JIPMAT 2021 (QA) - The digit in the unit's place of the number represented by (7^95 - 7^58) is | PYQs + Solutions

JIPMAT 2021

Number System

Unit Digit

Conceptual

The digit in the unit's place of the number represented by $(7^{95} - 7^{58})$ is

Correct Option: 2

Since we only need the unit's digit, patterns in powers of 7 matter:

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Unit's digit in powers of 7 follows pattern: 7,9,3,1,7,9,3,1,... and so on (cycles every 4 powers)

For

7^{58}

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58 mod 4 = 2

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7^{58}

ends in same digit as

7^2

= 49, which is 9

For

7^{95}

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95 mod 4 = 3

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7^{95}

ends in same digit as

7^3

= 343, which is 3

Therefore,

7^{95} - 7^{58}

ends in

(..3 - ..9) = ..4