How to find the answer from a table - ISEE Upper Level: Quantitative Reasoning

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 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 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.

(a) Add:

(b) Add:

(a) is the greater quantity.

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.

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.

(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.

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.

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 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.

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.

(a) The three Turkish coffees cost .

(b) The three Americanos cost .

(a) is the greater quantity.

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 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.

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.

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.

(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.

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 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.