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Math Expert V
Joined: 02 Sep 2009
Posts: 59125
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 72% (01:24) correct 28% (01:22) wrong based on 53 sessions

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Competition Mode Question What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?

(1) $$PR =\sqrt{325}$$
(2) $$QS =\sqrt{325}$$

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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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1
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?

STATEMENT (1)--PR=$$\sqrt{325}$$

this statement gives no new information about the trapezoid
we can derive it from the question prompt
still, we don't know anything about QS (trapezoid can be scalene , isosceles we don't know)
so we cant find RS

area of trapezoid = $$\frac{(PQ+RS)*15}{2}$$

we don't know anything about RS so, we can't find the area of a trapezoid
INSUFFICIENT

STATEMENT (2)--QS=$$\sqrt{325}$$

we know that PR = $$\sqrt{325}$$
from this statement we know QS = $$\sqrt{325}$$
this proves that trapezoid is isoceles

so we can find the value of RS that is = 10+30+10 = 50

area of trapezoid = $$\frac{(PQ+RS)*15}{2}$$ = $$\frac{(30+50)*15}{2}$$ = 600

SUFFICIENT

Senior Manager  P
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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2
IMO ANSWER IS OPTION B. Here's how I did:

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Senior Manager  P
Joined: 18 May 2019
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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1
From the information given in connection with the trapezoid, I need information on QS in order to compute the area of trapezoid.

1. Statement 1 gives the distance of PR=325^0.5, an information that can already be deduced from the question stem. In addition it gives no information whatsoever about QS, which is needed in order to determine the length of RS. Statement 1 is therefore insufficient.

2. Statement gives information about the QS=325^0.5, and that is sufficient to compute the area of the trapezoid. Statement 2 alone is therefore sufficient in this case.

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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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As we know Area of trapezoid = (a+b)h
HERE a=30,h=15, to find b we need RS length= 10+15+X(CAN BE FIND USING QS)
So OA:B
Senior Manager  G
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GMAT 1: 720 Q50 V38 GPA: 4
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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B.

We need B to locate point S. A is already Stated in the argument

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Senior Manager  P
Joined: 07 Mar 2019
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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Given here PQ = 30, Let T be the point at RS such that PT ⊥ RS. Given PT = 15 and RT = 10. Since RS > PQ
RS > 30

Area of Trapezoid PQSR $$=\frac{1}{2} (PQ + RS) * PT$$

Only unknown in the formula is RS. So RS = ?

(1) PR = √325
It only reiterates what is mentioned in the question. No new information given about RS neither can be deduced. Since QS can have following possibilities:

a. QS < PR
b. QS = PR
c. QS > PR

RS would vary accordingly.

INSUFFICIENT.

(2) QS = √325
Since RT = 10 and PT = 15, PR = √325. Hence PR = QS
 RS = 10 + 30 + 10 = 50

Thus, only one value of RS is possible.

SUFFICIENT.

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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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Quote:
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?

(1) PR=√325
(2) QS=√325

area trapezoid: $$\frac{base_1+base_2}{2}•height=\frac{31+(10+30+X)}{2}•15$$
X is the distance from S to the perpendicular drawn from Q to RS;

(1) PR=√325: no info about perpendicular, insufic.
(2) QS=√325: if we draw a right triangle from this perpendicular we can find X with this info, sufic.

Intern  B
Joined: 21 Mar 2019
Posts: 22
Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th  [#permalink]

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B
Area = (B1+B2) * h /2
= 30*x*15/2
st1 useless
st2 we can calculate the length of the base of the second " triangle " which is 10
like the one of the first triangle.
Therefore the middle part is also equal to 30 so x = 10+30+10 = 50 --> Sufficient

B Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th   [#permalink] 18 Sep 2019, 10:37
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