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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

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Example Question #11 :Equations

$\left (x-5 \right )^{2} = 36$

Which is the greater quantity?

(a)

(b)

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

Correct answer:

(a) is greater

Explanation:

Use the square root method to solve this equation:

$\left (x-5 \right )^{2} = 36$

$x-5 =- 6 \textrm{ or }x-5 = 6$

Solve each equation separately:

x-5 =- 6

x-5 +5=- 6 + 5

x = -1

x-5 = 6

x-5 +5= 6+5

x = 11

In either case, x > - 6

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Example Question #12 :Equations

$\frac{x}{3}-9=11$

5y+5=100

Column AColumn B
x y

Possible Answers:

The quantity in Column A is greater.

The quantity in Column B is greater.

The quantities are equal.

There can be no relationship determined from the two quantities.

Correct answer:

The quantity in Column A is greater.

Explanation:

First, off you need to find the quantities of x and y. For the first equation, add 9 to both sides so that $\frac{x}{3}=20.$ Multiply both sides by 3 so that x=60. Then, solve the second equation. First, subtract 5 from both sides so that 5y=95 . Divide both sides by 5 so that y=19. Therefore, the quantity in Column A is greater.

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Example Question #13 :Equations

$\frac{x}{2}+7=19$

3y-14=7

Column AColumn B

x y

Possible Answers:

The quantities in each column are equal.

The quantity in Column A is greater.

There is no way to determine the relationship between the columns.

The quantity in Column B is greater.

Correct answer:

The quantity in Column A is greater.

Explanation:

First, you must solve for x and y. To solve for x, first subtract 7 from both sides, so that you get $\frac{x}{2}=12$ . Multiply both sides by 2, giving you 24 for x. To solve for y, first add 14 to both sides, which gives you 3y=21. Divide both sides by 3 to give you 7. Therefore, Column A is greater.

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Example Question #14 :Equations

y + 8 = 17

t - 10 = 1

Which is greater?

(A)

(B)

Possible Answers:

(A) and (B) are equal

(A) is greater

(B) is greater

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

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 #15 :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 #16 :Equations

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 #17 :Equations

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 #18 :Equations

M > N . Which is the greater quantity?

(A) 10 - M

(B) 10 - N

Possible Answers:

(B) is greater

(A) is greater

(A) and (B) are equal

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

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 #19 :Equations

andare integers. M < 16 and N > 15 .

Which is the greater quantity?

(A)

(B)

Possible Answers:

(B) is greater

(A) is greater

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

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

M < 16 andis an integer, so $M \leq 15$ ; N > 15 andis 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:

(A) and (B) are equal

(B) is greater

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

(A) is greater

Correct answer:

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

Explanation:

Note that we are not given thatandarewhole 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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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 #11 :Equations

Example Question #12 :Equations

Example Question #13 :Equations

Example Question #14 :Equations

Example Question #15 :Equations

Example Question #16 :Equations

Example Question #17 :Equations

Example Question #18 :Equations

Example Question #19 :Equations

Example Question #20 :Equations

All ISEE Middle Level Quantitative Resources

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