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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 #11 : How To Find The Solution To An Equation

y + 8 = 17

t - 10 = 1

Which is greater?

(A)

(B)

Possible Answers:

(A) is greater

(A) and (B) are equal

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

(B) is greater

Correct answer:

(B) is greater

Explanation:

y + 8 = 17

y + 8 - 8 = 17 - 8

y = 9

t - 10 = 1

t - 10 + 10 = 1 + 10

t = 11

t > y , and (B) is greater.

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Example Question #13 : Equations

s + t + 6 = 27

What is 2s + 2t equal to?

Possible Answers:

It is impossible to answer the question from the information given.

Correct answer:

Explanation:

s + t + 6 = 27

s + t + 6 - 6 = 27- 6

s + t = 21

$2s +2 t = 2 (s+t) =2 \cdot 21 = 42$

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Example Question #141 : Algebraic Concepts

K + 13 = M - 6

Evaluate K - M .

Possible Answers:

It is impossible to determine the value of K - M from the equation.

Correct answer:

Explanation:

K + 13 = M - 6

K + 13 - M - 13 = M - 6 - M - 13

K - M = - 19

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Example Question #141 : Algebraic Concepts

x + 13 = 10 - y

Evaluate x + y .

Possible Answers:

It is impossible to determine the value of x + y from the equation.

Correct answer:

Explanation:

x + 13 = 10 - y

x + 13 + y - 13 = 10 - y + y - 13

x + y = -3

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Example Question #12 : How To Find The Solution To An Equation

M > N . Which is the greater quantity?

(A) 10 - M

(B) 10 - N

Possible Answers:

(A) and (B) are equal

(A) is greater

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

(B) is greater

Correct answer:

(B) is greater

Explanation:

If M > N , then -M <-N . Subsequently,

-M+ 10 <-N + 10

10-M < 10 - N

making (B) greater.

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Example Question #143 : Algebraic Concepts

and are integers. M < 16 and N > 15 .

Which is the greater quantity?

(A)

(B)

Possible Answers:

(B) is greater

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

(A) and (B) are equal

(A) is greater

Correct answer:

(B) is greater

Explanation:

M < 16 and is an integer, so $M \leq 15$ ; N > 15 and is an integer, so $N \geq 16$ . Therefore, N > M and (B) is the greater.

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Example Question #20 : Equations

M < 10

N > 9

Which is the greater quantity?

(A)

(B)

Possible Answers:

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

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

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

Explanation:

Note that we are not given that and are whole numbers.

Setting (M,N) to (9.1, 9.9) , (9.5,9.5) , or (9.9, 9.1) fulfills the condition that M < 10 and N > 9 , but in these cases, M < N , M = N , M > N , respectively. It cannot be determined which is greater.

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Example Question #142 : Algebraic Concepts

5x = 35

3y = 24

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) is greater

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

5x = 35

$5x \div 5 = 35 \div 5$

x=7

3y = 24

$3y \div 3 = 24 \div 3$

y = 8

y > x , so (B) is greater.

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Example Question #143 : Algebraic Concepts

$\frac{2}{3} a = 20$

$\frac{3}{5} b = 24$

Which is greater?

(A)

(B)

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:

$\frac{2}{3} a = 20$

$\frac{3}{2} \cdot \frac{2}{3} a =\frac{3}{2} \cdot 20$

$a = \frac{60}{2} = 30$

$\frac{3}{5} b = 24$

$\frac{5}{3}\cdot \frac{3}{5} b =\frac{5}{3}\cdot 24$

$b =\frac{120}{3} = 40$

b > a , so (B) is the greater quantity.

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Example Question #141 : Algebraic Concepts

How many elements of the set $\left \{ 1, 2, 3, 4, 5 \right \}$ can be substituted for to make the inequality y +8.6 < 3.3 a true statement?

Possible Answers:

Three

Two

None

One

Four

Correct answer:

None

Explanation:

y +8.6 < 3.3

y +8.6 - 8.6 < 3.3 - 8.6

y < 3.3 - 8.6

$y < -\left ( 8.6-3.3 \right )$

y < -5.3

None of choices fit this criterion, so the correct answer is none.

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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 #11 : How To Find The Solution To An Equation

Example Question #13 : Equations

Example Question #141 : Algebraic Concepts

Example Question #141 : Algebraic Concepts

Example Question #12 : How To Find The Solution To An Equation

Example Question #143 : Algebraic Concepts

Example Question #20 : Equations

Example Question #142 : Algebraic Concepts

Example Question #143 : Algebraic Concepts

Example Question #141 : Algebraic Concepts

All ISEE Middle Level Quantitative Resources

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