ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #27 : Quadrilaterals

What is the length of a rectangular room with a perimeter of \displaystyle 100ft and a width of \displaystyle 18ft

 

Possible Answers:

\displaystyle 68ft

\displaystyle 34ft

\displaystyle 58ft

\displaystyle 60ft

\displaystyle 32ft

Correct answer:

\displaystyle 32ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 100=2l+2(18)

\displaystyle 100=2l+36

Subtract \displaystyle 36 from both sides

\displaystyle 100-36=2l+36-36

\displaystyle 64=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{64}{2}=\frac{2l}{2}

\displaystyle 32=l

Example Question #28 : Quadrilaterals

What is the length of a rectangular room with a perimeter of \displaystyle 50ft and a width of \displaystyle 7ft?

Possible Answers:

\displaystyle 14ft

\displaystyle 18ft

\displaystyle 28ft

\displaystyle 20ft

\displaystyle 36ft

Correct answer:

\displaystyle 18ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 50=2l+2(7)

\displaystyle 50=2l+14

Subtract \displaystyle 14 from both sides

\displaystyle 50-14=2l+14-14

\displaystyle 36=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{36}{2}=\frac{2l}{2}

\displaystyle 18=l

Example Question #25 : Squares

What is the length of a rectangular room with a perimeter of \displaystyle 86ft and a width of \displaystyle 18ft?

 

Possible Answers:

\displaystyle 21ft

\displaystyle 22ft

\displaystyle 24ft

\displaystyle 23ft

\displaystyle 25ft

Correct answer:

\displaystyle 25ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 86=2l+2(18)

\displaystyle 86=2l+36

Subtract \displaystyle 36 from both sides

\displaystyle 88-36=2l+36-36

\displaystyle 50=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{50}{2}=\frac{2l}{2}

\displaystyle 25=l

Example Question #101 : How To Find The Area Of A Parallelogram

What is the length of a room with a perimeter of \displaystyle 44ft and a width of \displaystyle 11ft?

 

Possible Answers:

\displaystyle 12ft

\displaystyle 11ft

\displaystyle 9ft

\displaystyle 8ft

\displaystyle 10ft

Correct answer:

\displaystyle 11ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 44=2l+2(11)

\displaystyle 44=2l+22

Subtract \displaystyle 22 from both sides

\displaystyle 44-22=2l+22-22

\displaystyle 22=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{22}{2}=\frac{2l}{2}

\displaystyle 11=l

Example Question #71 : Solving For Length

What is the length of a room with a perimeter of \displaystyle 60ft and a width of \displaystyle 10ft?

 

Possible Answers:

\displaystyle 20ft

\displaystyle 18ft

\displaystyle 21ft

\displaystyle 22ft

\displaystyle 19ft

Correct answer:

\displaystyle 20ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 60=2l+2(10)

\displaystyle 60=2l+20

Subtract \displaystyle 20 from both sides

\displaystyle 60-20=2l+20-20

\displaystyle 40=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{40}{2}=\frac{2l}{2}

\displaystyle 20=l

Example Question #191 : Measurement & Data

What is the length of a room with a perimeter of \displaystyle 94ft and a width of \displaystyle 33ft?

 

Possible Answers:

\displaystyle 16ft

\displaystyle 17ft

\displaystyle 14ft

\displaystyle 15ft

\displaystyle 13ft

Correct answer:

\displaystyle 14ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 94=2l+2(33)

\displaystyle 94=2l+66

Subtract \displaystyle 66 from both sides

\displaystyle 94-66=2l+66-66

\displaystyle 28=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{28}{2}=\frac{2l}{2}

\displaystyle 14=l

Example Question #513 : Geometry

What is the length of a room with a perimeter of \displaystyle 58ft and a width of \displaystyle 16ft?

 

Possible Answers:

\displaystyle 13ft

\displaystyle 14ft

\displaystyle 16ft

\displaystyle 17ft

\displaystyle 15ft

Correct answer:

\displaystyle 13ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 58=2l+2(16)

\displaystyle 58=2l+32

Subtract \displaystyle 32 from both sides

\displaystyle 58-32=2l+32-32

\displaystyle 26=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{26}{2}=\frac{2l}{2}

\displaystyle 13=l

Example Question #72 : Solving For Length

What is the length of a room with a perimeter of \displaystyle 62ft and a width of \displaystyle 12ft?

\displaystyle P=2l+ 2w

 

Possible Answers:

\displaystyle 15ft

\displaystyle 17ft

\displaystyle 19ft

\displaystyle 18ft

\displaystyle 16ft

Correct answer:

\displaystyle 19ft

Explanation:

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 62=2l+2(12)

\displaystyle 62=2l+24

Subtract \displaystyle 24 from both sides

\displaystyle 62-24=2l+24-24

\displaystyle 38=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{38}{2}=\frac{2l}{2}

\displaystyle 19=l

Example Question #515 : Geometry

What is the length of a room with a perimeter of \displaystyle 70ft and a width of \displaystyle 16ft?

 

Possible Answers:

\displaystyle 20ft

\displaystyle 16ft

\displaystyle 17ft

\displaystyle 18ft

\displaystyle 19ft

Correct answer:

\displaystyle 19ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 70=2l+2(16)

\displaystyle 70=2l+32

Subtract \displaystyle 32 from both sides

\displaystyle 70-32=2l+32-32

\displaystyle 38=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{38}{2}=\frac{2l}{2}

\displaystyle 19=l

Example Question #516 : Geometry

What is the length of a room with a perimeter of \displaystyle 40ft and a width of \displaystyle 8ft?

 

Possible Answers:

\displaystyle 14ft

\displaystyle 10ft

\displaystyle 13ft

\displaystyle 11ft

\displaystyle 12ft

Correct answer:

\displaystyle 12ft

Explanation:

\displaystyle P=2l+ 2w

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown. 

\displaystyle 40=2l+2(8)

\displaystyle 40=2l+16

Subtract \displaystyle 16 from both sides

\displaystyle 40-16=2l+16-16

\displaystyle 24=2l

Divide \displaystyle 2 by both sides

\displaystyle \frac{24}{2}=\frac{2l}{2}

\displaystyle 12=l

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