Select the correct combination of mathematical signs to replace * signs and to…
2024
Select the correct combination of mathematical signs to replace * signs and to balance the given equation. 7*2*3*5*6
- A.
- + = x
- B.
+ x = +
- C.
= x + -
- D.
x = + +
Show answer & explanation
Correct answer: D
In this type of puzzle, the expression has four blanks between five numbers. Exactly one of the four blanks must be filled with the equality sign '=', and the remaining three blanks are filled with arithmetic operators from the ones offered (+, -, x) - not necessarily one of each. To find the correct combination, substitute each option into the expression, evaluate both sides using the standard order of operations (multiplication before addition or subtraction), and check whether the two sides come out equal. Only one combination gives a true numerical equality.
Testing each option in 7 * 2 * 3 * 5 * 6:
- + = x: substituting gives 7 - 2 + 3 = 5 x 6, i.e. 8 = 30 - the two sides are not equal.
+ x = +: substituting gives 7 + 2 x 3 = 5 + 6, i.e. 13 = 11 - the two sides are not equal.
= x + -: substituting gives 7 = 2 x 3 + 5 - 6, i.e. 7 = 5 - the two sides are not equal.
x = + +: substituting gives 7 x 2 = 3 + 5 + 6, i.e. 14 = 14 - the two sides are equal, so this combination balances the equation.
Independently verifying the balanced case: the left side 7 x 2 evaluates to 14, and the right side 3 + 5 + 6 also evaluates to 14, confirming that the two sides are equal, so x = + + is the combination that balances the given expression.
