Which two signs need to be interchanged to make the following equation correct?
{(78 + 70) − (6 × 2))} ÷ 2 = 10
−, +
To solve this question, we need to systematically test each option to see which interchange of signs results in the equation being true.
Option 1: (+, ×)
Interchanging + and × gives: {(78 × 70) − (6 + 2)} ÷ 2 = 10. This simplifies to (5460 - 8) ÷ 2 = 2726 ≠ 10.
Option 2: (−, +)
Interchanging − and + gives: {(78 + 70) + (6 × 2)} ÷ 2 = 10. This simplifies to (148 + 12) ÷ 2 = 160 ÷ 2 = 80 ≠ 10.
Option 3: (÷, +)
Interchanging ÷ and + gives: {(78 + 70) − (6 × 2)} + 2 = 10. This simplifies to (148 - 12) + 2 = 136 + 2 = 138 ≠ 10.
Option 4: (÷, ×)
Interchanging ÷ and × gives: {(78 + 70) × (6 × 2)} ÷ 2 = 10. This simplifies to (148 × 12) ÷ 2 = 1776 ÷ 2 = 888 ≠ 10.
Let's re-examine Option 2: (−, +).
The original equation is {(78 + 70) − (6 × 2)} ÷ 2 = 10. Let's interchange the subtraction and addition signs.
This gives us: {(78 + 70) + (6 × 2)} ÷ 2 = 10. This simplifies to (148 + 12) / 2 = 160 / 2 = 80. This is still not equal to 10. There seems to be a mistake in the provided options. A proper analysis of each option reveals that none of the given options will lead to a solution of 10. It's possible there's an error in the question or the provided answer.
Therefore, there's an error in either the problem statement or the provided options. None of the interchanges provided results in the equation equaling 10.
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Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
