# SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

## Example Questions

### Example Question #7 : How To Interpret Venn Diagrams

In the above Venn diagram, the universal set  is the set of Presidents of the United States.

represents the set of Presidents who were born after 1850.

represents the set of Presidents who were born in a state completely west of the Mississippi River.

represents the set of Presidents who served eight years or more.

Which of the following Presidents would fall in the pink region?

Woodrow Wilson, who was born on December 28, 1856 in New Jersey and served eight years in office.

Abraham Lincoln, who was born on February 12, 1809 in Kentucky and was shot to death during his fifth year in office.

Richard M. Nixon, who was born on January 9, 1913 in California and resigned during his seventh year in office,

Ronald Reagan, who was born on February 6, 1911 in Illinois and served eight years in office.

Warren G. Harding, who was born on November 2, 1865 in Ohio and died during his third year in office.

Warren G. Harding, who was born on November 2, 1865 in Ohio and died during his third year in office.

Explanation:

The shaded region is inside set , so we are looking for a President who was born after 1850; this eliminates Lincoln.

The region is outside of , so we want a President who served fewer than eight years. This eliminates Wilson and Reagan.

The region is outside of , so we want the state of the President's birth to be fully or partly east of the Mississippi River. This eliminates Nixon.

The correct response is Harding.

### Example Question #8 : Venn Diagrams

Given the Venn diagram below, which of the following does not belong to ?

Explanation:

The symbol  stands for the union between two sets.  Therefore,  means the set of all numbers that are in either A or B.  Looking at our choices, the only number that isn't in either A, B, or both is 23.

### Example Question #10 : Venn Diagrams

A group of high school juniors are taking Biology, Calculus, and Spanish as shown above. Which student is not in the set ?

Andy

Bob

Patrick

Molly

Steph

Patrick

Explanation:

The notation  stands for "union," which refers to everything that is in either set.  refers to the group of students taking either Calculus or Spanish (everyone on this diagram except those taking only Biology). From the diagram, Patrick and Ashley are the only students taking neither Calculus nor Spanish, so Patrick is the correct answer.

### Example Question #2 : Venn Diagrams

Giving the Venn diagram above, what is the sum of the numbers in the set ?

Explanation:

The notation  stands for "A union C," which refers to everything that is in either set  or set .

When we add the numbers together, we get:

### Example Question #1631 : Ssat Upper Level Quantitative (Math)

Refer to the above graph. Which of the following comes closest to the percent of increase in population enjoyed by Jones City between 1900 and 1950?

80% increase

100% increase

20% increase

40% increase

60% increase

60% increase

Explanation:

In 1900, the population was about 3,500; in 1950, it was about 5,600. A reasonable estimate of the percent of increase would be

so 60% would be the most reasonable choice.

### Example Question #1632 : Ssat Upper Level Quantitative (Math)

The above figure shows two black quarter-circles inscribed inside a rectangle. If the black region has area 200, what is the area of the white region (nearest tenth)?

Explanation:

If the radius of each quarter-circle is  , the black region has area

Set   and solve for :

The area of the rectangle, which we will call  , is

The area of the white region is the difference of these two areas, or

### Example Question #1633 : Ssat Upper Level Quantitative (Math)

Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.

Tim wants to know the high temperature for the Sunday of the next week. He does not have access to that information, but he knows that it was higher than those of exactly four of the five previous days, and lower than that of one of them. Which of the following temperatures could have been the high temperature for that day?

Explanation:

Since we are dealing with the day after the last one shown, and we are comparing that day's high temperature to those of the previous five days, we only need to concern ourselves with the high temperatures for Tuesday through Saturday.

Examine the figure below, which shows the high temperature line for those five days.

For the high temperature for the next Sunday to be greater than exactly four of the five and less than the remaining one, the temperature must be strictly between the highest and second-highest high temperatures, which are seen to be 78 and 74 degrees, respectively. That is, if we let  be the temperature in degrees,

Of the four choices, only 75 falls in this range.

### Example Question #1634 : Ssat Upper Level Quantitative (Math)

Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period. The temperatures at left are given in degrees Fahrenheit.

Temperatures given in degrees Fahrenheit can be converted to the Celsius scale using the formula

What was the difference, in degrees Celsius, between the high temperature and the low temperature for the week (nearest whole degree)?

Explanation:

As can be seen below, the highest temperature for the week was , on Tuesday; the low temperature, , on Monday.

To convert the former to degrees Celsius, set  and substitute in the given formula:

.

To convert the latter, do the same, with .

.

The difference is

, which rounds to .

### Example Question #1635 : Ssat Upper Level Quantitative (Math)

Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.

Which of the following temperatures occurred at least once on each of the seven days?

Explanation:

The graph is recreated in the figure below, with horizontal lines at the 57, 62, 67, and 72 degree levels.

It can be seen that of the four lines, only the 62 degree line falls between the high temperature and low temperature for each of the seven days. This is the correct choice.

### Example Question #1636 : Ssat Upper Level Quantitative (Math)

Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period. The temperatures at left are given in degrees Fahrenheit.

Temperatures given in degrees Fahrenheit can be converted to the Celsius scale using the formula

.

Express the lowest temperature of the week in degrees Celsius (nearest whole degree).

Explanation:

As can be seen below, the lowest temperature for the week was , on Monday.

To convert this to degrees Celsius, set  and substitute in the given formula:

degrees Celsius. The closest choice is .