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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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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #18 : Plane Geometry

Hexagon HEXGON $\displaystyle HEXGON$ and Square SQUA $\displaystyle SQUA$ both have perimeter 64. Which is the greater quantity?

(a) $\displaystyle HE$

(b) $\displaystyle SQ$

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which is greater from the information given

Correct answer:

It is impossible to determine which is greater from the information given

Explanation:

The length of one side of the square - in particular, that of $\overline{SQ}$ $\displaystyle \overline{SQ}$ - is equal to one fourth its perimeter, so it can be determined that $SQ = 64 \div 4 = 16$ $\displaystyle SQ = 64 \div 4 = 16$. However, no relation among the sides of the hexagon is given - in particular, it is not given that the hexagon is regular - so the length of $\overline{HE}$ $\displaystyle \overline{HE}$ cannot be determined. Insufficient information is given.

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Example Question #1 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

What is the length of a rectangular room with a perimeter of 42ft $\displaystyle 42ft$ and a width of 7ft? $\displaystyle 7ft?$

Possible Answers:

12ft $\displaystyle 12ft$

22ft $\displaystyle 22ft$

28ft $\displaystyle 28ft$

14ft $\displaystyle 14ft$

18ft $\displaystyle 18ft$

Correct answer:

14ft $\displaystyle 14ft$

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.

$\displaystyle 42=2l+2(7)$

$\displaystyle 42=2l+14$

Subtract $\displaystyle 14$ from both sides

$\displaystyle 42-14=2l+14-14$

28=2l $\displaystyle 28=2l$

Divide $\displaystyle 2$ by both sides

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

14=l $\displaystyle 14=l$

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Example Question #2 : Solving For Length

What is the length of a rectangular room with a perimeter of 62ft $\displaystyle 62ft$ and a width of 8ft? $\displaystyle 8ft?$

Possible Answers:

23ft $\displaystyle 23ft$

46ft $\displaystyle 46ft$

37ft $\displaystyle 37ft$

40ft $\displaystyle 40ft$

38ft $\displaystyle 38ft$

Correct answer:

23ft $\displaystyle 23ft$

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.

$\displaystyle 62=2l+2(8)$

$\displaystyle 62=2l+16$

Subtract $\displaystyle 16$ from both sides

$\displaystyle 62-16=2l+16-16$

46=2l $\displaystyle 46=2l$

Divide $\displaystyle 2$ by both sides

$\frac{46}{2}=\frac{2l}{2}$ $\displaystyle \frac{46}{2}=\frac{2l}{2}$

23=l $\displaystyle 23=l$

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Example Question #2 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

What is the length of a rectangular room with a perimeter of 92ft $\displaystyle 92ft$ and a width of 21ft? $\displaystyle 21ft?$

Possible Answers:

25ft $\displaystyle 25ft$

45ft $\displaystyle 45ft$

50ft $\displaystyle 50ft$

30ft $\displaystyle 30ft$

40ft $\displaystyle 40ft$

Correct answer:

25ft $\displaystyle 25ft$

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.

$\displaystyle 92=2l+2(21)$

$\displaystyle 92=2l+42$

Subtract $\displaystyle 42$ from both sides

$\displaystyle 92-42=2l+42-42$

50=2l $\displaystyle 50=2l$

Divide $\displaystyle 2$ by both sides

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

25=l $\displaystyle 25=l$

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Example Question #3 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

What is the length of a rectangular room with a perimeter of 59ft $\displaystyle 59ft$ and a width of 17ft? $\displaystyle 17ft?$

Possible Answers:

12.5ft $\displaystyle 12.5ft$

12ft $\displaystyle 12ft$

15ft $\displaystyle 15ft$

15.5ft $\displaystyle 15.5ft$

25ft $\displaystyle 25ft$

Correct answer:

12.5ft $\displaystyle 12.5ft$

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.

$\displaystyle 59=2l+2(17)$

$\displaystyle 59=2l+34$

Subtract $\displaystyle 34$ from both sides

$\displaystyle 59-34=2l+134-34$

25=2l $\displaystyle 25=2l$

Divide $\displaystyle 2$ by both sides

$\frac{25}{2}=\frac{2l}{2}$ $\displaystyle \frac{25}{2}=\frac{2l}{2}$

12.5=l $\displaystyle 12.5=l$

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Example Question #4 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

What is the length of a rectangular room with a perimeter of 66ft $\displaystyle 66ft$ and a width of 18ft? $\displaystyle 18ft?$

Possible Answers:

15ft $\displaystyle 15ft$

12ft $\displaystyle 12ft$

14ft $\displaystyle 14ft$

11ft $\displaystyle 11ft$

13ft $\displaystyle 13ft$

Correct answer:

15ft $\displaystyle 15ft$

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.

$\displaystyle 66=2l+2(18)$

$\displaystyle 66=2l+36$

Subtract $\displaystyle 36$ from both sides

$\displaystyle 66-36=2l+36-36$

30=2l $\displaystyle 30=2l$

Divide $\displaystyle 2$ by both sides

$\frac{30}{2}=\frac{2l}{2}$ $\displaystyle \frac{30}{2}=\frac{2l}{2}$

15=l $\displaystyle 15=l$

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Example Question #93 : Solve Problems Involving Measurement And Conversion Of Measurements

What is the length of a rectangular room with a perimeter of 60ft $\displaystyle 60ft$ and a width of 14ft? $\displaystyle 14ft?$

Possible Answers:

26ft $\displaystyle 26ft$

16ft $\displaystyle 16ft$

30ft $\displaystyle 30ft$

32ft $\displaystyle 32ft$

18ft $\displaystyle 18ft$

Correct answer:

16ft $\displaystyle 16ft$

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.

$\displaystyle 60=2l+2(14)$

$\displaystyle 60=2l+28$

Subtract $\displaystyle 28$ from both sides

$\displaystyle 60-28=2l+28-28$

32=2l $\displaystyle 32=2l$

Divide $\displaystyle 2$ by both sides

$\frac{32}{2}=\frac{2l}{2}$ $\displaystyle \frac{32}{2}=\frac{2l}{2}$

16=l $\displaystyle 16=l$

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Example Question #3 : Solving For Length

What is the length of a rectangular room with a perimeter of 40ft $\displaystyle 40ft$ and a width of 6ft? $\displaystyle 6ft?$

Possible Answers:

16ft $\displaystyle 16ft$

14ft $\displaystyle 14ft$

28ft $\displaystyle 28ft$

32ft $\displaystyle 32ft$

18ft $\displaystyle 18ft$

Correct answer:

14ft $\displaystyle 14ft$

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.

$\displaystyle 40=2l+2(6)$

$\displaystyle 40=2l+12$

Subtract $\displaystyle 12$ from both sides

$\displaystyle 40-12=2l+12-12$

28=2l $\displaystyle 28=2l$

Divide $\displaystyle 2$ by both sides

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

14=l $\displaystyle 14=l$

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Example Question #22 : Plane Geometry

What is the length of a rectangular room with a perimeter of 96ft $\displaystyle 96ft$ and a width of 30ft? $\displaystyle 30ft?$

Possible Answers:

24ft $\displaystyle 24ft$

22ft $\displaystyle 22ft$

20ft $\displaystyle 20ft$

19ft $\displaystyle 19ft$

18ft $\displaystyle 18ft$

Correct answer:

18ft $\displaystyle 18ft$

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.

$\displaystyle 96=2l+2(30)$

$\displaystyle 96=2l+60$

Subtract $\displaystyle 60$ from both sides

$\displaystyle 96-60=2l+60-60$

36=2l $\displaystyle 36=2l$

Divide $\displaystyle 2$ by both sides

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

18=l $\displaystyle 18=l$

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Example Question #31 : How To Find The Perimeter Of A Rectangle

What is the length of a rectangular room with a perimeter of 90ft $\displaystyle 90ft$ and a width of 12ft $\displaystyle 12ft$

Possible Answers:

22ft $\displaystyle 22ft$

55ft $\displaystyle 55ft$

33ft $\displaystyle 33ft$

66ft $\displaystyle 66ft$

44ft $\displaystyle 44ft$

Correct answer:

33ft $\displaystyle 33ft$

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.

$\displaystyle 90=2l+2(12)$

$\displaystyle 90=2l+24$

Subtract $\displaystyle 24$ from both sides

$\displaystyle 90-24=2l+24-24$

66=2l $\displaystyle 66=2l$

Divide $\displaystyle 2$ by both sides

$\frac{66}{2}=\frac{2l}{2}$ $\displaystyle \frac{66}{2}=\frac{2l}{2}$

33=l $\displaystyle 33=l$

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All ISEE Middle Level Quantitative Resources

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

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #18 : Plane Geometry

Example Question #1 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

Example Question #2 : Solving For Length

Example Question #2 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

Example Question #3 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

Example Question #4 : Apply Area And Perimeter Formulas For Rectangles: Ccss.Math.Content.4.Md.A.3

Example Question #93 : Solve Problems Involving Measurement And Conversion Of Measurements

Example Question #3 : Solving For Length

Example Question #22 : Plane Geometry

Example Question #31 : How To Find The Perimeter Of A Rectangle

All ISEE Middle Level Quantitative Resources

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