ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

Example Question #26 : How To Find Percentage

 is  of , which is 10,000 % of .

Which is a true statement?

Possible Answers:

Correct answer:

Explanation:

 is 10,000 % of , so .

 

 is , or , of , so .

Therefore, 

Example Question #291 : Numbers And Operations

Scrabble

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)

Possible Answers:

Correct answer:

Explanation:

There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of 

 vowel tiles.

12 of the tiles are "E's"; they therefore comprise

.

This rounds to 29%.

Example Question #951 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

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?

Possible Answers:

Correct answer:

Explanation:

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 #952 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

Correct answer:

(a) and (b) are equal

Explanation:

Apply the distributive and commutative properties to the expression in (a):

The two expressions are equivalent.

Example Question #953 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(a) and (b) are equal

(b) is greater

(a) is greater

Correct answer:

(b) is greater

Explanation:

Apply the distributive property to the expression in (a):

, so  regardless of .

Therefore, 

Example Question #954 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

Apply the distributive property to the expression in (a):

Since , and therefore, regardless of 

Example Question #3 : How To Find The Distributive Property

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is greater

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

It is impossible to tell from the information given

Explanation:

We show that there is at least one value of  that makes the (a) greater and at least one that makes (b) greater:

Case 1: 

(a) 

(b) 

(b) is greater here

Case 2: 

(a) 

(b) 

(a) is greater here

Example Question #3 : Distributive Property

Which of the following is equivalent to  ?

Possible Answers:

Correct answer:

Explanation:

We can best solve this by factoring 4 from both terms, and distributing it out:

Example Question #4 : How To Find The Distributive Property

 and  are positive integers.

Which of the following is greater?

(A) 

(b) 

Possible Answers:

It is impossible to determine which is greater from the information given

(A) is greater

(A) and (B) are equal

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of  and .

Example Question #955 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Simplify the below: 

Possible Answers:

Correct answer:

Explanation:

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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