ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning
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All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #67 : Percentage
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%.
Example Question #21 : How To Find Percentage
The Ace of Spades and the King of Spades are both removed from a standard deck of 52 playing cards. What percent of the remaining cards are spades?
13 of the 52 cards in a standard deck are spades. If two spades are removed, then there will remain 11 spades out of 50 cards, or
of the remaining cards.
Example Question #1 : How To Find The Distributive Property
Which is the greater quantity?
(a)
(b)
(b) is greater
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(a) and (b) are equal
Apply the distributive and commutative properties to the expression in (a):
The two expressions are equivalent.
Example Question #1 : Distributive Property
Which is the greater quantity?
(a)
(b)
(a) is greater
(b) is greater
(a) and (b) are equal
(b) is greater
Apply the distributive property to the expression in (a):
Therefore,
Example Question #2 : Distributive Property
Which is the greater quantity?
(a)
(b)
(b) is greater
It is impossible to tell from the information given
(a) is greater
(a) and (b) are equal
(b) is greater
Apply the distributive property to the expression in (a):
Since 
Example Question #1 : How To Find The Distributive Property
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
(a) is greater
It is impossible to tell from the information given
We show that there is at least one value of 
Case 1:
(a)
(b)
(b) is greater here
Case 2:
(a)
(b)
(a) is greater here
Example Question #4 : How To Find The Distributive Property
Which of the following is equivalent to 
We can best solve this by factoring 4 from both terms, and distributing it out:
Example Question #2 : How To Find The Distributive Property
Which of the following is greater?
(A)
(b)
It is impossible to determine which is greater from the information given
(B) is greater
(A) and (B) are equal
(A) is greater
(A) and (B) are equal
(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of 
Example Question #5 : How To Find The Distributive Property
Simplify the below:
In order to simiplify we must first distribute the -2 only to what is inside the ( ):
Now, we must combine like terms:
This gives us the final answer:
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