Tables - ISEE Upper Level Quantitative Reasoning
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The following is a portion of the menu at Moonbucks Coffee:
On this particular day, Moonbucks offers a 20% discount if four drinks of the same kind are purchased.
Which is the greater quantity?
(a) The price of four Turkish coffees
(b) The price of two Cafe Americanos and two lattes
The following is a portion of the menu at Moonbucks Coffee:
On this particular day, Moonbucks offers a 20% discount if four drinks of the same kind are purchased.
Which is the greater quantity?
(a) The price of four Turkish coffees
(b) The price of two Cafe Americanos and two lattes
(a) The four Turkish coffees cost 
before the discount. The discount is 
, so the price after discount is 
.
(b) The two Cafe Americanos cost 
; the two lattes cost 
. The total cost is 
.
This makes (b) the greater quantity.
(a) The four Turkish coffees cost
(b) The two Cafe Americanos cost
This makes (b) the greater quantity.
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The following is a portion of the menu at Moonbucks Coffee:
Today only, if you buy two espressos at regular price, you can buy any third beverage for $1.00.
Which is the greater quantity?
(a) The price of two espressos and a cappucino, bought today
(b) The price of three espressos, bought today
The following is a portion of the menu at Moonbucks Coffee:
Today only, if you buy two espressos at regular price, you can buy any third beverage for $1.00.
Which is the greater quantity?
(a) The price of two espressos and a cappucino, bought today
(b) The price of three espressos, bought today
In each case, two espressos are being purchased at a regular price, and a third beverage is being purchased at $1.00. This means both sets of drinks cost the same.
In each case, two espressos are being purchased at a regular price, and a third beverage is being purchased at $1.00. This means both sets of drinks cost the same.
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Refer to the above circle graph. Which of these quantities is greater?
(a) The number of students who voted
(b) The number of students who did not vote
Refer to the above circle graph. Which of these quantities is greater?
(a) The number of students who voted
(b) The number of students who did not vote
The above graph only reflects the relative numbers of students who voted for each of the six candidates; it does not give any information about the numbers of students who voted for each candidate, or the number of students who did not vote.
The above graph only reflects the relative numbers of students who voted for each of the six candidates; it does not give any information about the numbers of students who voted for each candidate, or the number of students who did not vote.
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Refer to the above diagram. Which is the greater quantity?
(a) The number of registered Republicans in Smith County
(b) 5,000
Refer to the above diagram. Which is the greater quantity?
(a) The number of registered Republicans in Smith County
(b) 5,000
The graph only gives the percent of the population registered in each party, not the number of people, or any way of finding the number of people. It is impossible to determine the number of Republicans in Smith County, so it is also impossible to determine how this number compares to 5,000.
The graph only gives the percent of the population registered in each party, not the number of people, or any way of finding the number of people. It is impossible to determine the number of Republicans in Smith County, so it is also impossible to determine how this number compares to 5,000.
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Refer to the above diagram. You are given that there are 
registered Democrats in Smith County. Which is the greater quantity?
(a) The number of registered Republicans in Smith County
(b) 
Refer to the above diagram. You are given that there are
(a) The number of registered Republicans in Smith County
(b)
Let 
be the number of Republicans in Smith County. The ratio of Republicans to Democrats is 
; since there are 
Democrats, we can set up a proportion as follows:
Solve for 
:
There are fewer than 
Republicans in Smith County, so (b) is the greater quantity.
Let
Solve for
There are fewer than
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The following is a portion of the menu at Moonbucks Coffee:
Today only, if you purchase two Turkish coffees, you get the third one for 
.
Which is the greater quantity?
(a) The price of three Turkish coffees, bought today
(b) The price of three Americanos.
The following is a portion of the menu at Moonbucks Coffee:
Today only, if you purchase two Turkish coffees, you get the third one for .
Which is the greater quantity?
(a) The price of three Turkish coffees, bought today
(b) The price of three Americanos.
(a) The three Turkish coffees cost 
.
(b) The three Americanos cost 
.
(a) is the greater quantity.
(a) The three Turkish coffees cost
(b) The three Americanos cost
(a) is the greater quantity.
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The following is a portion of the menu at Moonbucks Coffee:
Which is the greater quantity?
(a) The price of two lattes and a large milk
(b) The price of two espressos and a large milk
The following is a portion of the menu at Moonbucks Coffee:
Which is the greater quantity?
(a) The price of two lattes and a large milk
(b) The price of two espressos and a large milk
Although the price of the large milk is not given, it is not needed here since one large milk appears in both orders. All that is needed are the prices of the lattes and the espressos. Since an espresso costs more than a latte, two espressos and a milk cost more than two lattes and a milk. This makes (b) greater.
Although the price of the large milk is not given, it is not needed here since one large milk appears in both orders. All that is needed are the prices of the lattes and the espressos. Since an espresso costs more than a latte, two espressos and a milk cost more than two lattes and a milk. This makes (b) greater.
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The following is a portion of the menu at Moonbucks Coffee:
Which is the greater quantity?
(a) The price of a latte, a Cafe Americano, an espresso, and a Turkish coffee
(b) The price of a latte, a cappucino, a medium cola, and an espresso
The following is a portion of the menu at Moonbucks Coffee:
Which is the greater quantity?
(a) The price of a latte, a Cafe Americano, an espresso, and a Turkish coffee
(b) The price of a latte, a cappucino, a medium cola, and an espresso
The order in choice (b) includes a medium cola, the price of which is not given. It is therefore impossible to tell which order costs more.
The order in choice (b) includes a medium cola, the price of which is not given. It is therefore impossible to tell which order costs more.
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Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which is the greater quantity?
(a) The decrease in the peak temperature between Tuesday and Wednesday
(b) The decrease in the peak temperature between Wednesday and Thursday
Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which is the greater quantity?
(a) The decrease in the peak temperature between Tuesday and Wednesday
(b) The decrease in the peak temperature between Wednesday and Thursday
Observe the portions of the line graph between Tuesday and Wednesday and between Wednesday and Thursday. The portions have the same slope, so the decreases are the same.
Observe the portions of the line graph between Tuesday and Wednesday and between Wednesday and Thursday. The portions have the same slope, so the decreases are the same.
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Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which is the greater quantity?
(a) The high temperature for Sunday
(b) The low temperature for Saturday
Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which is the greater quantity?
(a) The high temperature for Sunday
(b) The low temperature for Saturday
From the graph, it can be seen that the high temperature for Sunday is higher that the high temperature for Saturday, which, by definition, must be greater than the low temperature for Saturday. That makes (a) greater.
From the graph, it can be seen that the high temperature for Sunday is higher that the high temperature for Saturday, which, by definition, must be greater than the low temperature for Saturday. That makes (a) greater.
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The following is a portion of the menu at Moonbucks Coffee:
Assume there is no tax on beverages.
Steve bought a Turkish coffee and paid for it with a five dollar bill. Marsha bought three cafe Americanos and paid for them with a ten-dollar bill. Which is the greater quantity?
(a) The amount of change Steve got back
(b) The amount of change Marsha got back
The following is a portion of the menu at Moonbucks Coffee:
Assume there is no tax on beverages.
Steve bought a Turkish coffee and paid for it with a five dollar bill. Marsha bought three cafe Americanos and paid for them with a ten-dollar bill. Which is the greater quantity?
(a) The amount of change Steve got back
(b) The amount of change Marsha got back
(a) Steve paid $3.09 for his Turkish coffee. Since he paid $5.00, his change was 
.
(b) Marsha paid 
for her three Americanos. Since she paid $10.00, her change was 
.
Marsha got more change back, making (b) higher.
(a) Steve paid $3.09 for his Turkish coffee. Since he paid $5.00, his change was
(b) Marsha paid
Marsha got more change back, making (b) higher.
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A fair coin is tossed five times. Which is the greater quantity?
(a) The probability that heads appear four or five times
(b) The probability that heads appear zero or one time
A fair coin is tossed five times. Which is the greater quantity?
(a) The probability that heads appear four or five times
(b) The probability that heads appear zero or one time
The event in (b) - that heads appear zero or one time - is exactly the same as the event that tails appear four or five times. Since heads and tails come up in each trial with equal probability, the events in (a) and (b) will be equally probable. This makes the quantities equal.
The event in (b) - that heads appear zero or one time - is exactly the same as the event that tails appear four or five times. Since heads and tails come up in each trial with equal probability, the events in (a) and (b) will be equally probable. This makes the quantities equal.
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Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which is the greater quantity?
(a) The low temperature on Thursday
(b) The low temperature on Saturday
Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which is the greater quantity?
(a) The low temperature on Thursday
(b) The low temperature on Saturday
The graph gives absolutely no information about the low temperatures on any of the seven days; the high temperatures have no relevance to the answer in this question.
The graph gives absolutely no information about the low temperatures on any of the seven days; the high temperatures have no relevance to the answer in this question.
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Two standard decks of cards are altered as follows: ten cards from Deck 1 are switched with ten cards from Deck 2.
Which is the greater quantity?
(a) The probability that a card randomly drawn from Deck 1 is black
(b) The probability that a card randomly drawn from Deck 2 is red
Two standard decks of cards are altered as follows: ten cards from Deck 1 are switched with ten cards from Deck 2.
Which is the greater quantity?
(a) The probability that a card randomly drawn from Deck 1 is black
(b) The probability that a card randomly drawn from Deck 2 is red
Since each deck will still have 52 cards, the number of red cards in Deck 1 will be equal to the number of black cards in Deck 2, and vice versa. Therefore, the two probabilities are the same.
Since each deck will still have 52 cards, the number of red cards in Deck 1 will be equal to the number of black cards in Deck 2, and vice versa. Therefore, the two probabilities are the same.
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Two standard decks of cards are altered as follows: two jacks from Deck 1 are switched with two deuces from Deck 2.
Which is the greater quantity?
(a) The probability that a card randomly drawn from Deck 1 is black
(b) The probability that a card randomly drawn from Deck 2 is black
Two standard decks of cards are altered as follows: two jacks from Deck 1 are switched with two deuces from Deck 2.
Which is the greater quantity?
(a) The probability that a card randomly drawn from Deck 1 is black
(b) The probability that a card randomly drawn from Deck 2 is black
The colors of the cards are not given, so it is now impossible to determine which deck has more black cards than red cards, if either does. For example, if the jacks are black and the deuces are red, Deck 1 now has more red cards and Deck 2 has more black cards; if the reverse holds true of the jacks and the deuces, the reverse holds true of the makeup of the decks.
Therefore, it is unknown whether you are more likely to draw a black card from Deck 1 or Deck 2.
The colors of the cards are not given, so it is now impossible to determine which deck has more black cards than red cards, if either does. For example, if the jacks are black and the deuces are red, Deck 1 now has more red cards and Deck 2 has more black cards; if the reverse holds true of the jacks and the deuces, the reverse holds true of the makeup of the decks.
Therefore, it is unknown whether you are more likely to draw a black card from Deck 1 or Deck 2.
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Below is a table that gives the population of Washington City for five census years.
Which is the greater quantity?
(a) The population increase in Washington City from 1970 to 1980
(b) The population increase in Washington City from 1980 to 1990
Below is a table that gives the population of Washington City for five census years.
Which is the greater quantity?
(a) The population increase in Washington City from 1970 to 1980
(b) The population increase in Washington City from 1980 to 1990
(a) Between 1970 and 1980, the population increase was 
(b) Between 1980 and 1990, the population increase was 
(a) is greater
(a) Between 1970 and 1980, the population increase was
(b) Between 1980 and 1990, the population increase was
(a) is greater
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Below is a table that gives the population of Washington City for five census years.
Which is the greater quantity?
(a) The population increase in Washington City from 1970 to 1975
(b) The population increase in Washington City from 1975 to 1980
Below is a table that gives the population of Washington City for five census years.
Which is the greater quantity?
(a) The population increase in Washington City from 1970 to 1975
(b) The population increase in Washington City from 1975 to 1980
No information is given in the table about the population of Washington City in 1975. Therefore, it cannot be determined with any certainty which population change was the greater.
No information is given in the table about the population of Washington City in 1975. Therefore, it cannot be determined with any certainty which population change was the greater.
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Two standard decks of cards are altered as follows: the jacks from Deck 1 are switched with the aces from Deck 2.
Which is the greater quantity?
(a) The probability that a card randomly drawn from Deck 1 is black
(b) The probability that a card randomly drawn from Deck 2 is black
Two standard decks of cards are altered as follows: the jacks from Deck 1 are switched with the aces from Deck 2.
Which is the greater quantity?
(a) The probability that a card randomly drawn from Deck 1 is black
(b) The probability that a card randomly drawn from Deck 2 is black
Two black cards and two red cards from Deck 1 are being switched with two black cards and two red cards from Deck 2, so even after the switch, in each deck, half the cards are black and half are red. Therefore, the probability of drawing a black card from Deck 1 remains 
, as does that of drawing a black card from Deck 2.
Two black cards and two red cards from Deck 1 are being switched with two black cards and two red cards from Deck 2, so even after the switch, in each deck, half the cards are black and half are red. Therefore, the probability of drawing a black card from Deck 1 remains
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Below is a table that gives the population of Washington City for five census years.
Which is the greater quantity?
(a) The mean increase in population per year from 1970 to 2010
(b) The mean increase in population per year from 1970 to 1980
Below is a table that gives the population of Washington City for five census years.
Which is the greater quantity?
(a) The mean increase in population per year from 1970 to 2010
(b) The mean increase in population per year from 1970 to 1980
(a) The mean increase in population per year from 1970 to 2010 is the difference in the populations divided by 40:
(b) The mean increase in population per year from 1970 to 1980 is the difference in the populations divided by 10:
(b) is greater.
(a) The mean increase in population per year from 1970 to 2010 is the difference in the populations divided by 40:
(b) The mean increase in population per year from 1970 to 1980 is the difference in the populations divided by 10:
(b) is greater.
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Below is a table that gives the population of Washington City for five census years.
It is known that 12% of the residents of Washington City were Black in 1970, and that 22% of the residents of Washington City were Black in 2010.
Which is the greater quantity?
(a) The number of residents of Washington City who were not Black in 1970
(b) The number of residents of Washington City who were not Black in 2010
Below is a table that gives the population of Washington City for five census years.
It is known that 12% of the residents of Washington City were Black in 1970, and that 22% of the residents of Washington City were Black in 2010.
Which is the greater quantity?
(a) The number of residents of Washington City who were not Black in 1970
(b) The number of residents of Washington City who were not Black in 2010
(a) 12% of the 3,872 residents of Washington City were Black in 1970. Therefore, 88% of the residents were not Black; this makes
residents.
(b) 22% of the 4,832 residents of Washington City were Black in 2010. Therefore, 78% of the residents were not Black; this makes
residents.
(b) is greater.
(a) 12% of the 3,872 residents of Washington City were Black in 1970. Therefore, 88% of the residents were not Black; this makes
(b) 22% of the 4,832 residents of Washington City were Black in 2010. Therefore, 78% of the residents were not Black; this makes
(b) is greater.
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