How to find the answer from a table - ISEE Upper Level Quantitative Reasoning
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The beverage menu from a coffeehouse reads as follows:
Eight friends go out for drinks. Three order cappucino, two order espresso, one orders Americano, one orders Turkish coffee, and one orders cafe latte. One of the eight agrees to leave the entire amount of the tip, which is to be 20% of the check. How much will be the amount of the tip (round to the nearest dime)?
The beverage menu from a coffeehouse reads as follows:
Eight friends go out for drinks. Three order cappucino, two order espresso, one orders Americano, one orders Turkish coffee, and one orders cafe latte. One of the eight agrees to leave the entire amount of the tip, which is to be 20% of the check. How much will be the amount of the tip (round to the nearest dime)?
The costs of the beverages will be as follows:
Add these amounts:
20% of this is
, which rounds to $5.30.
The costs of the beverages will be as follows:
Add these amounts:
20% of this is
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A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the sum will be at least eight
(b) The probability that the sum will be at most six
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that the sum will be at least eight
(b) The probability that the sum will be at most six
The following table illustrates the ways that the dice can come up. The orange cells indicate a roll of 6 or less; the pink cells indicate a roll of eight or more.
Since each of these outcomes are equally likely, and there are fifteen outcomes that are favorable to each of the two events, the probabilities are the same.
The following table illustrates the ways that the dice can come up. The orange cells indicate a roll of 6 or less; the pink cells indicate a roll of eight or more.
Since each of these outcomes are equally likely, and there are fifteen outcomes that are favorable to each of the two events, the probabilities are the same.
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Refer to the above circle graph. Which of these quantities is greater?
(a) The number of votes won by Hawley
(b) The number of votes won by Wells
Refer to the above circle graph. Which of these quantities is greater?
(a) The number of votes won by Hawley
(b) The number of votes won by Wells
The gray portion of the circle graph represents Wells; the yellow portion represents Hawley. The gray portion is larger, so Wells won more votes, making (b) greater.
The gray portion of the circle graph represents Wells; the yellow portion represents Hawley. The gray portion is larger, so Wells won more votes, making (b) greater.
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Refer to the above circle graph. Which of these quantities is greater?
(a) The number of students who voted for Phelps
(b) The number of students who voted for candidates other than Phelps
Refer to the above circle graph. Which of these quantities is greater?
(a) The number of students who voted for Phelps
(b) The number of students who voted for candidates other than Phelps
The portion of the circle graph representing Phelps is light blue; it takes up less than half of the graph, so fewer than half of the votes were won by Phelps. (b) is correct.
The portion of the circle graph representing Phelps is light blue; it takes up less than half of the graph, so fewer than half of the votes were won by Phelps. (b) is correct.
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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 cappucino
(b) The price of two Americanos and an espresso
The following is a portion of the menu at Moonbucks Coffee:
Which is the greater quantity?
(a) The price of two lattes and a cappucino
(b) The price of two Americanos and an espresso
(a) Add: 
(b) Add: 
(a) is the greater quantity.
(a) Add:
(b) Add:
(a) is the greater quantity.
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A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that a 6, a 7, or an 8 will come up
(b) The probability that a number other than 6, 7, or 8 will come up
A pair of fair dice are tossed. Which is the greater quantity?
(a) The probability that a 6, a 7, or an 8 will come up
(b) The probability that a number other than 6, 7, or 8 will come up
Out of thirty-six possible rolls, there are five ways to roll a six:
Six ways to roll a seven:
Five ways to roll an eight:
This is sixteen rolls out of thirty-six. Therefore, there are twenty rolls that do not result in one of these three numbers. Since all rolls are equally likely, this makes (b) the greater probability.
Out of thirty-six possible rolls, there are five ways to roll a six:
Six ways to roll a seven:
Five ways to roll an eight:
This is sixteen rolls out of thirty-six. Therefore, there are twenty rolls that do not result in one of these three numbers. Since all rolls are equally likely, this makes (b) the greater probability.
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Refer to the above circle graph. Which of these quantities is greater?
(a) The number of votes won by Creighton
(b) The number of votes won by either Barnes or Yale
Refer to the above circle graph. Which of these quantities is greater?
(a) The number of votes won by Creighton
(b) The number of votes won by either Barnes or Yale
The size of the orange portion of the circle, which represents Creighton, is larger than the combined sizes of the dark blue and green portions, which represent Barnes and Yale, respectively. This makes (a) the greater quantity.
The size of the orange portion of the circle, which represents Creighton, is larger than the combined sizes of the dark blue and green portions, which represent Barnes and Yale, respectively. This makes (a) the greater quantity.
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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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