A boy took a seven digit number ending in 9 and raised it to an even power greater than 2000. He then took the number 17 and raised it to a power which leaves the remainder 1 when divided by 4. If he now multiplies both the numbers, what will be unit's digit of the number he so obtains?

• Ans=7
  no. ending with digit 9 have even power gives unit position as 9^2
  i.e 1 at unit place.
  number 17 have power with given condition gives unit place as 7.
  so after multiplication it gives 1*7=7.
• 9 years agoHelpfull: Yes(6) No(0)
• first let us analyse the two numbers:-
  First no is in the form of ABCDEF9^(EVEN NUMBER GREATER THAN 2000), the unit place of which will always be 1-as 9^(even number) is always 1 at the unit place.
  Second no is a 17^n. where n is a no which will always give a remainder 1 when divided by 4, so n is basically a form of 4n+1. therefore the second no is 17^(4n+1) which will always yield 7 as the unit place. Therefore when 2 nos are multiplied it will give a remained of 1*7=7. So the answer is 7.
• 8 years agoHelpfull: Yes(1) No(0)
• A boy took 7 digits of no. which ends with 9. if it is raised to an even power... whatever it is.. gives 1 as its unit digit. Now, 17 ^ x = a no. which gives 1 as reminder when divided by 4. 7 ^ 2 = 289 which when divided by 4 gives reminder 1. So, 1*9 = 9 so, 9 is the required unit digit.
• 9 years agoHelpfull: Yes(0) No(4)