Question

Fill in '+' or '-' sign in between these numbers so that they give the correct answer. \(1\, 2^3\,\,3^3 \, \,1\,\,4^3=31\)

• A. + + - -
• B. + + + -
• C. - - + +
• D. - - - +

Answer 1

The Correct Option is C

To solve the problem, we need to insert '+' or '-' signs between the numbers in the expression \(1\, 2^3\,\,3^3 \, \,1\,\,4^3\) such that the expression equals 31. Let's evaluate each option:

Option 1: + + - -

\(1 + 2^3 + 3^3 - 1 - 4^3\)

Calculating, we get:

\(1 + 8 + 27 - 1 - 64\)

= \(36 - 65 = -29\)

This does not equal 31.

Option 2: + + + -

\(1 + 2^3 + 3^3 + 1 - 4^3\)

Calculating, we get:

\(1 + 8 + 27 + 1 - 64\)

= \(37 - 64 = -27\)

This also does not equal 31.

Option 3: - - + +

\(1 - 2^3 - 3^3 + 1 + 4^3\)

Calculating, we get:

\(1 - 8 - 27 + 1 + 64\)

= \(2 - 35 + 64 = 31\)

This equals 31, making this option correct.

Option 4: - - - +

\(1 - 2^3 - 3^3 - 1 + 4^3\)

Calculating, we get:

\(1 - 8 - 27 - 1 + 64\)

= \(0 - 35 + 64 = 29\)

This does not equal 31.

Therefore, the correct signs to insert are given by option 3: - - + +.