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

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

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Example Questions

Example Question #31 : How To Find The Solution To An Equation

4A + 30 = 76 - 4B

Evaluate A + B .

Possible Answers:

$26 \frac{1}{2}$

It is impossible to evaluate A + B from the information given

$-11 \frac{1}{2}$

$11 \frac{1}{2}$

$-26 \frac{1}{2}$

Correct answer:

$11 \frac{1}{2}$

Explanation:

We will not be able to solve for the values of and ; instead, we need to group them together by reorganizing the equation.

4A + 30 = 76 - 4B

Start by adding and subtracting on each side. This will allow both variables to be on the left and both whole numbers to be on the right.

4A + 30 + 4B - 30 = 76 - 4B + 4B - 30

4A + 4B = 76 - 30

4A + 4B = 46

can be factored out of the left side.

$4\left ( A + B \right )= 46$

Divide both sides by .

$4\left ( A + B \right ) \div 4 = 46\div 4$

$A + B = 11 \frac{1}{2}$

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Example Question #32 : How To Find The Solution To An Equation

Divide 1,000 by 30. The quotient is ; the remainder is . Which is the greater quantity?

(A)

(B)

Possible Answers:

(B) is greater

(A) and (B) are equal

(A) is greater

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

Correct answer:

(A) is greater

Explanation:

First, divide:

$1,000 \div 30 = 33 \textrm{ R } 10$

Q = 33 and R = 10 , so Q > R .

(A) is greater.

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Example Question #32 : Equations

A + 9 = B - 7

Evaluate A + B .

Possible Answers:

It is impossible to evaluate A + B from the information given

{2}

Correct answer:

It is impossible to evaluate A + B from the information given

Explanation:

We cannot solve for and on their own. Instead, we need to reorganize the equation to find A + B .

A + 9 = B - 7

A+9-B-9=B-7-B-9

A-B=-7-9

It quickly becomes clear that we cannot solve for A + B with certainty.

If A = 2 and B = 18 , then

A + 9 = B - 7 , since

2 + 9 = 18 - 7 = 11

This makes A + B = 2 + 18= 20

If A = 3 and B = 19 , then

A + 9 = B - 7 , since

3 + 9 = 19 - 7 = 12

This makes A + B = 3+ 19 = 22

Therefore, A + B cannot be evaluated with certainty.

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Example Question #33 : How To Find The Solution To An Equation

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

(A)

(B)

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

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

Correct answer:

(B) is greater

Explanation:

$200 \div 17 = 11 \textrm{ R }13$

A = 11 and B = 13 .

B > A and (B) the greater quantity.

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Example Question #34 : How To Find The Solution To An Equation

If y = -7 , then how many integers can be substituted for to make the equation $x^{2} + y^{2} = 0$ a true statement?

Possible Answers:

It cannot be determined from the information given

Infinitely many

Zero

Two

One

Correct answer:

Zero

Explanation:

If y = -7 , the equation can be restated and solved as follows:

$x^{2} + y^{2} = 0$

$x^{2} + (-7)^{2} = 0$

$x^{2} + 49 = 0$

$x^{2} + 49 - 49 = 0 - 49$

$x^{2} = - 49$

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

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Example Question #35 : How To Find The Solution To An Equation

How many elements of the set $\left \{ 1, 2, 3, 4, 5 \right \}$ can be substituted for to make the inequality 4y < 15 a true statement?

Possible Answers:

Two

One

Three

None

Four

Correct answer:

Three

Explanation:

4y < 15

$4y \div 4 < 15 \div 4$

$y < 3 \frac{3}{4}$

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

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Example Question #36 : Equations

-7K = 91

-6M = 72

Which is greater?

(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:

(B) is greater

Explanation:

-7K = 91

$-7K\div (-7) = 91 \div (-7)$

K= -13

-6M = 72

$-6M \div (-6) = 72 \div (-6)$

M = -12

13 > 12 , so -12 > -13 .

Therefore M > K , so (B) is greater.

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Example Question #36 : How To Find The Solution To An Equation

How many elements of the set $\left \{ -2, -1, 0, 1, 2 \right \}$ can be substituted for to make the inequality -6y > 12 a true statement?

Possible Answers:

Two

Five

None

Four

One

Correct answer:

None

Explanation:

-6y > 12

$-6y \div (-6) < 12 \div (-6)$ (Note that the inequality symbol switches here.)

y < -2

None of the elements of $\left \{ -2, -1, 0, 1, 2 \right \}$ fit this criterion.

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Example Question #38 : Equations

If y = 3 , then how many integers can be substituted for to make the equation $x^{3} + y^{3} = 0$ a true statement?

Possible Answers:

Two

One

Infinitely many

Zero

Three

Correct answer:

One

Explanation:

If y = 3 , then the equation can be rewritten and solved as follows:

$x^{3} + y^{3} = 0$

$x^{3} + 3^{3} = 0$

$x^{3} + 27= 0$

$x^{3} + 27- 27 = 0 - 27$

$x^{3} = - 27$

The only integer that can be substituted for to make this true is x = -3 , so the correct response is "one".

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Example Question #37 : How To Find The Solution To An Equation

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, a+b=90 .

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

a+33=90

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

a=57

Therefore, 57 is the correct answer.

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

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #31 : How To Find The Solution To An Equation

Example Question #32 : How To Find The Solution To An Equation

Example Question #32 : Equations

Example Question #33 : How To Find The Solution To An Equation

Example Question #34 : How To Find The Solution To An Equation

Example Question #35 : How To Find The Solution To An Equation

Example Question #36 : Equations

Example Question #36 : How To Find The Solution To An Equation

Example Question #38 : Equations

Example Question #37 : How To Find The Solution To An Equation

All ISEE Middle Level Quantitative Resources

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