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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

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Example Questions

Example Question #11 : How To Find The Solution To An Equation

$\displaystyle y + 8 = 17$

$\displaystyle t - 10 = 1$

Which is greater?

(A) $\displaystyle y$

(B) $\displaystyle t$

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:

$\displaystyle y + 8 = 17$

$\displaystyle y + 8 - 8 = 17 - 8$

y = 9 $\displaystyle y = 9$

$\displaystyle t - 10 = 1$

$\displaystyle t - 10 + 10 = 1 + 10$

t = 11 $\displaystyle t = 11$

t > y $\displaystyle t > y$ , and (B) is greater.

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Example Question #13 : Equations

$\displaystyle s + t + 6 = 27$

What is 2s + 2t $\displaystyle 2s + 2t$ equal to?

Possible Answers:

$\displaystyle 40$

$\displaystyle 42$

$\displaystyle 44$

$\displaystyle 38$

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

Correct answer:

$\displaystyle 42$

Explanation:

$\displaystyle s + t + 6 = 27$

$\displaystyle s + t + 6 - 6 = 27- 6$

$\displaystyle s + t = 21$

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

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Example Question #141 : Algebraic Concepts

$\displaystyle K + 13 = M - 6$

Evaluate K - M $\displaystyle K - M$ .

Possible Answers:

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

$\displaystyle -7$

$\displaystyle -19$

$\displaystyle 19$

$\displaystyle 7$

Correct answer:

$\displaystyle -19$

Explanation:

$\displaystyle K + 13 = M - 6$

$\displaystyle K + 13 - M - 13 = M - 6 - M - 13$

$\displaystyle K - M = - 19$

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Example Question #141 : Algebraic Concepts

$\displaystyle x + 13 = 10 - y$

Evaluate x + y $\displaystyle x + y$ .

Possible Answers:

$\displaystyle -23$

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

$\displaystyle 3$

$\displaystyle 23$

$\displaystyle -3$

Correct answer:

$\displaystyle -3$

Explanation:

$\displaystyle x + 13 = 10 - y$

$\displaystyle x + 13 + y - 13 = 10 - y + y - 13$

$\displaystyle x + y = -3$

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Example Question #141 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

M > N $\displaystyle M > N$ . Which is the greater quantity?

(A) 10 - M $\displaystyle 10 - M$

(B) 10 - N $\displaystyle 10 - N$

Possible Answers:

(B) is greater

(A) and (B) are equal

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

(A) is greater

Correct answer:

(B) is greater

Explanation:

If M > N $\displaystyle M > N$ , then -M <-N $\displaystyle -M < -N$ . Subsequently,

-M+ 10 <-N + 10 $\displaystyle -M+ 10 < -N + 10$

$\displaystyle 10-M < 10 - N$

making (B) greater.

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Example Question #143 : Algebraic Concepts

$\displaystyle M$ and $\displaystyle N$ are integers. M < 16 $\displaystyle M < 16$ and N > 15 $\displaystyle N > 15$ .

Which is the greater quantity?

(A) $\displaystyle M$

(B) $\displaystyle N$

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

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Example Question #20 : Equations

M < 10 $\displaystyle M < 10$

N > 9 $\displaystyle N > 9$

Which is the greater quantity?

(A) $\displaystyle M$

(B) $\displaystyle N$

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 $\displaystyle M$ and $\displaystyle N$ are whole numbers.

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

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Example Question #142 : Algebraic Concepts

5x = 35 $\displaystyle 5x = 35$

3y = 24 $\displaystyle 3y = 24$

Which is the greater quantity?

(A) $\displaystyle x$

(B) $\displaystyle y$

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 $\displaystyle 5x = 35$

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

x=7 $\displaystyle x=7$

3y = 24 $\displaystyle 3y = 24$

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

y = 8 $\displaystyle y = 8$

y > x $\displaystyle y > x$ , so (B) is greater.

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Example Question #21 : Equations

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

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

Which is greater?

(A) $\displaystyle a$

(B) $\displaystyle b$

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:

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

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

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

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

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

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

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

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Example Question #142 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

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

Possible Answers:

Three

Two

None

Four

One

Correct answer:

None

Explanation:

$\displaystyle y +8.6 < 3.3$

$\displaystyle y +8.6 - 8.6 < 3.3 - 8.6$

$\displaystyle y < 3.3 - 8.6$

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

$\displaystyle y < -5.3$

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 #141 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Example Question #143 : Algebraic Concepts

Example Question #20 : Equations

Example Question #142 : Algebraic Concepts

Example Question #21 : Equations

Example Question #142 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

All ISEE Middle Level Quantitative Resources

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