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ISEE Upper Level Quantitative : How to find out if a number is prime

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

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Example Questions

Example Question #41 : How To Find Out If A Number Is Prime

$\displaystyle x+ y = 12$ , and $\displaystyle x$ and $\displaystyle y$ are positive integers.

$\displaystyle x$ is a prime number; $\displaystyle y$ is not a prime number.

Which is the greater quantity?

(a) $\displaystyle x$

(b) $\displaystyle y$

Possible Answers:

(a) is the greater quantity

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

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

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

Explanation:

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

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

x=2 $\displaystyle x=2$

$\displaystyle 2+ y = 12$

y = 10 $\displaystyle y = 10$ , which is not prime.

x= 3 $\displaystyle x= 3$

$\displaystyle 3+ y = 12$

y = 9 $\displaystyle y = 9$ , which is not prime.

x= 5 $\displaystyle x= 5$

$\displaystyle 5+ y = 12$

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

x= 7 $\displaystyle x= 7$

$\displaystyle 7+ y = 12$

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

x= 11 $\displaystyle x= 11$

$\displaystyle 11+ y = 12$

y = 1 $\displaystyle y = 1$ , which is not prime.

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

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Example Question #42 : How To Find Out If A Number Is Prime

$\displaystyle x+ y = 10$ ; $\displaystyle x$ and $\displaystyle y$ are positive integers.

$\displaystyle x$ is a prime number. $\displaystyle y$ is not.

Which is the greater quantity?

(a) 5

(b) $\displaystyle y$

Possible Answers:

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

$\displaystyle x+ y = 10$ , and $\displaystyle x$ and $\displaystyle y$ are positive integers.

Therefore, $\displaystyle x$ must be an integer from 1 to 9, as must $\displaystyle y$ .

Since $\displaystyle x$ is prime, it can be any of 2, 3, 5, or 7.

Therefore, one of the following must hold:

$\displaystyle 2+ y = 10$

y = 8 $\displaystyle y = 8$

$\displaystyle 3+ y = 10$

y = 7 $\displaystyle y = 7$

$\displaystyle 5+ y = 10$

y = 5 $\displaystyle y = 5$

$\displaystyle 7+ y = 10$

y = 3 $\displaystyle y = 3$

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

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : How to find out if a number is prime

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #41 : How To Find Out If A Number Is Prime

Example Question #42 : How To Find Out If A Number Is Prime

All ISEE Upper Level Quantitative Resources

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