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ISEE Middle Level Quantitative : Algebraic Concepts

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

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Equations

Solve for x in the below equation:

5x+4-2x=25

Possible Answers:

x=21

x=7

x=3

x=29

Correct answer:

x=7

Explanation:

Solve for x in the below equation:

5x+4-2x=25

First we must add like terms on the left side. 5x-2x = 3x

3x+4=25

Next, we must subtract 4 from both sides.

3x=21

Lastly, we must divide both sides by 3.

x=7

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Example Question #172 : Algebraic Concepts

3x= 12

4y=16

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

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

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

3x= 12

$3x\div 3= 12 \div 3$

x= 4

4y=16

$4y \div 4 =16 \div 4$

y = 4

x= y

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Example Question #173 : Algebraic Concepts

$\frac{2}{9} x = \frac{4}{7}$

$\frac{7}{4}y = \frac{9}{2}$

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

(a) is the greater quantity

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

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

$\frac{2}{9} x = \frac{4}{7}$

$\frac{9} {2}\cdot \frac{2}{9} x = \frac{9} {2}\cdot \frac{4}{7}$

$x = \frac{9\cdot 4 } {2\cdot 7} = \frac{36}{14}$

$\frac{7}{4}y = \frac{9}{2}$

$\frac{4}{7} \cdot \frac{7}{4}y =\frac{4}{7} \cdot \frac{9}{2}$

$y =\frac{4 \cdot 9}{7 \cdot 2} = \frac{36}{14}$

x = y

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Example Question #172 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

The lines of the equations

x+y = 17

and

x- y = 13

intersect at a point (X, Y) .

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

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

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(a) is the greater quantity

Explanation:

Since the numbers and satisfy both equations, we need only look at the second one,

x- y = 13 .

It follows that

X- Y= 13

X- Y+Y= 13 +Y

X= Y + 13

and

X> Y .

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Example Question #174 : Algebraic Concepts

A + B = 16

Both and are prime.

Which is the greater quantity?

(a) $A \cdot B$

(b) 50

Possible Answers:

(a) and (b) are equal

(a) is the greater quantity

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

(b) is the greater quantity

Correct answer:

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

Explanation:

A + B = 16 , and both are positive integers, so both will be between 1 and 15 inclusive. Since both are prime numbers - numbers with exactly two factors, 1 and the number itself - both are elements of the set

$\left \{ 2, 3, 5, 7, 11, 13 \right \}$

There are two ways to select two of these numbers so that their sum is 16 - 3 and 13, and 5 and 11.

If we select A = 3 and B = 13 , or vice versa, then $AB = 3 \cdot 13 = 39 < 50$ .

If we select A = 5 and B = 11 , or vice versa, then $AB = 5 \cdot 11 = 55 > 50$ .

Therefore, it is unclear whether or 50 is greater.

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Example Question #42 : Equations

and are both positive integers. is a prime number and is a composite number.

x+ y= 14

Which is the greater quantity?

(a)

(b)

Possible Answers:

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

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

A prime number is a number with exactly two factors - 1 and itself.

If and are both positive integers whose sum is 14, then each is an integer from 1 to 13 inclusive. The prime numbers in this range are 2, 3, 5, 7, 11, and 13. x+y = 14 , so y = 14 - x , and this must be a composite number - one which has more than two factors.

Taking each case:

x= 2

y = 14-2 = 12

x= 3

y = 14-3 = 11

x= 5

y = 14-5 = 9

x= 7

y = 14-7 = 7

x= 11

y = 14-11 = 3

x= 13

y = 14-13= 1

The only two prime values of that yields a composite are x=2 and x = 5 . in both cases, y > x .

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Example Question #175 : Algebraic Concepts

$A ^{2} = 64$

|B| = 8

Which is the greater quantity?

(a)

(b)

Possible Answers:

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

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Correct answer:

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

Explanation:

$A ^{2} = 64$ , so is the positive or negative square root of 64; those are 8 and , respectively.

Two numbers - and 8 - have absolute value 8, so if |B| = 8 , either B = -8 or B = 8 .

$A \in \left \{ -8, 8\right \}$ and $B \in \left \{ -8, 8\right \}$ , but without further information, it cannot be determined which is the greater, if either.

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Example Question #51 : How To Find The Solution To An Equation

4t + 13 = 72

3u + 13 = 54

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is the greater quantity

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

(a) and (b) are equal

(a) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

Solving both equations:

4t + 13 = 72

4t + 13 - 13 = 72 - 13

4t = 59

$4t \div 4 = 59 \div 4$

$t = 14 \frac{3}{4}$

3u + 13 = 54

3u + 13- 13 = 54 - 13

3u = 41

$3u \div 3 = 41 \div 3$

$u = 13\frac{2}{3}$

t > u .

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Example Question #171 : Algebraic Concepts

B + (-40 ) = 100 - A

Which is the greater quantity?

(a) A + B

(b) 60

Possible Answers:

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

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

B + (-40 ) = 100 - A

B + (-40 ) + A + 40 = 100 - A + A + 40

A+ B + (-40 ) + 40 = 100 + 40- A + A

A + B = 140 , which is greater than 60.

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Example Question #53 : How To Find The Solution To An Equation

A + (-30) = B + 50

Evaluate B - A .

Possible Answers:

B - A = 80

B - A = -80

B - A = -20

B - A = 20

Correct answer:

B - A = -80

Explanation:

A + (-30) = B + 50

A + (-30) - A - 50 = B + 50 - A - 50

A - A + (-30) - 50 = B - A + 50 - 50

B - A = (-30) - 50 = - 30 + (-50) = -(30+50) = -80 .

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : Algebraic Concepts

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

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #41 : Equations

Example Question #172 : Algebraic Concepts

Example Question #173 : Algebraic Concepts

Example Question #172 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #174 : Algebraic Concepts

Example Question #42 : Equations

Example Question #175 : Algebraic Concepts

Example Question #51 : How To Find The Solution To An Equation

Example Question #171 : Algebraic Concepts

Example Question #53 : How To Find The Solution To An Equation

All ISEE Middle Level Quantitative Resources

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