CAT 2008QA Question 11

Last 2 digitsEasy

What are the last two digits of 72008?

Answer & solution

Correct answer: 01

  • A

    21

  • B

    61

  • 01

  • D

    41

  • E

    81

Solution

Last 2 digits of

71 = 07
72 = last 2 digits of (07 × 7) = 49
73 = last 2 digits of (49 × 7) = 43
74 = last 2 digits of (43 × 7) = 01
75 = last 2 digits of (01 × 7) = 07
76 = last 2 digits of (07 × 7) = 49
77 = last 2 digits of (49 × 7) = 43
78 = last 2 digits of (43 × 7) = 01

As we can see, for every 4th power of 7, the last two digits are 01.

Since 2008 is divisible by 4, we can conclude that last two digits of 72008 are 01.

Hence, option (c).

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CAT 2008 QA Q11: What are the last two digits of 7 2008 ? — Solution | TheCATExam