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ISEE Upper Level Quantitative : Numbers and Operations

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 #1 : How To Find Out If A Number Is Prime

Which is the greater quantity?

(a) The number of primes between 20 and 50

(b) The number of primes between 10 and 40

Possible Answers:

(a) is greater.

It is impossible to tell from the information given.

(a) and (b) are equal.

(b) is greater.

Correct answer:

(b) is greater.

Explanation:

The primes between 20 and 40 are included in both sets, so all we need to do is to compare the number of primes between 40 and 50 with the number of primes between 10 and 20.

(a) The primes between 40 and 50 are 41, 43, and 47 - three.

(b) The primes between 10 and 20 are 11, 13, 17, and 19 - four.

Since the number of primes between 10 and 20 outnumbers those between 40 and 50, the number of primes between 10 and 40 outnumber those between 20 and 50. Therefore, (b) is the greater.

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Example Question #61 : Numbers And Operations

Which is the greater quantity?

(a) The product of the first five prime numbers

(b) $\displaystyle 7!$

Possible Answers:

(a) and (b) are equal.

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(b) is greater.

Explanation:

(a) The product of the first five prime numbers is $2 \times 3\times5\times 7\times 11 = 2,310$ $\displaystyle 2 \times 3\times5\times 7\times 11 = 2,310$.

(b) $7! = 1 \times 2\times3\times4\times5\times6\times7 = 5,040$ $\displaystyle 7! = 1 \times 2\times3\times4\times5\times6\times7 = 5,040$

(b) is greater.

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Example Question #61 : Numbers And Operations

Which is the greater quantity?

(a) The sum of the prime numbers between and inclusive

(b) The sum of the prime numbers between and inclusive

Possible Answers:

(a) and (b) are equal.

(a) is greater.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

(a) The prime numbers in the to range are 2, 3, 5, 7, 11, 13, 17 , and . Their sum is

$\displaystyle 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77$.

(b) The prime numbers in the to range are and ; their sum is

$\displaystyle 23 + 29 = 52$.

(a) is greater.

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Example Question #62 : Numbers And Operations

Which is the greater quantity?

(a) The product of the two greatest primes less than or equal to 100

(b) 9,000

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

The two greatest primes less than or equal to 100 are 97 and 89; their product is $97 \times 89 = 8,633 < 9,000$ $\displaystyle 97 \times 89 = 8,633 < 9,000$, making (b) greater.

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Example Question #63 : Numbers And Operations

Which is the greater quantity?

(a) The product of the two least primes greater than or equal to 50

(b) 3,000

Possible Answers:

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

Correct answer:

(a) is greater

Explanation:

The two least primes greater than or equal to 50 are 53 and 59; their product is $53 \times 59 = 3,127 > 3,000$ $\displaystyle 53 \times 59 = 3,127 > 3,000$.

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Example Question #64 : Numbers And Operations

Which is the greater quantity?

(a) The sum of the five greatest primes less than or equal to 100

(b) 400

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) is greater

Explanation:

The five greatest primes less than or equal to 100 are $\displaystyle 73, 79, 83, 89, 97$. Their sum is

$\displaystyle 73+ 79+ 83+ 89+97 = 421 > 400$

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Example Question #65 : Numbers And Operations

Which of the following is not a prime number between $\frac{5}{2}$ $\displaystyle \frac{5}{2}$ and $\frac{43}{5}$ $\displaystyle \frac{43}{5}$?

Possible Answers:

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 4$

$\displaystyle 7$

$\displaystyle 2$

Correct answer:

$\displaystyle 4$

Explanation:

A prime number is a number that is only divisible by itself and $\displaystyle 1$.

$\displaystyle 4$ is the only number that is not prime.

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Example Question #61 : Factors / Multiples

Which one is greater?

(a) $\displaystyle (a)$ The number of prime numbers between $\displaystyle 20$ and $\displaystyle 30$

(b) $\displaystyle (b)$ The number of prime numbers between $\displaystyle 30$ and $\displaystyle 40$

Possible Answers:

it is not possible to tell based on the information given.

(a) $\displaystyle (a)$ is greater

(a) $\displaystyle (a)$ and (b) $\displaystyle (b)$ are equal.

(b) $\displaystyle (b)$ is greater

Correct answer:

(a) $\displaystyle (a)$ and (b) $\displaystyle (b)$ are equal.

Explanation:

A prime number is a natural number greater than $\displaystyle 1$ that can be divided only by $\displaystyle 1$ and itself.

The prime numbers between $\displaystyle 20$ and $\displaystyle 30$ are:

23,29 $\displaystyle 23,29$

The prime numbers between $\displaystyle 30$ and $\displaystyle 40$ are:

31,37 $\displaystyle 31,37$

So (a) $\displaystyle (a)$ and (b) $\displaystyle (b)$ are equal.

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Example Question #17 : Prime Numbers

Which one is greater?

(a) $\displaystyle (a)$ The number of prime numbers between $\displaystyle 70$ and $\displaystyle 90$

(b) $\displaystyle (b)$ The number of prime numbers between $\displaystyle 90$ and 110 $\displaystyle 110$

Possible Answers:

it is not possible to tell based on the information given.

(a) $\displaystyle (a)$ and (b) $\displaystyle (b)$ are equal

(b) $\displaystyle (b)$ is greater

(a) $\displaystyle (a)$ is greater

Correct answer:

(a) $\displaystyle (a)$ and (b) $\displaystyle (b)$ are equal

Explanation:

A prime number is a natural number greater than $\displaystyle 1$ that can be divided only by $\displaystyle 1$ and itself.

The prime numbers between $\displaystyle 70$ and $\displaystyle 90$ are:

$\displaystyle 71,73,79,83,89$

The prime numbers between $\displaystyle 90$ and 110 $\displaystyle 110$ are:

$\displaystyle 97,101,103,107,109$

So there are five prime numbers between $\displaystyle 70$ and $\displaystyle 90$ and there are five prime numbers between $\displaystyle 90$ and 110 $\displaystyle 110$ too. Therefore (a) $\displaystyle (a)$ and (b) $\displaystyle (b)$ are equal.

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Example Question #425 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Which of the following numbers is not a prime number between $\frac{8}{3}$ $\displaystyle \frac{8}{3}$ and $\frac{34}{3}$ $\displaystyle \frac{34}{3}$?

$\displaystyle 3,5,6,7,11$

Possible Answers:

$\displaystyle 7$

$\displaystyle 5$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 11$

Correct answer:

$\displaystyle 6$

Explanation:

A prime number is a natural number greater than $\displaystyle 1$ that can be divided only by $\displaystyle 1$ and itself. In this problem $\displaystyle 6$ is the only number which is not prime.

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All ISEE Upper Level Quantitative Resources

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

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ISEE Upper Level Quantitative : Numbers and Operations

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : How To Find Out If A Number Is Prime

Example Question #61 : Numbers And Operations

Example Question #61 : Numbers And Operations

Example Question #62 : Numbers And Operations

Example Question #63 : Numbers And Operations

Example Question #64 : Numbers And Operations

Example Question #65 : Numbers And Operations

Example Question #61 : Factors / Multiples

Example Question #17 : Prime Numbers

Example Question #425 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

All ISEE Upper Level Quantitative Resources

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