In the sum for which digit does the symbol stand

In the sum: ⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗

for which digit does the symbol ⊗ stand?

Answer: B

Explanation

Method I:

Let ⊗ = x

So, x + 1x + 5x + xx + x1 = 1xx

x + (10 + x) + (50 + x) + (10x + x) + (10x + 1) = 100 + 10x + x

24x + 61 = 100 + 11x

13x = 39

x = 3

Method II:

The unit digit of the sum of the expression is x. So, you can only check the unit place of expression by substituting the value of symbol x from the given options.

Option (a): by substituting x = 2, we get:

2 + 12 + 52 + 22 + 21 = 122

Sum of unit digits = 2 + 2 + 2 + 2 + 1 = 9

But unit digit of sum, 9 ≠ 2

Option (b): by substituting x = 3, we get:

3 + 13 + 53 + 33 + 31 = 133

Sum of unit digits = 3 + 3 + 3 + 3 + 1 = 13.

So, unit digit of sum, 3 = 3

Option (c): by substituting x = 4, we get:

4 + 14 + 54 + 44 + 41 = 144

Sum of unit digits = 4 + 4 + 4 + 4 + 1 = 17

So, unit digit of sum, 7 ≠ 4

Option (d): by substituting x = 5, we get:

5 + 15 + 55 + 55 + 51 = 155

Sum of unit digits = 5 + 5 + 5 + 5 + 1 = 21.

So, unit digit of sum, 1 ≠ 5

Hence, x = 3

Exam Year: 2020