my post above -- the figure in statement 1 could look like this:

In this case, xâ‰ y.

When solving DS geometry problems:
Trust only what you read, not what you see.
Here, nothing stated in the prompt or in statement 1 requires that x=y.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Jul 31, 2015 9:52 am

In DS, Variable approach is the easitest way to find the answer without actually solving the problem.

Remember equal number of variables and equations ensures a solution.

In original condition, angle N + angle M + angle O + 105 =360.
We have 3 variable (N,M,O) and 1 equation. we need 2 more equations. So C is the answer.

Why C? If you know our own unique logic, you don't need to actually solve it. But let me prove this for you
In (1)&(2), x=y=75 it is sufficient so C is the answer.

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Last edited by Max@Math Revolution on Thu Aug 20, 2015 11:30 am, edited 2 times in total.

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Aug 20, 2015 8:54 am

In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and equations ensures a solution.

In original condition, angle N+angle M+angle O+105=360. We have 3 variable and 1 equation we need 2 more equations. So C is the answer.

Why C? If you know our own innovative logics to find the answer, you don't need to actually solve the problem.

www.mathrevolution.com

Regardless of your math skills, our world's first Variable Approach (DS) and IVY Approach (PS) help students dramatically reduce their time spent per question and improve accuracy. You will have 10 min. to spare before the test ends.

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by [email protected] » Thu Aug 20, 2015 9:47 am

Hi Max@MathRevolution,

This DS prompt does NOT require a 'system' of equations to answer the given question. Given the geometry rules involved, Fact 2 actually provides enough information on its own, so the answer is NOT C.

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