Unit digit of 125 × 324 × 196 ×291 is x.

Consider the following statement:

Statement I: x is an Even number.

Statement II: x2 – x is divisible by 7, 11, 13 and 17.

Which of the following statements is/are not correct?

(a) Only Statement I

(b) Only Statement II

(c) Both Statement I and II

(d) Neither Statement I nor II

Question

Unit digit of 125 &times; 324 &times; 196 &times;291 is x. 

Consider the following statement: 

Statement I: x is an Even number. 

Statement II: x2 &ndash; x is divisible by 7, 11, 13 and 17.

Which of the following statements is/are not correct? 

(a) Only Statement I 

(b) Only Statement II

(c) Both Statement I and II 

(d) Neither Statement I nor II

ONLiNE UPSC · Accepted Answer

To find the unit digit of the product 125&times; 324 &times; 196 &times; 291, we only need the unit digit of each number:

&bull; Unit digit of 125 = 5

&bull; Unit digit of 324 = 4

&bull; Unit digit of 196 = 6

&bull; Unit digit of 291 = 1

Now multiply the unit digits:
5 &times; 4 = 20 &rarr; unit digit = 0
0 &times; 6 = 0, 0 &times; 1 = 0
So, the final unit digit, x = 0

Statement I is correct as it says x is an even number.

Statement II says x2&minus;x is divisible by 7, 11, 13, and 17
Here, x = 0, so x2 &ndash; x = 0, which is divisible by all numbers (since 0 is divisible by any integer) 

Statement II is also correct.

So, option d is correct.

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