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Retired Moderator
Joined: 16 Apr 2020
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Location: India
WE:Education (Education)
PQRS is a rectangle with PQ < 65 and PQ + QR + RS = 100
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27 Sep 2021, 09:06
27 Sep 2021, 09:06
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Question Stats:
6% (02:27) correct
93% (02:36) wrong based on 32 sessions
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PQRS is a rectangle with PQ < 65 and PQ + QR + RS = 100
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Maximum possible area of the rectangle PQRS |
1250 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
PQRS is a rectangle with PQ < 65 and PQ + QR + RS = 100
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05 Oct 2021, 03:35
05 Oct 2021, 03:35
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Explanantion:
PQ = RS = L
QR = SP = B
2L + B = 100
L = 50 - \(\frac{B}{2}\)
Area of rectangle PQRS = (L)(B) = (50 - \(\frac{B}{2}\))(B)
i.e. A = -\(\frac{B^2}{2}\) + 50B
NOTE: we have a quadratic equation and we can find its maximum by finding its vertex
x-coordinate of the vertex in a quadratic equation: \(ax^2 + bx + c\) is given by \(\frac{-b}{2a}\)
\(x_v = \frac{-(50)}{2(-0.5)} = 50\)
Maximum value of A = -\(\frac{50^2}{2}\) + 50(50) = -1250 + 2500 = 1250
Col. A: 1250
Col. B: 1250
Hence, option C
PQ = RS = L
QR = SP = B
2L + B = 100
L = 50 - \(\frac{B}{2}\)
Area of rectangle PQRS = (L)(B) = (50 - \(\frac{B}{2}\))(B)
i.e. A = -\(\frac{B^2}{2}\) + 50B
NOTE: we have a quadratic equation and we can find its maximum by finding its vertex
x-coordinate of the vertex in a quadratic equation: \(ax^2 + bx + c\) is given by \(\frac{-b}{2a}\)
\(x_v = \frac{-(50)}{2(-0.5)} = 50\)
Maximum value of A = -\(\frac{50^2}{2}\) + 50(50) = -1250 + 2500 = 1250
Col. A: 1250
Col. B: 1250
Hence, option C
General Discussion
Re: PQRS is a rectangle with PQ < 65 and PQ + QR + RS = 100
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04 Oct 2021, 12:01
04 Oct 2021, 12:01
solution pleasee.
