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

Divide 200 by 17. The quotient is ; the remainder is . Which is the greater quantity?

(A) 

(B) 

Possible Answers:

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

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(B) is greater

Explanation:

 and .

 and (B) the greater quantity.

Example Question #161 : Algebraic Concepts

If , then how many integers can be substituted for  to make the equation  a true statement?

Possible Answers:

One 

Zero

It cannot be determined from the information given

Infinitely many

Two

Correct answer:

Zero

Explanation:

If , the equation can be restated and solved as follows:

However, no integer can be squared to yield a negative result; therefore, there is no solution, and the correct response is "zero."

Example Question #162 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

How many elements of the set  can be substituted for  to make the inequality  a true statement?

Possible Answers:

Three

Two

Four

None

One 

Correct answer:

Three

Explanation:

Three elements of the set—1, 2, and 3—fit this criterion.

Example Question #31 : Equations

Which is greater?

(A) 

(B) 

Possible Answers:

(A) and (B) are equal

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

(B) is greater

(A) is greater

Correct answer:

(B) is greater

Explanation:

 

, so .

Therefore , so (B) is greater.

Example Question #163 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

How many elements of the set  can be substituted for  to make the inequality  a true statement?

Possible Answers:

Five 

One

Four

None

Two

Correct answer:

None

Explanation:

 (Note that the inequality symbol switches here.)

 

None of the elements of  fit this criterion.

Example Question #31 : Equations

If , then how many integers can be substituted for  to make the equation  a true statement?

Possible Answers:

Infinitely many

Two

Three

One

Zero

Correct answer:

One

Explanation:

If , then the equation can be rewritten and solved as follows:

The only integer that can be substituted for  to make this true is , so the correct response is "one".

Example Question #164 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

If a and b are complementary angles, what is the value of a if b is equal to 33 degrees?

Possible Answers:

Correct answer:

Explanation:

Complementary angles add up to 90 degrees. Therefore, 

Given that b is equal to 33 degrees, the equation is:

Next, 33 should be subtracted from each side of the equation. 

Therefore, 57 is the correct answer. 

Example Question #41 : How To Find The Solution To An Equation

Angles g and h are supplementary. Angle g is 3 times as big as angle h. What is the value of angle h?

Possible Answers:

Correct answer:

Explanation:

If angles g and h are supplementary, then they will add up to 180 degrees.

Given that angle g is 3 times as big as angle h, then:

 

Therefore, 

Example Question #161 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve an equation, you first want to get like terms on the same sides: variables should be on one side and whole numbers on the other. To do this, you must add 6 to both sides of the equation.

             

The equation will then look like this:

In order to solve for , you must make it so that there is only one of the variable . Since the 3 is multiplied times the variable, you must divide by 3 on both sides of the equation to remove it.

The result you are left with is .

Example Question #162 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

If x and y are angles that are equal to each other and are also complementary, what is the value of x?

Possible Answers:

Correct answer:

Explanation:

If two angles are complementary, then they add up to 90 degrees. 

Therefore, .

Given that x and y are equal to each other, .

Thus, .

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