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the altitude on side

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by sanju09 » Mon Apr 16, 2012 11:56 pm
In ∆PQR, D is a point on the side PR such that QD is the altitude on it. What is the measure of side QR?
I. The measure of side PQ is 4√2 and ∠QPR = 45°.
II. The measure of side DR in the ∆QDR is 3.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
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Source: — Data Sufficiency |
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by killer1387 » Tue Apr 17, 2012 12:05 am
sanju09 wrote:In ∆PQR, D is a point on the side PR such that QD is the altitude on it. What is the measure of side QR?
I. The measure of side PQ is 4√2 and ∠QPR = 45°.
II. The measure of side DR in the ∆QDR is 3.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
statement I:
we have the side PD=QD=4
But we dont have info for calculating QR

INSUFFICIENT

statement II:
DR = 3
WE CANT FIND ANYTHING ELSE WITH THIS INFO

INSUFFICIENT

I& II;

In right triangle QDR we have QD= 4; DR= 3
HENCE QR= sq rt (16+9)=5

SUFFICIENT

HENCE C.
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by klmehta03 » Tue Apr 17, 2012 4:17 pm
agree IMO C. OA pls?
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by bryan88 » Wed Apr 18, 2012 7:42 am
+1 for C
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by fyllmax » Fri Apr 20, 2012 3:04 pm
killer1387 wrote:
sanju09 wrote:In ∆PQR, D is a point on the side PR such that QD is the altitude on it. What is the measure of side QR?
I. The measure of side PQ is 4√2 and ∠QPR = 45°.
II. The measure of side DR in the ∆QDR is 3.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]
statement I:
we have the side PD=QD=4
But we dont have info for calculating QR

INSUFFICIENT

statement II:
DR = 3
WE CANT FIND ANYTHING ELSE WITH THIS INFO

INSUFFICIENT

I& II;

In right triangle QDR we have QD= 4; DR= 3
HENCE QR= sq rt (16+9)=5

SUFFICIENT

HENCE C.
How do u know that pd=qd=4? I don`t get this ?
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by neelgandham » Fri Apr 20, 2012 3:54 pm
fyllmax,

Let me answer the question on killers behalf. Before you go through the explanation, can I request you to open the attachment and have a quick look.

Solution:
In right angled riangle QPD, we know that angle PDQ = 90 degrees and angle Angle QPD = 45 degrees.
As sum of angles of a triangle is equal to 180 degrees.
Angle QPD + Angle PDQ + Angle DQP = 180.
i.e. 45 + 90 + Angle DQP = 180
Angle DQP = 45 degrees

Now, we have a right angled triangle with two equal angles(45 degrees each). Since, the two angles in the right triangle are equal, the sides opposite to the angles must be equal. i.e. PD = QD

But from Pythagorean theorem,
In right angled triangle PDQ,
PD^2 + QD^2 = PQ^2, i.e.
2 * PD^2 = (4√2)^2 (PQ = 4√2 and QD = PD)
2 * PD^2 = 4^2 * 2
PD = 4
PD = QD = 4.

I hope that answers your question. Let me know if you need any further help
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by bobdylan » Sat Apr 21, 2012 12:38 am
And why isn't statement 1 sufficient by itself ??
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by bobdylan » Sat Apr 21, 2012 12:39 am
And why isn't statement 1 sufficient by itself ??
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by sanju09 » Sat Apr 21, 2012 12:59 am
bobdylan wrote:And why isn't statement 1 sufficient by itself ??

For the determination of a triangle, we must have any one of the following set of information known:

1. Its two sides and their included angle are known.

2. Its one side and angles at the endpoints of this side are known.

From statement (I), we can only determine ∆PQD, which cannot answer QR. We are able to answer QR only if we are able to determine either ∆PQR or ∆QDR, which cannot be done without knowing either ∠DQR or the measure of side DR of ∆QDR. Hence statement (I) alone is not sufficient.
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