CAT 2008 — QA Question 11
Directions for next 2 questions:
The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.
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What are the last two digits of 72008?
Answer & solution
- A
21
- B
61
01
- D
41
- E
81
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).