Latest CAT Aptitude Question SOLUTION: 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

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(#M40152408) CAT Numerical Ability question Number System Keep an EYE

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?

Asked In CAT Sibani Sankar Panigrahi (8 years ago)

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Ajay Kumar Gupta  (8 years ago)

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.

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sagar  (7 years ago)

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.

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tarshika biswas  (8 years ago)

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.

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