ISEE Upper Level Quantitative Reasoning › Factors / Multiples
Which is the greater quantity?
(a) The number of prime numbers between 70 and 110
(b) The number of prime numbers between 80 and 120
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
The primes between 80 and 110 are included in both sets, so all we need to do is to compare the number of primes between 70 and 80 and the number of primes between 110 and 120.
(a) The primes between 70 and 80 are 71, 73, and 79 - three primes
(b) The only prime between 110 and 120 is 113.
(a) is the greater quantity
Which is the greater quantity?
(a) The number of prime numbers between 1 and 20 inclusive
(b) The number of composite numbers between 21 and 30 inclusive
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
(a) The prime numbers between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight total.
(b) The prime numbers between 21 and 30 inclusive are 23 and 29 - two prime numbers out of ten integers. This leaves eight composite numbers.
(a) and (b) are therefore equal.
Which is the greater quantity?
(a) The number of factors of 169
(b) The number of factors of 121
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.
Which is the greater quantity?
(a) The number of prime numbers between 70 and 110
(b) The number of prime numbers between 80 and 120
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
The primes between 80 and 110 are included in both sets, so all we need to do is to compare the number of primes between 70 and 80 and the number of primes between 110 and 120.
(a) The primes between 70 and 80 are 71, 73, and 79 - three primes
(b) The only prime between 110 and 120 is 113.
(a) is the greater quantity
Which is the greater quantity?
(a) The number of factors of 169
(b) The number of factors of 121
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.
Which is the greater quantity?
(a) The number of prime numbers between 70 and 110
(b) The number of prime numbers between 80 and 120
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
The primes between 80 and 110 are included in both sets, so all we need to do is to compare the number of primes between 70 and 80 and the number of primes between 110 and 120.
(a) The primes between 70 and 80 are 71, 73, and 79 - three primes
(b) The only prime between 110 and 120 is 113.
(a) is the greater quantity
Which is the greater quantity?
(a) The number of factors of 169
(b) The number of factors of 121
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
Each number has only three factors. 121 has 1, 11, and 121 as factors; 169 has 1, 13, and 169 as factors. The answer is that the quantities are equal.
Which is the greater quantity?
(a) The number of prime numbers between 1 and 20 inclusive
(b) The number of composite numbers between 21 and 30 inclusive
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
(a) The prime numbers between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight total.
(b) The prime numbers between 21 and 30 inclusive are 23 and 29 - two prime numbers out of ten integers. This leaves eight composite numbers.
(a) and (b) are therefore equal.
Which is the greater quantity?
(a) The number of prime numbers between 1 and 20 inclusive
(b) The number of composite numbers between 21 and 30 inclusive
(a) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
(a) The prime numbers between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight total.
(b) The prime numbers between 21 and 30 inclusive are 23 and 29 - two prime numbers out of ten integers. This leaves eight composite numbers.
(a) and (b) are therefore equal.
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.
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
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.