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 #61 : Equations

In an aquarium, the ratio of sharks to clown fish is . If there are  more clown fish than sharks, how many sharks are there?

Possible Answers:

Correct answer:

Explanation:

Set up a proportion, where .

Cross multiply:

Distribute:

Combine like terms:

Divide both sides of the equation by 5:

There are 64 sharks.

Example Question #61 : How To Find The Solution To An Equation

In June, a company had a profit of  million. In July, the company doubled that profit. In August, the company's profits rose by  percent. If profits rise by another  percent in September, what is the September profit?

Possible Answers:

 million

 million

 million

 million

 million

Correct answer:

 million

Explanation:

The profit in July is twice the profit in June, or $6 million. 

Because profits rise by 15% in August, August's profit is really 115% of July's profit:

Similarly, September's profit is 115% of August's profit:

Example Question #63 : Equations

Evaluate .

Possible Answers:

Correct answer:

Explanation:

 

Subtract expressions:

 

or 

Example Question #64 : Equations

If  and , evaluate 

Possible Answers:

It is impossible to tell from the information given.

Correct answer:

Explanation:

 

 

Example Question #65 : Equations

Solve for 

Possible Answers:

Correct answer:

Explanation:

 

Example Question #66 : 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:

This makes (A) greater.

Example Question #67 : Equations

Which of the following 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) and (B) are equal

Explanation:

 

 

The quantities are equal.

Example Question #68 : Equations

If , then what is ?

Possible Answers:

Correct answer:

Explanation:

To solve this problem, simply plug the numbers into the equation: . Then, just simplify. This gives you , which is

Example Question #69 : Equations

Column A                 Column B

                     

Possible Answers:

The quantity in Column B is greater.

The realtionship between the columns cannnot be determined.

The quantities in both columns are equal.

The quantity in Column A is greater.

Correct answer:

The quantities in both columns are equal.

Explanation:

and mean that you must plug in what it's inside the parantheses to x in the function. Therefore, when you plug in -2 to the function, you get , which is 11. Then, plug in 2 to the function, which gives you , which is also 11. Therefore, the columns are equal.

Example Question #70 : Equations

Column A                              Column B

The slope of                           The slope of

the line                                  the line perpendicular

.                      to the line in Column A.

Possible Answers:

There can be do relationship determined.

The quantity in Column B is greater.

The quantities are equal.

The quantity in Column A is greater.

Correct answer:

The quantity in Column A is greater.

Explanation:

The slope of the line is 4. You can determine this by remembering the y=mx+b slope-intercept form. "M" is slope, so the number in front of x is the slope. Therefore, it's 4. The slope of a line perpendicular to the line is the negative reciprocal of the first slope. Therefore, if the slope of the first line is 4, then the slope of the perpendicular line is . Therefore, Column A is greater.

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