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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

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All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : How To Find The Volume Of A Cylinder

What is the volume of a cylinder with a height of in. and a radius of 2.5 in?

Possible Answers:

$87.5\pi$ in^3

$82.5\pi$ in^3

$42.25\pi$ in^3

$70\pi$ in^3

$35\pi$ in^3

Correct answer:

$87.5\pi$ in^3

Explanation:

This is a rather direct question. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$A = \pi * 2.5^2 * 14=87.5\pi$

This is the volume of the cylinder.

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Example Question #351 : Geometry

What is the radius of a cylinder with a volume of $562.5\pi$ in^3 and a height of ?

Possible Answers:

$56.25\pi$

56.25

$15\pi$

7.5

Correct answer:

7.5

Explanation:

Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$562.5\pi = \pi * r^2 * 10$

Solve for :

56.25=r^2

Using a calculator to calculate $\sqrt{56.25}$ , you will see that r = 7.5

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Example Question #1 : Cylinders

What is the surface area of a cylinder of height in., with a radius of in?

Possible Answers:

$136\pi$ in^2

$152\pi$ in^2

$240\pi$ in^2

$122\pi$ in^2

$120\pi$ in^2

Correct answer:

$152\pi$ in^2

Explanation:

Recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * r^2$

For our problem, this is:

$\pi * 4^2 = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

The area of the "outer face" is a little bit trickier, but it is not impossible. It is actually a rectangle that has the height of the cylinder and a width equal to the circumference of the base; therefore, it is:

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

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Example Question #2 : Cylinders

What is the surface area of a cylinder having a base of radius in and a height of in?

Possible Answers:

$212\pi$ in^2

$308\pi$ in^2

$99\pi$ in^2

$363\pi$ in^2

$33\pi$ in^2

Correct answer:

$308\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 11^2 = \pi * 121$

You need to double this for the two bases:

$2 * 121 * \pi = 242 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 11* 3 = 66 * \pi$

Therefore, the total surface area is:

$242 * \pi + 66 * \pi = 308\pi$

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Example Question #3 : Cylinders

What is the surface area of a cylinder with a height of in. and a diameter of in?

Possible Answers:

$22\pi$ in^2

$57\pi$ in^2

$28\pi$ in^2

$36\pi$ in^2

$14\pi$ in^2

Correct answer:

$36\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 2^2 = \pi * 4$

You need to double this for the two bases:

$2 * 4 * \pi = 8 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 2 * 7 = 28 * \pi$

Therefore, the total surface area is:

$28\pi + 8\pi = 36\pi$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

The volume of a cylinder with height of is $275\pi$ in^3 . What is its surface area?

Possible Answers:

$135\pi$ in^2

$55\pi$ in^2

$66\pi$ in^2

$160\pi$ in^2

$82\pi$ in^2

Correct answer:

$160\pi$ in^2

Explanation:

To begin, we must solve for the radius of this cylinder. Recall that the equation of for the volume of a cylinder is:

$V = \pi * r^2 * h$

For our values this is:

$275\pi = \pi * r^2 * 11$

Solving for , we get:

r^2 = 25

Hence, r = 5

Now, recall that to find the surface area of a cylinder, you need to find the surface area of its two bases and then the surface area of its "outer face." The first two are very easy since they are circles. The equation for one base is:

$A = \pi * r^2$

For our problem, this is:

$\pi * 5^2 = \pi * 25$

You need to double this for the two bases:

$2 * 25 * \pi = 50 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 5 * 11 = 110 * \pi$

Therefore, the total surface area is:

$50\pi + 110\pi = 160\pi$

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Example Question #1 : How To Find The Surface Area Of A Cylinder

What is the surface area of a cylinder of height in, with a radius of in?

Possible Answers:

$136\pi$ in^2

$122\pi$ in^2

$152\pi$ in^2

$240\pi$ in^2

$120\pi$ in^2

Correct answer:

$152\pi$ in^2

Explanation:

$A = \pi * r^2$

For our problem, this is:

$\pi * 4^2 = \pi * 16$

You need to double this for the two bases:

$2 * 16 * \pi = 32 * \pi$

$2 * \pi * r * h$

For our problem, this is:

$2 * \pi * 4 * 15 = 120 * \pi$

Therefore, the total surface area is:

$32\pi + 120\pi = 152\pi$

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Example Question #1 : Numbers And Operations

3/5 + 4/7 – 1/3 =

Possible Answers:

7/9

72/89

88/105

3/37

Correct answer:

88/105

Explanation:

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

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Example Question #1 : Factors / Multiples

25 is the greatest common factor of 175 and which of these numbers?

Possible Answers:

150

None of the answers are correct.

Correct answer:

150

Explanation:

Of the four numbers given, 25 is only a factor of 150, since all multiples of 25 end in the digits 25, 50, 75, or 00. To determine whether 150 is correct, we inspect the factors of 150 and 175:

Factors of 150: $\left \{ 1, 2, 3,5,6,10,15,\underline{25},30, 50, 75, 150\right \}$

Factors of 175: $\left \{ 1,5,7,\underline{25}, 35,175\right \}$

Since 25 is the greatest number in both lists, GCF (150,175) = 25 .

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Example Question #3 : How To Find The Greatest Common Factor

is an odd prime.

Which is the greater quantity?

(a) GCF (N,16)

(b) $GCF (N^{4},2)$

Possible Answers:

It is impossible to tell from the information given.

(b) is equal.

(a) is greater.

(a) and (b) are equal.

Correct answer:

(a) and (b) are equal.

Explanation:

The greatest common factor of two numbers is the product of the prime factors they share; if they share no prime factors, it is .

(a) $16 = 2 \times 2\times 2\times2$ . Since is an odd prime, and share no prime factors, and GCF (N,16) = 1 .

(b) $N^{4} = N \times N \times N \times N$ , since is prime. Since is an even prime, $N^{4}$ and share no prime factors, and $GCF (N^{4},2) = 1$ .

The quantities are equal since each is equal to .

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #5 : How To Find The Volume Of A Cylinder

Example Question #351 : Geometry

Example Question #1 : Cylinders

Example Question #2 : Cylinders

Example Question #3 : Cylinders

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : How To Find The Surface Area Of A Cylinder

Example Question #1 : Numbers And Operations

Example Question #1 : Factors / Multiples

Example Question #3 : How To Find The Greatest Common Factor

All ISEE Upper Level Quantitative Resources

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