Insert appropriate arithmetic symbols between 5, 0, 3 and 5 so that the resulting expression equals 20, using the usual order of operations. Which set of symbols will correctly complete the equation 5 0 3 5 = 20?

Difficulty: Medium

Correct Answer: -, +, x

Explanation:


Introduction / Context:
This question asks you to place the correct arithmetic operations between four numbers in order to obtain a specific result. It is a test of both mental arithmetic and your understanding of how multiplication, addition and subtraction interact under operator precedence rules. You must choose the set of symbols that makes the equation evaluate exactly to 20.


Given Data / Assumptions:

  • The pattern is 5 ? 0 ? 3 ? 5 = 20.
  • Each "?" is to be replaced by one of the symbols +, − or × as indicated by the options.
  • Standard precedence applies: multiplication before addition and subtraction.
  • No brackets are to be added; only operators are inserted.


Concept / Approach:
We examine each candidate set of symbols, insert them in order between 5, 0, 3 and 5, and then evaluate using the standard rules. Because there are relatively few options, it is efficient to test them one by one. The correct option will give exactly 20 on the left-hand side.


Step-by-Step Solution:
Option B proposes -, +, ×, so the expression becomes 5 − 0 + 3 × 5.Evaluate multiplication first: 3 × 5 = 15.Now the expression is 5 − 0 + 15. Compute left to right: 5 − 0 = 5, and then 5 + 15 = 20.Thus, 5 − 0 + 3 × 5 = 20, so option B satisfies the equation.


Verification / Alternative check:
Option A, with ×, ×, ×, gives 5 × 0 × 3 × 5 = 0, because anything multiplied by zero becomes zero.Option C, with ×, +, ×, yields 5 × 0 + 3 × 5 = 0 + 15 = 15, which is not 20.Option D, with +, −, ×, yields 5 + 0 − 3 × 5 = 5 + 0 − 15 = −10, which is also incorrect.


Why Other Options Are Wrong:
Any choice that includes multiplication by zero at the start, such as option A or C, immediately forces the product part of the expression to zero, making it impossible to reach the required value 20 without additional terms.Option D fails because the negative contribution from 3 × 5 dominates, leading to a negative result rather than the positive target.


Common Pitfalls:
One common mistake is to ignore operator precedence and treat the expression strictly left to right. For example, misreading 5 − 0 + 3 × 5 as (5 − 0 + 3) × 5 gives 40 instead of 20.Another pitfall is to underestimate the effect of multiplying by zero, which immediately wipes out any product term in which it appears.


Final Answer:
The correct set of symbols is minus, plus, and multiplication in that order, so the answer is -, +, x.

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