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In a newly constructed city, plots were rectangular in shape with

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In a newly constructed city, plots were rectangular in shape with  [#permalink]

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New post 07 Mar 2019, 01:25
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In a newly constructed city, plots were rectangular in shape with a length being 2 units more than the breadth. If the area of all the plots are between 25 sq. units and 400 sq. units, which of the following can be the minimum and the maximum possible breadth of any plot? (length and breadth are integers)

A. 5,19
B. 4,19
C. 5,21
D. 6,21
E. 6,19
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Posts: 7415
Re: In a newly constructed city, plots were rectangular in shape with  [#permalink]

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New post 07 Mar 2019, 07:20
kiran120680 wrote:
In a newly constructed city, plots were rectangular in shape with a length being 2 units more than the breadth. If the area of all the plots are between 25 sq. units and 400 sq. units, which of the following can be the minimum and the maximum possible breadth of any plot? (length and breadth are integers)

A. 5,19
B. 4,19
C. 5,21
D. 6,21
E. 6,19


Let the length be l, where l=b+2, and breadth be b...
so area = l*b=b(b+2)
The range of area 25<b(b+2)<400...

We have two values

MINIMUM => b(b+2)>25....
In the options we have 4, 5 and 6. Since we are looking for minimum, let us test the smallest 4, so area = 4(4+2)=24<25... NOT possible
Next value is 5, so area = 5(5+2)=35>25... possible value So, 5 is the least

MAXIMUM => b(b+2)<400....
In the options we have 19 and 21. Since we are looking for maximum, let us test the largest 21, so area = 21(21+2)>400... NOT possible
Next value is 19, so area = 19(19+2)<400... possible value So, 5 is the least

Value 5, 19

A
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Re: In a newly constructed city, plots were rectangular in shape with  [#permalink]

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New post 07 Mar 2019, 07:31
We can right away delete answer options B, C and D...
The area is between 25 and 400 .. if the breadth is 21.. then length would be 23.. and area would be way more than 400.
If the breadth is 4 , length would be 6 and area would be less than 25..

Thus leaving us with options A AND E... option A would be the right one because 5<6.

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Re: In a newly constructed city, plots were rectangular in shape with   [#permalink] 07 Mar 2019, 07:31
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