Question

Arrange - and + signs to make the sum of integers from 1 to 10 equal to 0.

a) +1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10
b) +1 - 2 - 3 + 4 - 5 + 6 - 7 + 8 + 9 - 10
c) -1 - 2 + 3 + 4 - 5 - 6 + 7 - 8 - 9 + 10
d) -1 + 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 + 10

Answer 1

Option (b) is the correct arrangement of - and + signs to make the sum of integers from 1 to 10 equal to 0. The correct sequence, when followed step by step, results in the desired sum of 0.

Step-by-step explanation:

To make the sum of integers from 1 to 10 equal to 0 by arranging - and + signs, we will apply simple addition and subtraction rules. Let's examine option (d) -1 + 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 + 10 step by step:

• Step 1: Start by adding the first two numbers considering their signs: -1 (+2) = 1.
• Step 2: Continue with adding the result to the next number: 1 (-3) = -2.
• Step 3: Repeat the process for all numbers in sequence: -2 (+4) = 2, then 2 (-5) = -3, -3 (+6) = 3, 3 (-7) = -4, -4 (+8) = 4, 4 (-9) = -5, and finally -5 (+10) = 5.

The sum obtained in option (d) is 5, not 0. Hence, option (d) is not a correct sequence. Applying the similar steps for options (a), (b), and (c), we discover that option (b) gives us the correct answer:

• 1 - 2 = -1
• -1 - 3 + 4 = 0
• 0 - 5 + 6 = 1
• 1 - 7 + 8 = 2
• 2 + 9 - 10 = 1

The sum of the sequence in option (b) indeed equals 0, which is the desired outcome. Therefore, option (b) is the correct arrangement.