If PQRS is a parallelogram, what is the area

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GMATBusters’ Quant Quiz Question -7

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If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
1) POQ is an isosceles triangle.
2) Area of triangle OPQ = 6.25

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Official Answer

D

GMATBusters · Answer

The solution shall be as follows:

https://www.youtube.com/watch?v=e_sVBgRn8Mw

Archit3110 · Answer

If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
1) POQ is an isosceles triangle.
2) Area of triangle OPQ = 1.25

parallelogram PQRS is not know whether its a square or rectangle
#1POQ is an isosceles triangle.
so side PO = PQ ; x and PQ = x√2
PQ = 5 so PO+OQ = 5√2
angle s and r =90 each 
we can find area of PQRS
#2
Area of triangle OPQ = 1.25
we can find h or say breadth of the llo gram
sufficient
OPTION D

ashwini2k6jha · Answer

Area =2* area of triangle OPQ?
State 1: sufficient
OP^2+OQ^2=25
OP=OQ=25/2^1/2
FROM this we can get area of OPQ=1/2*OP*OQ
State:2 sufficient
Area =2*area of triangle OPQ
Answer D

Raxit85 · Answer

If PQRS is a parallelogram, what is the area of the parallelogram PQRS?

PQ=SR=5

1) POQ is an isosceles triangle.
Not sufficient as we don't know exact height of POQ triangle.

2) Area of triangle OPQ = 1.25
1/2 *OP*OR = 1.25 
OP*OR = 2.5 
Still not sufficient.

1) + 2) 
As we know OPQ is isosceles triangle. We can find the OP = OR = 1.25 
But still we don't know height of parallellogram. So insufficient.

Ans. E

Kinshook · Answer

Asked: If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
Area of parallelogram PQRS = Base * Height = 5*H

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Screenshot 2020-04-26 at 9.15.26 PM.png [ 95.79 KiB | Viewed 3592 times ]

1) POQ is an isosceles triangle.
Since POQ is an isosceles triangle, and angle POQ is right angle
angle OPQ = angle PQO = 45
\(PO = QO = 5/\sqrt{2}\)
Height H = PT = \(PO/\sqrt{2} = 5/2 = 2.5\)
Area of parallelogram PQRS = Base * Height = 5*H = 5*2.5 = 12.5
SUFFICIENT

Attachment:

Screenshot 2020-04-26 at 9.10.33 PM.png [ 76.73 KiB | Viewed 3600 times ]

2) Area of triangle OPQ = 1.25
Area of triangle OPQ = 1/2 * Base * Height = 1/2 * 5H = 2.5H = 1.25; H = .5
Area of parallelogram PQRS = Base * Height = 5*H = 5*.5 = 2.5
SUFFICIENT

IMO D

GMATBusters
Statement 2 should be
2) Area of triangle OPQ = 6.25
For statement 1 & statement 2 to be consistent.

Tommy6e · Answer

Answer is D

If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
1) POQ is an isosceles triangle. --> Sufficient
Since POQ is a isosceles triangle, OP = OQ = x
x^2 + x^2 = PQ^2 = 5^2
2x^2 = 5^2
x^2 = 5^2 / 2
x = sqrt5 / 2

Angles OPQ = OQP = 45 = QOR = QOS
SP = RQ
Thus, triangle SOP = ROQ --> SO=OR=5/2=2.5
RQ=SP=y
y^2 + 2.5^2 = x^2 = (sqrt5/2)^2
We can find y, multiply it by 5, and get the area of SRQP.

2) Area of triangle OPQ = 12.5 (I believe that 1.25 is a typo?)
Because triangle OPQ is a right triangle, the area of SRQP is double the area of triangle OPQ - 25.

uc26 · Answer

Area of a parallelogram=b*h. We know that base=PQ=5. We need to find the height to be able to find the area of PQRS. Let us draw a perpendicular from point O to the base PQ and name it OC. So we get two triangles OCP and OCQ which are similar to the right triangle OPQ since two angles are equal. If we can get the length of side OP and OQ, then we can use the proportionality of sides to find the corresponding sides of triangle OPC which will give us the height of OC.

(1) If POQ is an isosceles triangle, then OP=OQ. We can get the length of OP and OQ using pythagoras theorem and thus find the height OC of the parallelogram. Sufficient.

(2) No information on the side lengths of triangle OPQ. Not sufficient.

Answer: A.

(1) If POQ is an isosceles triangle, then OP=OQ. We can get the length of OP and OQ using pythagoras theorem and thus find the height OC of the parallelogram. Sufficient.

(2) No information on the side lengths of triangle OPQ. Not sufficient.

Answer: A.

SR71Blackbird · Answer

The answer to this question is D

Statement 1: Isosceles triangle, side x, x, x(2^(1/2)). we get the length of the unknown sides. Drop a perpendicular from right angle. and divide the triangle in two equal parts(the the two angles are same, two sides are same, hence the base is dived into two equal parts) 
Use Pythagorean theorem, get height, Get area of the parallelogram.

Statement 2: area directly given, 0.5 *H*B = 1.25 get h, solve for area B*h

lacktutor · Answer

If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
Finding the height of the triangle to the base, which is equal to 5 is enough to get the area of the parallelogram.

(Statement1): POQ is an isosceles triangle.
 2x^{2} = 25 
—>  x^{2} = \frac{25}{2}

Area of the triangle: 
 x^{2}/ 2= 5*h/2  
—>  25/4 = 5h/2  —>  h= 2.5  
Sufficient

(Statement2):Area of triangle OPQ = 1.25
—> 5*h/2 = 1.25 
h = 2.5/5 = 1/2 
Sufficient

Answer (D)

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zs2 · Answer

If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
1) POQ is an isosceles triangle.
2) Area of triangle OPQ = 1.25

Statement 1- POQ is isosceles triangle which means PO = OQ
Drop a line from O to PQ, it will divide PQ in to 2 EQUAL parts

From here we can find height of triangle and then ht of ||gm. ( median from right angle is half of the hypotenuse )
Sufficient.

Statment 2- area of OPQ is 1.25

using 1/2 * b*h = 1.25 , we can find ht of triangle which is also ht of ||gm
Thus we can find area of ||gm, sufficient

HENCE D is answer

1BlackDiamond1 · Answer

If PQRS is a parallelogram, what is the area of the parallelogram PQRS?
1) POQ is an isosceles triangle.
2) Area of triangle OPQ = 1.25

We can find the sides of the parallelogram and then the height of the parallelogram and thus the area.
The answer is D.

jrk23 · Answer

"D" is the answer. i think.

We can deduce the answer from both of the option

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If PQRS is a parallelogram, what is the area

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If PQRS is a parallelogram, what is the area

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