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ISEE Upper Level Quantitative : Factors / Multiples

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

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All ISEE Upper Level Quantitative Resources

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Example Questions

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Example Question #39 : How To Find Out If A Number Is Prime

and are prime numbers.

80 < M < 90 <N < 100

Which is the greater quantity?

(A) M + N

(B) 175

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:

97 is the only prime number between 90 and 100, so N = 97 . The only two primes between 80 and 90 are 83 and 89, so M = 83 or M = 89 . Therefore, either of the following holds:

M + N = 83 + 97 = 180 > 175

M + N = 89 + 97 = 186 > 175

(A) must be the greater quantity regardless.

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Example Question #91 : Factors / Multiples

and are prime numbers.

30 < M <40 < N < 50

Which is the greater quantity?

(A) M + N

(B) 80

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

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:

We show that it cannot be determined whether M + N is greater than, less than, or equal to 80 by choosing two pairs of primes within the given ranges and adding.

Case 1:

$M = 31, N = 41 \Rightarrow M + N = 31+ 41 = 72 < 80$ .

Case 2:

$M = 37, N = 47 \Rightarrow M + N = 37+ 47 = 84 > 80$

In each case, 30 < M <40 < N < 50 , with and prime.

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Example Question #41 : Prime Numbers

x+ y = 12 , and and are positive integers.

is a prime number; is not a prime number.

Which is the greater quantity?

(a)

(b)

Possible Answers:

It cannot be determined which of (a) and (b) is greater

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

It cannot be determined which of (a) and (b) is greater

Explanation:

x+ y = 12 , and and are positive integers, so each of and is an integer from 1 to 11 inclusive.

is a prime number, meaning that it can be equal to 2, 3, 5, 7, or 11. Testing each case:

x=2

2+ y = 12

y = 10 , which is not prime.

x= 3

3+ y = 12

y = 9 , which is not prime.

x= 5

5+ y = 12

y = 7 , which is prime - we throw this case out.

x= 7

7+ y = 12

y = 5 , which is prime - we throw this case out.

x= 11

11+ y = 12

y = 1 , which is not prime.

In the first two cases, y > x ; in the last case, y < x . It cannot be determined which is the greater.

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Example Question #451 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

x+ y = 10 ; and are positive integers.

is a prime number. is not.

Which is the greater quantity?

(a) 5

(b)

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

It cannot be determined which of (a) and (b) is greater

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

x+ y = 10 , and and are positive integers.

Therefore, must be an integer from 1 to 9, as must .

Since is prime, it can be any of 2, 3, 5, or 7.

Therefore, one of the following must hold:

2+ y = 10

y = 8

3+ y = 10

y = 7

5+ y = 10

y = 5

7+ y = 10

y = 3

Only in the first case is not a prime number (8 has four factors - 1, 2, 4, 8), so x = 2 and y = 8 > 5 .

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : Factors / Multiples

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #39 : How To Find Out If A Number Is Prime

Example Question #91 : Factors / Multiples

Example Question #41 : Prime Numbers

Example Question #451 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

All ISEE Upper Level Quantitative Resources

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