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 #71 : Equations

Column A                                     Column B

The price of a                               $27

$30 jacket that's

on sale for

10% off.

Possible Answers:

The quantity in Column A is greater.

The quantities in both columns are equal.

The quantity in Column B is greater.

There can be no relationship determined.

Correct answer:

The quantities in both columns are equal.

Explanation:

First, calculate the price of the jacket in Column A. If the $30 jacket is on sale for 10% off, that means that it is $3 lower. (10% of $30 is $3). Therefore, the price of the jacket is $27. The quantities in both columns are equal.

Example Question #72 : Equations

Give the -coordinate of the point on the line of the equation  that has -coordinate 9.

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

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

Example Question #73 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

(A) and (B) are equal

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

(A) is greater

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

The -intercept of any line is the point at which the line intersects the -axis; therefore, its -coordinate is 0. Similarly, the -coordinate of the -intercept is 0. The quantities are equal.

Example Question #74 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

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

(A) and (B) are equal

(B) is greater

(A) is greater

Correct answer:

(A) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set  and solve for :

Similarly, to find the -coordinate of the -intercept, set  and solve for :

(A), the -coordinate of the -intercept of the line, is greater.

 

Example Question #75 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

(A) and (B) are equal

(B) is greater

(A) is greater

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

Correct answer:

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set  and solve for :

Similarly, to find the -coordinate of the -intercept, set  and solve for :

(B), the -coordinate of the -intercept of the line, is greater.

Example Question #76 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

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:

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, set  and solve for :

Similarly, to find the -coordinate of the -intercept, set  and solve for :

(B), the -coordinate of the -intercept of the line, is greater.

Example Question #77 : Equations

Given the line of the equation , which is the greater quantity?

(A) The -coordinate of the -intercept of the line

(B) The -coordinate of the -intercept of the line

Possible Answers:

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

(A) and (B) are equal

(B) is greater

(A) is greater

Correct answer:

(B) is greater

Explanation:

The -coordinate of the -intercept of the line is 0, so to find the -coordinate, we set  and solve for :

 

Similarly, to find the -coordinate of the -intercept, we set  and solve for :

(B), the -coordinate of the -intercept of the line, is greater.

Example Question #78 : Equations

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) is greater

(B) is greater

(A) and (B) are equal

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

Correct answer:

(A) is greater

Explanation:

 so 

Substitute for  in the other equation:

 so (A) is greater.

Example Question #79 : Equations

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) is greater

(B) is greater

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

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

The first equation actually provides all of the needed information. 

, so

making 

Example Question #80 : Equations

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) is greater

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

(A) and (B) are equal

(B) is greater

Correct answer:

(A) is greater

Explanation:

Add both sides of the equations as follows:

 

, so

 

, so (A) is greater.

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