ISEE Upper Level Quantitative : Prime Numbers
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Example Question #41 : How To Find Out If A Number Is Prime
, and and are positive integers.
is a prime number; is not a prime number.
Which is the greater quantity?
(a)
(b)
(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
It cannot be determined which of (a) and (b) is greater
, 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:
, which is not prime.
, which is not prime.
, which is prime - we throw this case out.
, which is prime - we throw this case out.
, which is not prime.
In the first two cases, ; in the last case, . It cannot be determined which is the greater.
Example Question #42 : How To Find Out If A Number Is Prime
; and are positive integers.
is a prime number. is not.
Which is the greater quantity?
(a) 5
(b)
(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
(b) is the greater quantity
, 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:
Only in the first case is not a prime number (8 has four factors - 1, 2, 4, 8), so and .
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