ISEE Upper Level Quantitative : How to find the solution to an equation

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

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Example Questions

Example Question #81 : Algebraic Concepts

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) and (B) are equal

(A) is greater

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

(B) is greater

Correct answer:

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

Explanation:

The two equations are actually equivalent, as is proved here:

Therefore, we need only test the first equation. However, it can be shown that it is possible for either of the two to be greater or both to be equal; as can be determined from that third equation  , any two values of  and  that add up to  will solve the system, such as , or .

 

Example Question #82 : Algebraic Concepts

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(B) is greater

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

(A) and (B) are equal

(A) is greater

Correct answer:

(A) is greater

Explanation:

 

 

, so , making (A) greater.

Example Question #83 : Equations

Give the -coordinate of the point on the graph of the equation  that has -coordinate .

Possible Answers:

No such point exists.

Correct answer:

Explanation:

The point  is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating  for . Substitute, and we get: 

The -coordinate is therefore .

Example Question #81 : How To Find The Solution To An Equation

Give the -coordinate of the point on the graph of the equation  that has -coordinate 64.

Possible Answers:

No such point exists.

Correct answer:

Explanation:

The point  is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating  for . Substitute, and we get: 

Example Question #85 : Equations

Give the -coordinate of the point on the graph of the equation  that has -coordinate 64.

Possible Answers:

No such point exists.

Correct answer:

No such point exists.

Explanation:

The point  is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating  for . Substitute, and we get: 

Since the square root of a number must be positive, there is no solution. Therefore, there is no point on this graph with -coordinate 64.

Example Question #761 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Give the -coordinate of the point on the graph of the equation  that has -coordinate .

Possible Answers:

No such point exists.

Correct answer:

No such point exists.

Explanation:

The point  is on the graph of the equation . Finding the -coordinate of this point is the same as evaluating  for . Substitute, and we get: 

However, there is no number that can be divided into 3 to yield a quotient of 0, so there is no solution. Therefore, there is no point on this graph with -coordinate .

Example Question #87 : Equations

What is ?

Possible Answers:

Correct answer:

Explanation:

Substitute  for  in the second equation:

Example Question #88 : Equations

What is  ?

Possible Answers:

Correct answer:

Explanation:

Solve for  in the top equation:

 

Substitute  for  in the second equation:

Example Question #89 : Equations

If , then what is an expression for x in terms of y?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, isolate for x. First, move the y term over to the left side. This gives you . Then, multiply both sides by 4. This gives you . Then, distribute the four to the terms inside the parantheses. This gives you a final answer of .

Example Question #762 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Evaluate .

Possible Answers:

The answer cannot be determined from the information given.

Correct answer:

Explanation:

Substitute  for  in the second equation as follows:

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