ISEE Upper Level Quantitative : How to find the missing part of a list
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #21 : How To Find The Missing Part Of A List
The Fibonacci sequence begins
with each subsequent term being the sum of the previous two.
Which is the greater quantity?
(a) The product of the seventh and eighth terms of the Fibonacci sequence
(b) The product of the sixth and ninth terms of the Fibonacci sequence
(a) and (b) are equal.
(b) is greater.
It is impossible to tell from the information given.
(a) is greater.
(a) is greater.
By starting with 
(a) The seventh and eighth terms are 13 and 21; their product is 
(b) The sixth and ninth terms are 8 and 34; their product is 
(a) is greater.
Example Question #22 : How To Find The Missing Part Of A List
The first six terms of a sequence are as follows:
Which is the greater quantity?
(a) The eighth term of the sequence
(b)
(a) is greater.
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(a) is greater.
Each successive term is derived by adding a quantity to the previous term that increments by 1 with each term:
Example Question #23 : How To Find The Missing Part Of A List
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
It is impossible to tell from the information given.
(b) is greater.
(a) and (b) are equal.
(a) is greater.
(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 #24 : How To Find The Missing Part Of A List
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)
(a) and (b) are equal.
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
(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 #25 : How To Find The Missing Part Of A List
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
(a) and (b) are equal.
It is impossible to tell from the information given.
(b) is greater.
(a) 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 #26 : How To Find The Missing Part Of A List
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.
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
(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 #27 : How To Find The Missing Part Of A List
The first six terms of a sequence are:
Which is the greater quantity?
(a) The tenth term of the sequence
(b)
(a) is greater.
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(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 #28 : How To Find The Missing Part Of A List
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 
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All ISEE Upper Level Quantitative Resources
