ISEE Middle Level Quantitative : Percentage
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #61 : Percentage
What percentage of 12 is 3?
We can start to solve by setting up a proportion:
In order to figure out what percentage a smaller makes up of a larger value, divide the smaller number by the larger one. So, divide 3 by 12.
Multiply the result of this operation by 100. The new result will be your percentage.
Example Question #281 : Numbers And Operations
On a farm, there are 12 pigs, 10 cows, and 8 horses. What percent of the animals are pigs?
In order to figure out what percentage a number is of a larger amount, divide the smaller number by the larger one.
Since there are 12 pigs, divide 12 by 30, the total.
When you multiply the decimal by 100, you are left with your percent.
Example Question #282 : Numbers And Operations
Refer to the above figure. The star is divided into triangles of equal area. Which is the greater quantity?
(a) The percent of the figure that is shaded.
(b) 67%
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
It is impossible to determine which quantity is the greater from the information given
(b) is the greater quantity
The star is divided into twelve triangles of equal measure, eight of which are shaded. This is
This is less than 67%, so (b) is the greater,
Example Question #283 : Numbers And Operations
(a) 25% of one third of
(b) 33% of one fourth of
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(a) is the greater quantity
25% of a number is the same as that number multiplied by 
Similarly, 33% of a number is the same as that number multiplied by 
We can compare these quantities by finding a common denominator. 
and
25% of one third of 
Example Question #284 : Numbers And Operations
Examine the above shapes. Which is the greater quantity?
(a) The percent of the shapes that are squares
(b) 50%
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(a) is the greater quantity
(a) and (b) are equal
There are twelve shapes; 50% of them is 
Of the twelve shapes, six are squares - therefore, the percent of the figures that are squares is 50%, and the quantities are equal.
Example Question #285 : Numbers And Operations
(a)
(b)
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
Example Question #285 : Numbers And Operations
(a) 33% of
(b) 17% of
(b) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(b) is the greater quantity
33% of a number is the same as multiplying it by its fractional equivalent, 
Similarly, 17% of 
Since 
and
17% of 
Example Question #286 : Numbers And Operations
(a) 10% of
(b) 8% of
(a) is the greater quantity
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(a) and (b) are equal
10% of a number is equivalent to that number multiplied by 0.10, so
10% of 
8% of a number is equivalent to that number multiplied by 0.08, so
8% of 
The quantities are equal.
Example Question #287 : Numbers And Operations
Which is a true statement?
Therefore,
Example Question #291 : Numbers And Operations
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.
To the nearest whole percent, what percent of the vowel tiles are "E's"?
(Note: for this problem, "Y" is considered a consonant)
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
12 of the tiles are "E's"; they therefore comprise
This rounds to 29%.
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