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 #546 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Define a sequence as follows:
For integers 
Which is the greater quantity?
(a)
(b)
(b) is greater
(a) and (b) are equal
It is impossible to tell which is greater from the information given
(a) is greater
(a) is greater
Subsituting:
Since the initial term of the sequence is positive, each subsequent term, 3 times the previous one, is positive, so
This makes (a) greater.
Example Question #62 : Data Analysis
Above is a part of a schedule of flight arrivals; the common destination is New Orleans, Lousiana, which is located in the Central Time Zone (CT). Chicago and Houston are also in the CT; New York is in the Eastern Time Zone, which is one hour ahead of CT; Denver is in the Mountain Time Zone, one hour behind CT; Los Angeles is in the Pacific Time Zone, two hours behind CT. All arrival times are PM and are given in Central Time.
When Flight 289 took off, it was 1:39 PM at its point of departure. How long did the flight take? (You may assume all flights arrived on time.)
2 hours, 52 minutes
1 hour, 52 minutes
2 hours, 8 minutes
3 hours, 8 minutes
3 hours, 52 minutes
2 hours, 52 minutes
Flight 289 departed from New York, which is in the Eastern Time Zone, one hour ahead of New Orleans. Since the flight took off when it was 1:39, subtract one hour; the flight took off when it was 12:39 in New Orleans. We need to subtract the adjusted departure time from the arrival time - however, this must be done by rewriting 12:39 as 0:39:
"Borrow" one hour as follows:
The flight was 2 hours, 52 minutes long.
Example Question #63 : Data Analysis
Above is a part of a schedule of flight arrivals; the common destination is Atlanta, Georgia, which is located in the Eastern Time Zone. New York is also in the Eastern Time Zone; Chicago and Houston are in the Central Time Zone, which is one hour behind ET; Denver is in the Mountain Time Zone, two hours behind ET; Los Angeles is in the Pacific Time Zone, three hours behind ET. All arrival times are PM and are given in Eastern Time.
When Flight 23 took off, it was 11:21 AM at its point of departure. How long did the flight take? (You may assume all flights arrived on time.)
4 hours and 42 minutes
2 hours and 42 minutes
3 hours and 18 minutes
3 hours and 42 minutes
2 hours and 42 minutes
2 hours and 42 minutes
Flight 23 took off from Denver, which is in the Mountain Time Zone - two hours behind Atlanta time. Since it was 11:21 AM there, two hours must be added to this time to determine the time in Atlanta - this is 1:21 PM. Since the flight arrived in Atlanta at 4:03, the flight time was
We can "borrow" one hour, then subtract, as follows:
The flight took 2 hours and 42 minutes.
Example Question #64 : Data Analysis
Above is a part of a schedule of flight arrivals; the common destination is Atlanta, Georgia, which is located in the Eastern Time Zone. New York is also in the Eastern Time Zone (ET); Chicago and Houston are in the Central Time Zone, which is one hour behind ET; Denver is in the Mountain Time Zone, two hours behind ET; Los Angeles is in the Pacific Time Zone, three hours behind ET. All arrival times are PM and are given in Eastern Time.
Flight 289 lasted 1 hour 57 minutes. When it took off, what time was it at the location of its departure?
10:34 AM
12:34 PM
11:34 AM
2:34 PM
1:34 PM
1:34 PM
Flight 289 took off from New York, which is in the same time zone as Atlanta, so no adjustments for Time Zone need to be made. Subtract 1 hour 57 minutes from the arrival time of 3:31:
We can "borrow" one hour and subtract as follows:
It was 1:34 PM in New York when the airplane departed.
Example Question #65 : Data Analysis
One ordinary six-sided die is altered such that the probability of tossing a six on that die is 
Which of the following is the greater quantity?
(a) The probability that the roll of two fair dice will come up a total of 12
(b) The probability that the roll of the two altered dice will come up a total of 12
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
(b) is the greater quantity
The only way for a roll of two dice to come up with a sum of 12 is for the dice to show a double-six. Apply the multiplication principle using the probability of a roll of six on each die.
The probability of a roll of six on a fair die is 
The probability of a double-six on the altered dice is 
Example Question #61 : Data Analysis
One ordinary six-sided die is altered such that the probability of tossing a six on that die is 
Which of the following is the greater quantity?
(a) The probability that the roll of two fair dice will come up a total of 2
(b) The probability that the roll of the two altered dice will come up a total of 2
(a) is the greater quantity
(b) is the greater quantity
(a) and (b) are equal
It cannot be determined which of (a) and (b) is greater
(a) is the greater quantity
There is only one way that the roll of two dice can come up 2 - for both dice to come up a one.
The probability of a fair die coming up a one is 
The probability of a "1" coming up on the first altered die is
The probability of a "1" coming up on the second altered die is
Therefore, the probability of a roll of double one on the altered dice is
Therefore, "2" is more likely to come up on the fair dice.
Example Question #61 : Data Analysis And Probability
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
Which is the greater quantity?
(a) The temperature in Kingdom City at 6 AM Wednesday
(b) The temperature in Kingdom City at 6 PM Wednesday
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(b) is the greater quantity
It is impossible to determine which is greater from the information given
The line graph only indicates the high and low temperatures for the individual days; it says nothing about the temperature at any specific time of any day. Therefore, the question cannot be answered from the graph alone.
Example Question #62 : Data Analysis And Probability
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
Which is the greater quantity?
(a) The lowest high temperature for any of the seven days
(b) The highest low temperature for any of the seven days
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(b) is the greater quantity
(a) is the greater quantity
Examine the low point of the line representing the high temperatures and the high point of the line representing the low temperatures.
It can be seen that the lowest of the high temperatures is 65 degrees (Friday), and that the highest of the low temperatures is 60 degrees (Wednesday). This makes the former quantity the greater.
Example Question #63 : Data Analysis And Probability
Refer to the above graph, which shows the high and low temperatures in degrees Fahrenheit for Kingdom City over a one-week period.
Which is the greater quantity?
(a) The temperature in Kingdom City at noon on Friday
(b) 70 degrees
(a) and (b) are equal
(b) is the greater quantity
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(b) is the greater quantity
The graph does not tell us the temperatures at any specific time of day on any of the seven days. However, as seen below, we know from the graph that the high temperature on Friday was 65 degrees.
The temperature at noon Friday cannot have been greater than 65 degrees, so 70 is the greater quantity.
Example Question #65 : Data Analysis
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
All of the tiles are put in a box except for the unique tiles and the blanks. A tile is drawn at random. Which is the greater quantity?
(a) The probability that the tile is a vowel
(b)
(Note: "Y" is considered a consonant here)
(b) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(b) is the greater quantity
There are five unique tiles - "J", "K", "Q", "X", and "Z" - and two blanks, for a total of 7 tiles not placed in the box. Therefore, the box contains 93 tiles.
The number of tiles with each vowel is as follows:
A: 9 tiles
E: 12 tiles
I: 9 tiles
O: 8 tiles
U: 4 tiles
This is a total of 
All ISEE Upper Level Quantitative Resources
