ISEE Upper Level Quantitative : Sets
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All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #11 : Sets
Which is the greater quantity?
(a) The number of odd integers 
(b) The number of even integers 
(b) is greater.
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
(a) is greater.
This question can be most easily answered by matching each element in the set in (a) with the next consecutive integer, which is in the set in (b):
...
Every element in the second set has a match, but there is an unmatched element in the first set. Therefore (a) is the greater quantity.
Example Question #641 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Which of the following is the greater quantity?
(a) The sum of the even integers from to
(b) Twice the sum of the integers from to
(b) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
(a) is greater.
(a) and (b) are equal.
The quantities are equal. This can be proved as follows:
The sum of the integers from to
is
(b) is twice this:
This is the same value as (a), the sum of the even integers from to
.
Example Question #11 : Sets
An arithmetic sequence begins as follows:
Which is the greater quantity?
(a) The fourth term of the sequence
(b) 200
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(b) is greater
(a) is greater
The common difference of the sequence is 
215 is the fourth term. This makes (a) greater.
Example Question #12 : Sets
A geometric sequence begins as follows:
Which is the greater quantity?
(a) The fourth element of the sequence
(b) 30
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
(a) is greater
The common ratio of the sequence is
The next two terms of the sequence can be found as follows:
This is the fourth term, which is greater than 30.
Example Question #15 : Sets
A geometric sequence begins as follows:
Which is the greater quantity?
(a) The fourth term of the sequence
(b) The sixth term of the sequence
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(b) is greater
(a) is greater
The common ratio of the geometric sequence is
The next four terms of the sequence are:
Example Question #13 : Sets
An arithmetic sequence begins as follows:
Which of the following is the greater quantity?
(a) The tenth element of the sequence
(b) 70
It is impossible to tell from the information given
(b) is greater
(a) and (b) are equal
(a) is greater
(a) is greater
The common difference of the sequence is 
which is greater than 70.
Example Question #14 : Sets
A standard deck of cards is altered by removing the red queens and the three of the jacks. A card is drawn at random from this altered deck.
Which is the greater quantity?
(a) The probability of drawing a red card
(b) The probability of drawing a black card
(b) is greater.
(a) and (b) are equal.
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
The three removed jacks must either comprise two red cards and one black card, or one red card and two black cards. Since the two red queens are also removed, the net result is either the removal of four red cards and one black card, or three red cards and two black cards. Either way, more black cards than red cards are left in the altered deck, and (b) must be greater.
Example Question #15 : Sets
An arithmetic sequence begins as follows:
Which is the greater quantity?
(a) The fifth number in the sequence
(b)
(b) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
(a) is greater.
(b) is greater.
The common difference of the sequence is
The fifth number in the sequence is
This makes (b) greater.
Example Question #16 : Sets
A geometric sequence begins as follows:
Which is the greater quantity?
(a) The fifth term of the sequence
(b)
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) is greater.
The common ratio of the sequence is
The next three terms of the sequence are:
Example Question #17 : Sets
A geometric sequence begins as follows:
Which is the greater quantity?
(a) The nine hundred ninety-ninth term of the sequence
(b) The one-thousandth term of the sequence
(b) is greater.
It is impossible to tell from the information given.
(a) is greater.
(a) and (b) are equal.
(b) is greater.
The common ratio is 
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