• Placement Papers
• /
• CAT

CAT Question Papers:

(#M40020300) CAT question remainder Keep an EYE

32^32^32/9 leaves the remainder?
i)2
ii)4
iii)1
iv)7

Asked In CAT Arpit Srivastava (10 years ago)

Unsolved Read Solution (3)

Is this Puzzle helpful?   (0)   (0) Submit Your Solution

Read Solution (3) :

Ashutosh Anshu  (10 years ago)

4 will be the answer. because 32^32^32/9 = 2^160^32/9 = 7^32/9 = 4

Is this solution Helpfull? Yes (4) | No (1)  

shubham  (10 years ago)

32 = 2⁵
(2⁵)³² = 2¹⁶⁰
(2¹⁶⁰)³² = 2⁵¹²⁰
You are looking for the remainder of 2⁵¹²⁰ ÷ 9.

2¹ mod 9 = 2
2² mod 9 = 4
2³ mod 9 = 8
2⁴ mod 9 = 7
2⁵ mod 9 = 5
2⁶ mod 9 = 1
2⁷ mod 9 = 2
2⁸ mod 9 = 4
2⁹ mod 9 = 8
2¹⁰ mod 9 = 7
2¹¹ mod 9 = 5
2¹² mod 9 = 1
...
Note that the pattern repeats, and when the exponent is divisible by 6, the remainder is 1.
5120 = 6(853) + 2, therefore
2⁵¹²⁰ mod 9 = 4

Is this solution Helpfull? Yes (2) | No   

mohan lal garg  (10 years ago)

32^32^32/9=(27+5)^32^32/9
rem=5^32^32/9=(27-2)^16^32
rem=2^16^32=[2(9-1)^3]^32/9
rem=2^32/9=4(9-1)^10
so finally reminder=4...........

Is this solution Helpfull? Yes (1) | No   

Please Login to Read Solution.