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Solution: By Fermat's theorem as 24 and 7 are co­primes, remainder of 24^6 mod 7 =1. Hence,24^13 can be split up as 24^6* 24^6* 24 mod 7 = 1*1*3 mod 7 =3. Hence, remainder is 3. How is 24 mod 7 calculated here

Four unique even numbers are arranged in ascending order and the first two are decreased by 50%, while the last two are increased by 50%. If the original sum of the 4 numbers was 162, the new sum can be?
In the solution it is mentioned that the last two numbers must be 4 greater than the first two. Why?

I am basically from commerce field,so I cant understand geometry very well....what should I do to improve geometry?

Manifacha

A student appears for 4 papers-english,math,physics,chemistry.Max Marks for which are in the ratio 1:1:2:2. His marks are in the ratio of4:8:13:15. If he got 80% of the total max marks, in how many papers did he got more than 80%?

Total number of students in classes 4, 5 and 6 are 100. The average scores of students in class 4 and class 6 are 70 and 95 respectively. The average scores of students in class 4 and class 5 combined is 83 and the average scores of students in class 5 and class 6 combined is 87.5. Find the number of students in class 4 if it is given that the average of the scores of the students in all the classes is 84.

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4 men and 3 women finish a Job in 6 days. 5 men and 7 women can do the same Job in 4 days. how long will 1 man and 1 woman take to do the job?

Mr. Shah has to divide his assets worth rupees 30 crores in 3 parts to be given to three id his sons Ajay, Vijay and Arun ensuring that every son gets at least worth rupees 5 crores . In how many ways can this be done if it is given that three sons should get their shares in multiple of rupees 1 crore?.Please provide detailed solution

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