Mathematical Operations Question and Answers 1 — Questions and Answers

Question 1: Interchanges given: + and - signs, 4 and 8.

8 + 4 - 12 = 24
8 - 4 + 12 = 8
4 - 8 + 12 = 0 (Correct answer)
4 + 8 - 12 = 12

Correct answer: 4 - 8 + 12 = 0

The question requires applying two sets of interchanges to the given options: swapping '+' and '-' signs, and swapping '4' and '8' digits. For the correct option, `4 - 8 + 12 = 0`, applying these interchanges transforms it into `8 + 4 - 12 = 0`. Calculating this new equation, `8 + 4` equals `12`, and `12 - 12` equals `0`. This makes the statement `0 = 0` true, confirming the validity of option C after the specified swaps.

Question 2: Determine which two signs need to be switched in order for the following equation to be accurate. 5 + 3 x 8 - 12 / 4 = 3

"+" and /
"+" and "+"
"-" and / (Correct answer)
"+" and "-"

Correct answer: "-" and /

To make the equation `5 + 3 x 8 - 12 / 4 = 3` accurate, we need to swap the '-' and '/' signs. This transforms the equation into `5 + 3 x 8 / 12 - 4 = 3`. Following the order of operations, `3 x 8` is `24`, and `24 / 12` is `2`. The equation then simplifies to `5 + 2 - 4 = 3`, which correctly evaluates to `7 - 4 = 3`, making the statement `3 = 3` true.

Question 3: Given that A + B = 2C and C + D = 2A,

A + C = 2B
A + D = B + C
A + C = 2D
A + C = B + D (Correct answer)

Correct answer: A + C = B + D

To find the correct relationship, add the two given equations: (A + B) + (C + D) = 2C + 2A. This simplifies to A + B + C + D = 2A + 2C. Subtracting A and C from both sides yields B + D = A + C. This matches option D, demonstrating the equivalence of the two expressions.

Question 4: Which collection of symbols should be used to fill in the provided equation? 5 0 3 5 = 20

-, +, x (Correct answer)
x, +, x
"+", "-", x
x, x, x

Correct answer: -, +, x

To solve the equation 5 _ 0 _ 3 _ 5 = 20, we need to test the given symbol combinations while following the order of operations (multiplication before addition/subtraction). For option A, substituting the symbols gives 5 - 0 + 3 x 5. First, calculate 3 x 5 = 15. Then, perform the subtraction and addition from left to right: 5 - 0 = 5, and 5 + 15 = 20. This correctly matches the target value.

Question 5: If × denotes addition, ÷ denotes subtraction, + denotes multiplication, and - denotes division, then 20 × 8 ÷ 8 - 4 + 2 =?

5
24 (Correct answer)
80
25

Correct answer: 24

First, substitute the new operations into the expression: 20 + 8 - 8 ÷ 4 × 2. Next, follow the order of operations (PEMDAS/BODMAS). Perform division first: 8 ÷ 4 = 2. Then, perform multiplication: 2 × 2 = 4. Finally, perform addition and subtraction from left to right: 20 + 8 = 28, and 28 - 4 = 24. Thus, the result is 24.

Question 6: In the following questions, what should be entered in lieu of the question mark (?)? 3 1/6 + 4 1/2 − 2 2/3 − 1 11/12 =?

1 5/12
1 7/12
3 1/12 (Correct answer)
3 7/12

Correct answer: 3 1/12

To evaluate the expression with the given interchanges, apply the changes to option D: 5 x 4 + 20 = 104. The interchanges are '+' with 'x' and '4' with '5'. Applying these, the expression becomes 4 + 5 x 20. Following the order of operations, calculate 5 x 20 = 100, then add 4 + 100 = 104. This result matches the right side of the equation in option D.

Question 7: Assuming intercharges: + and x signs, as well as 4 and 5.

5 x 4 + 20 = 85
5 x 4 + 20 = 40
5 x 4 + 20 = 95
5 x 4 + 20 = 104 (Correct answer)

Correct answer: 5 x 4 + 20 = 104

To solve the system of equations, first expand them: 3u + 9v = 11uv and 6u + 3v = 7uv. Assuming u and v are non-zero, divide both equations by uv to get 3/v + 9/u = 11 and 6/v + 3/u = 7. Let x = 1/u and y = 1/v, resulting in a linear system: 9x + 3y = 11 and 3x + 6y = 7. Solving this system (e.g., by multiplying the second equation by 3 and subtracting from the first) yields x = 1 and y = 2/3. Therefore, u = 1/x = 1 and v = 1/y = 3/2.

Question 8: The answer to the equations 3(u + 3v) = 11 uv and 3(2u + v) = 7 uv is _____.

u = 1, v = 3/2 (Correct answer)
u = 1, v = 0
u = 0, v = 1
u = 0, v = 3/4

Correct answer: u = 1, v = 3/2

First, convert all mixed numbers to improper fractions and find a common denominator, which is 12. The expression becomes (3 + 2/12) + (4 + 6/12) - (2 + 8/12) - (1 + 11/12). Combine the whole numbers: 3 + 4 - 2 - 1 = 4. Combine the fractional parts: (2 + 6 - 8 - 11) / 12 = -11/12. Finally, combine the whole and fractional results: 4 - 11/12 = 3 and 1/12.

Question 9: 12:30:: 14:?

42
35 (Correct answer)
28
36

Correct answer: 35

The relationship between 12 and 30 is a ratio of 12:30, which simplifies to 2:5 (dividing both by 6). To find the missing number in 14:?, we apply the same ratio. If 14 represents the '2' part of the ratio, then the multiplier is 14 / 2 = 7. Applying this multiplier to the '5' part of the ratio gives 5 * 7 = 35. Therefore, the missing number is 35.

Question 10: Given the definitions of Q, J, T, and K as "add to," "multiply by," "subtract from," and "divide by," what does 30 K 2 Q 3 J 6 T 5 =?

31
103
28 (Correct answer)
18

Correct answer: 28

First, substitute the defined operations into the expression: 30 ÷ 2 + 3 × 6 - 5. Next, follow the order of operations (PEMDAS/BODMAS). Perform division first: 30 ÷ 2 = 15. Then, perform multiplication: 3 × 6 = 18. Finally, perform addition and subtraction from left to right: 15 + 18 = 33, and 33 - 5 = 28. Thus, the result is 28.

Question 11: Five batsmen (P, Q, R, S, and T) averaged 36 runs in a cricket match. Q scored as many as S and T combined, Q and R scored 107 between them, and S scored five more than T. T, on the other hand, scored eight less than P. How many runs did T score?

29
28
24
20 (Correct answer)

Correct answer: 20

The five batsmen averaged 36 runs, so their total score is 5 * 36 = 180. Set up equations: Q = S + T, Q + R = 107, S = T + 5, and P = T + 8. Substitute S into the first equation to get Q = 2T + 5. Then substitute Q into the second equation to find R = 102 - 2T. Finally, substitute P, Q, R, S (all in terms of T) into the total score equation: (T + 8) + (2T + 5) + (102 - 2T) + (T + 5) + T = 180. This simplifies to 3T + 120 = 180, so 3T = 60, meaning T = 20 runs.

Mathematical Operations Question and Answers 1

Interchanges given: + and - signs, 4 and 8.