ISEE Upper Level Quantitative : Data Analysis and Probability
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #171 : Data Analysis And Probability
An arithmetic sequence begins as follows:
Which is the greater quantity?
(a) The fifth number in the sequence
(b)
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(b) is greater.
The common difference of the sequence is
The fifth number in the sequence is
This makes (b) greater.
Example Question #172 : Data Analysis And Probability
A geometric sequence begins as follows:
Which is the greater quantity?
(a) The fifth term of the sequence
(b)
(a) and (b) are equal.
(a) is greater.
(b) is greater.
It is impossible to tell from the information given.
(a) is greater.
The common ratio of the sequence is
The next three terms of the sequence are:
Example Question #11 : 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
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
(a) and (b) are equal.
(b) is greater.
The common ratio is 
Example Question #171 : Data Analysis And Probability
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
(b) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(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 #172 : Data Analysis And Probability
The first six terms of a sequence are as follows:
Which is the greater quantity?
(a) The eighth term of the sequence
(b)
(b) is greater.
(a) and (b) are equal.
(a) is greater.
It is impossible to tell from the information given.
(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 #173 : Data Analysis And Probability
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) 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 #174 : Data Analysis And Probability
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.
(a) and (b) are equal.
(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 #175 : Data Analysis And Probability
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
(b) is greater.
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(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 #176 : Data Analysis And Probability
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.
All ISEE Upper Level Quantitative Resources
