Latest IBPS Aptitude Question SOLUTION: Q. Last digit of given expression (36572)^145 * (30766)^132 will be..

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Q. Last digit of given expression
(36572)^145 * (30766)^132 will be..

Asked In IBPS Suman (11 years ago)

Unsolved Read Solution (6)

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RAKESH  (11 years ago)

(36572)^145 * (30766)^132
last digit of expression will be the last digit of (2)^145 * (6)^132

last digit of 2^145 = (2^4)^36 *2 = (16)^36 *2 = 6*2 = 12 => 2

last digit of 6^132 = 6
so, Last digit of given expression = 2*6 =12 => 2

ans 2

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AMIT KUMAR  (11 years ago)

2^145
2 to power foloow pattern 2^1=2
2^2=4
2^3=8
2^4=6
.
.
2^145 last digit=145/4=1 reminder
so last digit=2
6^132 always gives last digit =6
2*6=12
ans. 2

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Rituparna Chakraborty  (11 years ago)

(36572)^145*(30766)^132
Required digit= unit digit in(2)^145*(6)^132
(6)^132 always give the unit digit 6.
(2)^145=(2)^144*2=(2^6)^24*2=(4)^24*2=(64^2)^12*2=(4^2)^12*2=(16)^12*2=(6)^12*2
=6*2=12=2
so digit in unit place=2*6=12=>2, so 2 is the answer.

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Palwinder Singh  (10 years ago)

unit digit of 36572 is 2
then 2^145 or 2^5 or 32 then unit digit will be 2
Again unit digit of 30766^132 will be 6.
Now we have 2*6 or 12 or unit digit will be 2
Final answer is 2

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Mani kandan  (10 years ago)

hi rakesh
how (16)^36 *2 =6*2 = 12 => 2 becomes?
pls explain....

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KAPU RAVI KUMAR  (10 years ago)

unit digit of x^y is same as (x mod 10) ^(y mod 4).
if y is divisible by 4 then we take 4 as power.
then the problem will be
2^145 * 6^132
= 2^1 * 6^ 4 ( since 145mod4 =1 and 132 is divisible by 4)
=2*1296
=2592
therefore unit digit of 2592 = unit digit of (36572)^145 * (30766)^132
i.e. = 2

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