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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 #72 : Factors / Multiples

Which one is greater?

(a) $\displaystyle (a)$ The product of the two greatest prime numbers less than $\displaystyle 50$

$(b)\ 2000$ $\displaystyle (b)\ 2000$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

A prime number is a natural number greater than $\displaystyle 1$ that can be divided only by $\displaystyle 1$ and itself. The two greatest prime numbers less than $\displaystyle 50$ are $\displaystyle 47$ and $\displaystyle 43$ .

So their product is:

$47\times 43=2021$ $\displaystyle 47\times 43=2021$ , which is greater than 2000 $\displaystyle 2000$ . So (a) $\displaystyle (a)$ is greater than (b) $\displaystyle (b)$ .

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Example Question #73 : Numbers And Operations

Which one is greater?

(a) $\displaystyle (a)$ The sum of the prime numbers between $\displaystyle 50$ and $\displaystyle 60$

(b) $\displaystyle (b)$ The sum of the prime numbers between $\displaystyle 55$ and $\displaystyle 65$

Possible Answers:

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

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

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

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

Correct answer:

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

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 $\displaystyle 50$ and $\displaystyle 60$ are 53,59 $\displaystyle 53,59$ , so we have:

$\displaystyle (a)=53+59=112$

The prime numbers between $\displaystyle 55$ and $\displaystyle 65$ are 59, 61 $\displaystyle 59, 61$ , so we have:

$\displaystyle (b)=59+61=120$

So (b) $\displaystyle (b)$ is greater than (a) $\displaystyle (a)$ .

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Example Question #21 : Prime Numbers

Which is the greater quantity?

(A) The sum of the even integers from 21 to 30 inclusive

(B) Three times the sum of the prime integers from 21 to 30 inclusive

Possible Answers:

(A) and (B) are equal

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

(B) is greater

(A) is greater

Correct answer:

(B) is greater

Explanation:

The even integers from 21 to 30 inclusive are 22, 24, 26, 28, and 30; their sum is

$\displaystyle 22+24+26+28+30 = 130$

The prime integers from 21 to 30 inclusive are 23 and 29. their sum is

$\displaystyle 23+29 = 52$

and three times this sum is

$3 \cdot 52 = 156$ $\displaystyle 3 \cdot 52 = 156$

This makes (B) greater

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Example Question #22 : Prime Numbers

What is the sum of the prime integers between 75 and 100?

Possible Answers:

269 $\displaystyle 269$

274 $\displaystyle 274$

439 $\displaystyle 439$

351 $\displaystyle 351$

348 $\displaystyle 348$

Correct answer:

348 $\displaystyle 348$

Explanation:

The prime integers between 75 and 100 are

$\displaystyle 79, 83, 89, 97$

Their sum is

$\displaystyle 79 + 83+ 89+97 = 348$

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Example Question #23 : Prime Numbers

Which is the greater quantity?

(A) The number of composite integers between 41 and 50 inclusive.

(B) The number of prime integers between 41 and 50 inclusive.

Possible Answers:

(B) is greater

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

(A) and (B) are equal

(A) is greater

Correct answer:

(A) is greater

Explanation:

The only prime numbers among the ten in the range 41 through 50 are 41, 43, and 47; this makes three prime numbers and seven composite numbers, so (A) is greater.

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Example Question #23 : Prime Numbers

Multiply the least and greatest primes between 80 and 100.

Possible Answers:

8,439 $\displaystyle 8,439$

7,553 $\displaystyle 7,553$

8,051 $\displaystyle 8,051$

7,719 $\displaystyle 7,719$

7,857 $\displaystyle 7,857$

Correct answer:

8,051 $\displaystyle 8,051$

Explanation:

The least and greatest primes between 80 and 100 are 83 and 97; their product is

$83 \times 97 = 8,051$ $\displaystyle 83 \times 97 = 8,051$

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Example Question #25 : Prime Numbers

Which of the following is the greater quantity?

(A) The sum of the prime numbers between 80 and 90

(B) The sum of the prime numbers between 90 and 100

Possible Answers:

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

(A) is greater

(B) is greater

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

The prime numbers between 80 and 90 are 83 and 89, whose sum is $\displaystyle 83 + 89 = 172$ ; the only prime number between 90 and 100 is 97. (A) is the greater quantity.

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Example Question #26 : Prime Numbers

Which is the greater quantity?

(A) Twice the number of prime numbers between 41 and 50 inclusive

(B) The number of composite numbers between 41 and 50 inclusive

Possible Answers:

(A) is greater

(A) and (B) are equal

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

(B) is greater

Correct answer:

(B) is greater

Explanation:

Out of the ten integers from 41 to 50, the prime numbers are 41, 43, and 47 - therefore, there are three prime numbers and seven composite numbers. Since

$2 \times 3 = 6 < 7$ $\displaystyle 2 \times 3 = 6 < 7$ ,

(B) is greater.

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Example Question #81 : Factors / Multiples

Which of the following is the greater quantity?

(A) The sum of the prime numbers between 50 and 60

(B) The sum of the odd composite numbers between 50 and 60

Possible Answers:

(A) and (B) are equal

(B) is greater

(A) is greater

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

Correct answer:

(B) is greater

Explanation:

The prime numbers between 50 and 60 are 53 and 59; their sum is $\displaystyle 53+59 = 112$ . The odd composite numbers between 50 and 60 are 51, 55, and 57; their sum is $\displaystyle 51+55+57 = 163$ . Therefore, (B) is greater.

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Example Question #31 : Prime Numbers

$\displaystyle M$ and $\displaystyle N$ are prime integers. $\displaystyle 60 < M < 70$ and $\displaystyle 80 < N < 90$ . What is the minimum value of M + N $\displaystyle M + N$ ?

Possible Answers:

146 $\displaystyle 146$

150 $\displaystyle 150$

144 $\displaystyle 144$

142 $\displaystyle 142$

148 $\displaystyle 148$

Correct answer:

144 $\displaystyle 144$

Explanation:

The least prime integer between 60 and 70 is 61, so this is the minimum value of $\displaystyle M$ . The least prime integer between 80 and 90 is 83, so this is the minimum value of $\displaystyle N$ . Since

$M \geq 61$ $\displaystyle M \geq 61$ and $N \geq 83$ $\displaystyle N \geq 83$ ,

then , by the addition property of inequality,

$M + N \geq 61 + 83 = 144$ $\displaystyle M + N \geq 61 + 83 = 144$ .

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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 #72 : Factors / Multiples

Example Question #73 : Numbers And Operations

Example Question #21 : Prime Numbers

Example Question #22 : Prime Numbers

Example Question #23 : Prime Numbers

Example Question #23 : Prime Numbers

Example Question #25 : Prime Numbers

Example Question #26 : Prime Numbers

Example Question #81 : Factors / Multiples

Example Question #31 : Prime Numbers

All ISEE Upper Level Quantitative Resources

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