ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning
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All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #22 : Sets
Seven freshmen and seven sophomores are running for student council. Each freshman will choose three of the candidates from his or her class; each sophomore will choose four from his or her class.
Which is the greater quantity?
(a) The number of ways a freshman can fill out his or her ballot
(b) The number of ways a sophomore can fill out his or her ballot
(b) is greater.
It is impossible to tell from the information given.
(a) is greater.
(a) and (b) are equal.
(a) and (b) are equal.
In both cases, candidates are selected without regard to order, making them combinations (as opposed to permutations).
(a) The freshmen are choosing three elements from a group of seven, or 
(b) The sophomores are choosing four elements from a group of seven, or 
These quantities are equal.
Example Question #177 : Data Analysis
An arithmetic sequence begins as follows:
The Fibonacci sequence begins
with each subsequent term being the sum of the previous two.
Which is the greater quantity?
(a) The tenth term of the arithmetic sequence
(b) The tenth term of the Fibonacci sequence
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) is greater.
(b) is greater.
(a) and (b) are equal.
(a) The arithmetic sequence has common difference 
(b) By beginning with 
Therefore the two are equal.
Example Question #23 : Sets
Twelve candidates are running for four vacancies on the school board. Six of the candidates are Democrats, and six are Republicans. Samantha wants to vote for two Democrats and two Republicans.
Which is the greater quantity?
(a) The number of ways Samantha can cast her ballot so that she votes for two Democrats and two Republicans
(b)
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
(a) and (b) are equal.
(b) is greater.
The number of ways Samantha can choose two Democrats out of the six is the number of combinations of 2 chosen from a set of 6:
This is also the number of ways Samantha can choose two Republicans out of the six.
These are two independent events, so we multiply them to get the number of total ways Samantha can vote with these specifications:
Therefore (b) is greater.
Example Question #24 : Sets
The Fibonacci sequence begins
with each subsequent term being the sum of the previous two.
Which is the greater quantity?
(a) The sum of the seventh, eighth, ninth, and tenth terms of the Fibonacci sequence
(b) The twelfth term of the Fibonacci sequence
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) is greater.
(b) is greater.
(b) is greater.
By beginning with 
The seventh through tenth terms, added together, yield a sum of
which is less than the twelfth term, 
Example Question #25 : Sets
The Student Council comprises thirty students, from which four are chosen to fill the offices of President, Vice-President, Secretary, and Treasurer. Which is the greater quantity?
(a) The number of ways the four offices can be filled
(b)
(a) and (b) are equal.
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
(a) There are 30 ways to fill the office of President. Afterward, there will be 29 ways to fill the office of Vice-President, 28 ways to fill the office of Secretary, and 27 ways to fill the office of Treasurer. Multiply:
(b)
This makes (b) greater.
Example Question #181 : Data Analysis
The first six terms of a sequence are:
Which is the greater quantity?
(a) The tenth term of the sequence
(b)
(b) is greater.
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
(b) is greater.
The terms are generated by alternately subtracting two and adding two. The next four terms are:
Therefore (b) is greater.
Example Question #666 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
A bag has 
Quantity A: The probability of choosing 
Quantity B: The probability of choosing 
Quantity A is greater.
The two quantities are equal.
Quantity B is greater.
The relationship cannot be determined from the information given.
Quantity B is greater.
Quantity A: There are a total of 
Quantity B: The probability of choosing 
Quantity B is larger.
Example Question #182 : Data Analysis
If Joe flips a coin twice, what is the probability that at least one tail will occur?
There are four possible outcomes (with H being heads and T being tails): HH, HT, TT, TH. There are three outcomes that contain a tail: TH, HT, and TT. Therefore the probaility that at least one flip will show tails is 
Example Question #31 : How To Find The Missing Part Of A List
An arithmetic sequence begins
What number replaces the square?
Since this is an arithmetic sequence, each entry in the sequence is obtained by adding the same number to the previous entry - this number is
Let 
Example Question #31 : Sets
The first two terms of an arithmetic sequence are
Which of the following expressions is equivalent to the fifth term?
An arithmetic sequence is formed by adding the same expression to each term to get the next term; this common difference is
To obtain the fifth term, add 
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