How to find the answer from a table
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ISEE Upper Level Quantitative Reasoning › How to find the answer from a table
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) and (b) are equal
(a) is greater
(b) is greater
It is impossible to tell from the information given
Explanation
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.
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
It is impossible to tell from the information given
(a) and (b) are equal
(a) is greater
(b) is greater
Explanation
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.
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?
1:34 PM
12:34 PM
11:34 AM
10:34 AM
2:34 PM
Explanation
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.
The beverage menu from a coffeehouse reads as follows:
Eight friends go out for drinks. Three order cappuccino, 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)?
Explanation
The costs of the beverages will be as follows:
Add these amounts:
20% of this is
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
(b) is greater
(a) is greater
(a) and (b) are equal
It is impossible to tell from the information given
Explanation
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.
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
It is impossible to tell from the information given
(a) is greater
(b) is greater
(a) and (b) are equal
Explanation
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.
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
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
Explanation
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.
The table below gives the population of Buchanan City in each census year from 1930 to 1980.
It is known that the population increased from 1945 to 1950.
Which is the greater quantity?
(a) The population of Buchanan City in 1940
(a) The population of Buchanan City in 1945
(a) is greater.
(b) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
Explanation
Since the population increased from 1945 to 1950, then in 1945, the population must have been less than 3,049, and, subsequently, less than the 1940 population of 3,221.
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
(b) is greater.
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
Explanation
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.
The above figure shows a spinner used in a game. The upper semicircle has twice the radius of the lower semicircle.
Which of the following is the greater quantity?
(a) The probability that a random spin will cause the spinner to land in a green region.
(b) The probability that a random spin will cause the spinner to land in a red region.
(b) is the greater quantity
(a) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
Explanation
The size of the regions do not matter in this problem; it is the central angles of the sectors that are relevant. The best way to understand this is to look at the spinner again, but after cutting out the central circle:
If we rearrange the sectors, we see the following:
The probability of the spinner landing in red exceeds that of it landing in green.