SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)
Study concepts, example questions & explanations for SSAT Middle Level Math
All SSAT Middle Level Math Resources
Example Questions
Example Question #23 : Venn Diagrams
Kayla used a popular social media website to survey her friends' hobbies. All of her friends either play sports or enjoy playing video games, and some of her friends do both.
What percentage of Kayla's friends play sports and video games?
In order to solve this problem, identify that the common portion of this Venn diagram represents Kayla's friends who play sports and video games. Since 
The solution is:
Note: the most efficient way to convert this fraction to a percent is to find an equivalent fraction to 
Example Question #661 : Ssat Middle Level Quantitative (Math)
The above Venn diagram represents the total number of respondents from a survey administered in 
What percentage of respondents were categorized into only group
To find the missing quantity for category 
The algebraic solution is:
Example Question #1 : Numbers And Operations
Which ratio is equivalent to 
A ratio can be rewritten as a quotient; do this, and simplify it.
Rewrite as
or
Example Question #1 : Ratio And Proportion
A soccer team played 20 games, winning 5 of them. The ratio of wins to losses is
The ratio of wins to losses requires knowing the number of wins and losses. The question says that there are 5 wins. That means there must have been
The ratio of wins to losses is thus 5 to 15 or 1 to 3.
Example Question #2 : Numbers And Operations
Rewrite this ratio in the simplest form:
Rewrite in fraction form for the sake of simplicity, then divide each number by 
The ratio, in simplest form, is
Example Question #3 : How To Find A Ratio
Rewrite this ratio in the simplest form:
A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:
Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:
The ratio simplifies to
Example Question #4 : How To Find A Ratio
Rewrite this ratio in the simplest form:
A ratio involving fractions can be simplified by rewriting it as a complex fraction, and simplifying it by division:
Write as a product by taking the reciprocal of the divisor, cross-cancel, then multiply it out:
The ratio simplifies to
Example Question #1 : Numbers And Operations
Rewrite this ratio in the simplest form:
Rewrite in fraction form for the sake of simplicity, then divide each number by 
In simplest form, the ratio is
Example Question #2 : Numbers And Operations
Note: Figure NOT drawn to scale.
Refer to the above diagram. If one side of the smaller square is three-fifths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?
Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength 5; if this is the case, the smaller square has sidelength 3. The areas of the large and small squares are, respectively, 
The white region is the small square and has area 9. The grey region is the small square cut out of the large square and has area 
Example Question #3 : Numbers And Operations
Note: Figure NOT drawn to scale.
Refer to the above diagram. If one side of the smaller square is three-fourths the length of one side of the larger square, what is the ratio of the area of the gray region to that of the white region?
Since the answer to this question does not depend on the actual lengths of the sides, we will assume for simplicity that the larger square has sidelength 
The white region is the small square and has area 
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All SSAT Middle Level Math Resources
