CAT 2016 Quantitative Ability

Question : 21 of 34

Marks: +1, -0

N=5^{1!+2!+3!+4!}

The digits of the number N are added to get another number. Then the digits of the number obtained are added to get yet another number. The process is repeated till a single digit number is obtained. What is that single digit number?

Your Answer:

Validate

Solution:

The number finally obtained will be the “digit sum” ofthe original number. It can be directly obtained bydividing the original number by 9 and finding the remainder.

\Rem [{5^{1!+2!+3!+4!}}/9]

= {\Rem}[\;\;{5^{33}}/{9}]

= {\Rem}[\;\;{(5^{3})^{1!}}/{9}]

= {\Rem}[\;\;{(-1)^{1!}}/{9}]

=-1=8

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