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 #4 : How To Find The Missing Part Of A List
Which quantity is greater?
(a) The number of even integers 
(b) The number of multiples of 4 
It is impossible to tell from the information given.
(a) is greater
(a) and (b) are equal
(b) is greater
(a) and (b) are equal
The easiest way to answer this is to try to match each element in the first set to one the second set as follows:
...
In other words, each element in the set in (a) is paired with the element in the set in (b) that is its double. Since there is a one-to-one correspondence, the two sets are of equal aize, and (a) and (b) are equal quantities.
Example Question #9 : Sets
Which quantity is greater?
(a) The number of even integers
(b) The number of odd integers
(a) and (b) are equal.
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
(a) and (b) are equal.
The easiest way to answer this is to try to match each element in the first set to one in the second set as follows:
...
Since there is a one-to-one correspondence between the elements of the two sets, (a) and (b) are equal.
Example Question #4 : How To Find The Missing Part Of A List
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the product of the numbers will be at least 
(b)
(a) and (b) are equal.
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
(b) is greater.
Out of a possible thirty-six rolls, the following result in a product of 
This is ten equally probable rolls out of thirty-six, resulting in a probability of
Since 
Example Question #11 : How To Find The Missing Part Of A List
Which is the greater quantity?
(a) The number of odd integers 
(b) The number of even integers 
(a) is greater.
It is impossible to tell from the information given.
(a) and (b) are equal.
(b) is greater.
(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 #161 : Data Analysis And Probability
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
(a) is greater.
(a) and (b) are equal.
(b) is greater.
It is impossible to tell from the information given.
(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 #162 : Data Analysis And Probability
An arithmetic sequence begins as follows:
Which is the greater quantity?
(a) The fourth term of the sequence
(b) 200
(b) is greater
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
(a) is greater
The common difference of the sequence is 
215 is the fourth term. This makes (a) greater.
Example Question #163 : Data Analysis And Probability
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) and (b) are equal
(a) is greater
(b) is greater
(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 : How To Find The Missing Part Of A List
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) is greater
(b) is greater
(a) and (b) are equal
(a) is greater
The common ratio of the geometric sequence is
The next four terms of the sequence are:
Example Question #161 : Data Analysis
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
(a) is greater
(a) and (b) are equal
(b) is greater
(a) is greater
The common difference of the sequence is 
which is greater than 70.
Example Question #162 : Data Analysis
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.
It is impossible to tell from the information given.
(a) is greater.
(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.
All ISEE Upper Level Quantitative Resources
