Interpretation of Tables and Graphs - SSAT Upper Level Quantitative
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The menu of a local coffeehouse reads as follows:
A boss is treating his employees to drinks. Seven of them want iced tea, five want cafe latte, four want espresso, three want cappucino, one wants Americano, and one wants Turkish coffee. How much will the boss spend, disregarding tax?
The menu of a local coffeehouse reads as follows:
A boss is treating his employees to drinks. Seven of them want iced tea, five want cafe latte, four want espresso, three want cappucino, one wants Americano, and one wants Turkish coffee. How much will the boss spend, disregarding tax?
Multiply each price by the quantity ordered:
Seven iced teas:
Five cafe lattes:
Four espressos:
Three cappucinos:
Add the \$2.39 for the Americano and the \$2.09 for the Turkish coffee. The sum:
Multiply each price by the quantity ordered:
Seven iced teas:
Five cafe lattes:
Four espressos:
Three cappucinos:
Add the \$2.39 for the Americano and the \$2.09 for the Turkish coffee. The sum:
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The above is an annual income tax table for married couples for a given state.
Mr. Phillips earned \$27,287 last year; Mrs. Phillips earned \$25,879. How much will the couple pay in income tax for that year (nearest hundred dollars)?
The above is an annual income tax table for married couples for a given state.
Mr. Phillips earned \$27,287 last year; Mrs. Phillips earned \$25,879. How much will the couple pay in income tax for that year (nearest hundred dollars)?
The Phillips's income totaled
.
This puts them in the 1.3% tax bracket, so they will pay
in taxes.
The correct response is \$700.
The Phillips's income totaled
This puts them in the 1.3% tax bracket, so they will pay
The correct response is \$700.
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The above is an annual income tax table for single persons in a given state.
Michael earned 
per month over a one-year period in his regular job. He also claimed 
in interest income and 
in stock dividends. Based on the above table, which of the following comes closest to the amount of income tax he will pay?
The above is an annual income tax table for single persons in a given state.
Michael earned
From salary, interest, and dividends, Michael earned
,
putting him in the 1.3% tax bracket.
His income tax will be
making \$500 the correct response.
From salary, interest, and dividends, Michael earned
putting him in the 1.3% tax bracket.
His income tax will be
making \$500 the correct response.
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The above is an annual income tax table for single persons in a given state.
Grant earned \$4,389 per month over a one-year period in his regular job. He also claimed \$1,736 in interest income and \$3,781 in stock dividends. Based on the above table, how much income tax will he pay (nearest dollar)?
The above is an annual income tax table for single persons in a given state.
Grant earned \$4,389 per month over a one-year period in his regular job. He also claimed \$1,736 in interest income and \$3,781 in stock dividends. Based on the above table, how much income tax will he pay (nearest dollar)?
Grant earned, in salary, interest, and dividends:
This puts him in the \$40-60,000 range, so he will pay \$210 plus 1.3% of his income above \$40,000. This will be
Grant earned, in salary, interest, and dividends:
This puts him in the \$40-60,000 range, so he will pay \$210 plus 1.3% of his income above \$40,000. This will be
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The above is an annual income tax table for married couples for a given state.
Mr. Clarke earned a monthly salary of 
throughout last year; Mrs. Clarke earned a monthly salary of 
, although she started on April 1. Also the couple claimed interest earnings of 
and 
in stock dividends. How much will the couple pay in income tax for that year (nearest dollar)?
The above is an annual income tax table for married couples for a given state.
Mr. Clarke earned a monthly salary of
Mr. and Mrs. Clarke earned a total of
(noting that Mrs. Clarke worked for nine months)
This places them in the highest tax bracket, so they will pay \$810 plus 2.3% of their income over \$80,000:
Round this to \$2,756.
Mr. and Mrs. Clarke earned a total of
(noting that Mrs. Clarke worked for nine months)
This places them in the highest tax bracket, so they will pay \$810 plus 2.3% of their income over \$80,000:
Round this to \$2,756.
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The above is an annual income tax table for single persons in a given state.
Mr. Wells, a single man, paid \$690 in taxes last year. Which of the following amounts comes closest to his income for the year?
The above is an annual income tax table for single persons in a given state.
Mr. Wells, a single man, paid \$690 in taxes last year. Which of the following amounts comes closest to his income for the year?
Since he paid between \$470 and \$810, his earnings had to have been in the \$60,000 to \$80,000 range.
Let 
be his earnings; then, since he paid \$470 plus 1.7% of his income in excess of \$60,000, which is equal to \$690, we can set up and solve the equation:
The correct choice is \$75,000.
Since he paid between \$470 and \$810, his earnings had to have been in the \$60,000 to \$80,000 range.
Let
The correct choice is \$75,000.
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Column1 Column2 1 0 2 0 3 2 4 3 5 4 6 5 7 8 8 8 9 8 10 8 11 5 12 0
Looking the the table given above, what is the range of the data set?
| Column1 | Column2 |
|---|---|
| 1 | 0 |
| 2 | 0 |
| 3 | 2 |
| 4 | 3 |
| 5 | 4 |
| 6 | 5 |
| 7 | 8 |
| 8 | 8 |
| 9 | 8 |
| 10 | 8 |
| 11 | 5 |
| 12 | 0 |
Looking the the table given above, what is the range of the data set?
The range of the data is the difference between the highest and lowest independent variable values.
In this set, the lowest is 
and the highest is 
.
The difference between these two is 
.
The range of the data is the difference between the highest and lowest independent variable values.
In this set, the lowest is
The difference between these two is
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What is the probability of rolling a single die and it landing on 2 and 4?
What is the probability of rolling a single die and it landing on 2 and 4?
When you roll on die you can only get one possible value facing up. The expression "the probability of getting a 2 and 4" means that they both occur at the same time. Since you can not get two results with one die, the probability must be 
.
When you roll on die you can only get one possible value facing up. The expression "the probability of getting a 2 and 4" means that they both occur at the same time. Since you can not get two results with one die, the probability must be
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A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
In the game, the four letters that are the most difficult to play are the "J", the "Q", the "X", and the "Z". John and Jane, who are in third grade, agree to remove these letters. After this is done, what percent of the letter tiles are marked with consonants (Note: "Y" counts as a consonant)?
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
In the game, the four letters that are the most difficult to play are the "J", the "Q", the "X", and the "Z". John and Jane, who are in third grade, agree to remove these letters. After this is done, what percent of the letter tiles are marked with consonants (Note: "Y" counts as a consonant)?
The easiest way to count the consonants is to count the vowels and blanks first.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, four "U" tiles, and two "blanks". This is a total of
tiles that are not consonants.
There are 96 tiles left after the removal of the "J", the "Q", the "X", and the "Z". Therefore, the number of consonants remaining is
, which is
This rounds to 54%.
The easiest way to count the consonants is to count the vowels and blanks first.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, four "U" tiles, and two "blanks". This is a total of
There are 96 tiles left after the removal of the "J", the "Q", the "X", and the "Z". Therefore, the number of consonants remaining is
This rounds to 54%.
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Examine the above Venn diagram. The universal set 
is defined to be 
, with each element placed in its correct region in the diagram. What is 
?
Examine the above Venn diagram. The universal set
is the complement of 
, the set of all elements in the universal set not in 
. In the diagram, it is represented by all elements not inside the circle that represents 
. This is the set:
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Examine the above Venn diagram. The universal set 
is defined to be 
, with each element placed in its correct region in the diagram. What is 
?
Examine the above Venn diagram. The universal set
is the union of the sets 
and 
- that is, the set of all elements in either 
or 
. 
is the complement of set 
- that is, the set of elements in 
not in 
; 
is defined similarly. Therefore, we need all of the elements either outside of 
or outside of 
. The excluded elements will be those inside both sets, which, by the diagram, can be seen to be 3, 5, 13, and 14. Therefore,
.
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The above represents a Venn diagram. The universal set 
is the set of all positive integers.
Let 
represent the set of multiples of 7; let 
represent all of the multiples of 11; let 
represent all of the multiples of 13. As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 2,431?
The above represents a Venn diagram. The universal set
Let
The region in which 2,431 appears depends on the sets of which 2,431 is an element, which in turn depends on which of 7, 11, and 13 divides it evenly:
2,431 is a multiple of 11 and 13, but not 7, so 2,431 is in 
and 
, but not 
. We look for a number among the choices that is in 
and 
, but not 
- that is, a number divisible by 11 and 13 but not 7.
, so 2,772 is divisible by 7. We can eliminate it.
, so 2,184 is divisible by 7. We can eliminate it.
, so 3,081 is not divisible by 11, and we can eliminate it.
, so 2,409 is not divisible by 13, and we can eliminate it.
However:
2,145 is divisible by 11 and 13 but not 7, so this is the correct choice.
The region in which 2,431 appears depends on the sets of which 2,431 is an element, which in turn depends on which of 7, 11, and 13 divides it evenly:
2,431 is a multiple of 11 and 13, but not 7, so 2,431 is in
However:
2,145 is divisible by 11 and 13 but not 7, so this is the correct choice.
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Given the Venn diagram below, which of the following does not belong to 
?
Given the Venn diagram below, which of the following does not belong to
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.
The symbol
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The universal set 
represented by the above Venn diagram is the set of all natural numbers from 
to 
inclusive.
The subsets are:
: The set of all multiples of 
: The set of all multiples of 
: The set of all multiples of 
How many elements are in the set represented by the shaded region?
The universal set
The subsets are:
How many elements are in the set represented by the shaded region?
The shaded region is 
, which will comprise all of the numbers that are multiples of 10 and of either or both 8 or 9.
will comprise multiples of 10 and 8 - that is, multiples of 
. Since 
,
will comprise multiples of 10 and 9 - that is, multiples of 
. Since 
,
To find 
, we first find 
.
, the set of numbers that are multiples of 8, 9, and 10. 
, so we look for multiples of 360, of which there are two under 1,000 (360 and 720).
The shaded region is
To find
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The universal set 
represented by the above Venn diagram is the set of all natural numbers from 1 to 1,000 inclusive.
The subsets are:
: The set of all multiples of 
: The set of all multiples of 
: The set of all multiples of 
How many elements are in the set represented by the shaded region?
The universal set
The subsets are:
How many elements are in the set represented by the shaded region?
The shaded region is inside 
and 
, and outside of 
, meaning that the shaded set represents
Examine 
first. Each number in 
must be a multiple of 7 and 8; since the two are relatively prime, each number is a multiple of 56.
so seventeen elements are in 
.
We eliminate all elements in 
- that is, all elements that also multiples of 6. These elements are 168, 336, 504, 672, 840 - a total of five.
This leaves twelve elements in 
.
The shaded region is inside
Examine
so seventeen elements are in
We eliminate all elements in
This leaves twelve elements in
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The above Venn diagram represents all of this year's graduating seniors at Rockwell High School, the universal set 
.
represents all of the students who are in the National Honor Society.
represents all of the students who became old enough to vote in the November 5 election during their senior year.
represents all of the students who enrolled in a French course during senior year.
Cathy was inducted into the National Honor Society in her junior year, and is still a member. She turned 18 on January 4 during her senior year, and she is carrying a respectable B average in her school's third-year French course. If her name were to be written in the above diagram in the correct place, in which of the five numbered regions would her name fall?
The above Venn diagram represents all of this year's graduating seniors at Rockwell High School, the universal set
Cathy was inducted into the National Honor Society in her junior year, and is still a member. She turned 18 on January 4 during her senior year, and she is carrying a respectable B average in her school's third-year French course. If her name were to be written in the above diagram in the correct place, in which of the five numbered regions would her name fall?
Cathy is in the Honor Society, meaning that she is in set 
; she turned 18 after election day, so she is not in set 
; she is taking a French course, so she is in set 
. She is in set 
, represented by region 2.
Cathy is in the Honor Society, meaning that she is in set
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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?
In the above Venn diagram, the universal set
Which of the following Presidents would fall in the pink region?
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.
The shaded region is inside set
The region is outside of
The region is outside of
The correct response is Harding.
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Giving the Venn diagram above, what is the sum of the numbers in the set 
?
Giving the Venn diagram above, what is the sum of the numbers in the set
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:
The notation
When we add the numbers together, we get:
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A group of high school juniors are taking Biology, Calculus, and Spanish as shown above. Which student is not in the set 
?
A group of high school juniors are taking Biology, Calculus, and Spanish as shown above. Which student is not in the set
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.
The notation
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The menu of a local coffeehouse reads as follows:
A boss is treating his employees to drinks. Seven of them want iced tea, five want cafe latte, four want espresso, three want cappucino, one wants Americano, and one wants Turkish coffee. How much will the boss spend, disregarding tax?
The menu of a local coffeehouse reads as follows:
A boss is treating his employees to drinks. Seven of them want iced tea, five want cafe latte, four want espresso, three want cappucino, one wants Americano, and one wants Turkish coffee. How much will the boss spend, disregarding tax?
Multiply each price by the quantity ordered:
Seven iced teas:
Five cafe lattes:
Four espressos:
Three cappucinos:
Add the \$2.39 for the Americano and the \$2.09 for the Turkish coffee. The sum:
Multiply each price by the quantity ordered:
Seven iced teas:
Five cafe lattes:
Four espressos:
Three cappucinos:
Add the \$2.39 for the Americano and the \$2.09 for the Turkish coffee. The sum:
Compare your answer with the correct one above