 0
June 30, 2020, 12:10 a.m.
What are the last two digits of 72008 ?

What are the last two digits of 72008 ?

1. 21
2. 61
3. 01
4. 81
5. 41
quant
numbers 0
June 30, 2020, 6:20 p.m.

There are two methods

Method 1: try to find some pattern

71= 07
72= 49
73= 343
74= 2401
75= 16807
76= 117649
77= 823543
78= 5764801

We can see that last 2 digits are repeating every 4 times.
so we can say that
last two digit in 7n=07 when n=4k+3
last two digit in 7n=49 when n=4k+2
last two digit in 7n=43 when n=4k+1
last two digit in 7n=01 when n=4k

Hence last two digit in 72008 is 01.

Method 2:

For finding last two digit of odd number(in our case 7 is odd).
we will reduce the base to a number with unit digit 1.

72008 = 491004 = 2401502

Now for base ending with 1.
formula is ([digit at tens place of base multiplied by last/unit digit of power] * 10 + 1)
In our case tens place of base is 0 and unit digit of power is 2
therefore it will be ([0*2]*10 + 1) = (0*10 + 1) = 1
Hence last two digit in 72008 is 01.

Tags
quant
numbers
cat-2019
varc
rc
set-theory
time-speed-distance