Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

A

11

B…

Question

Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

A

11

B

12

C

13

D

None of these

Explanation

The possible arrangements are 1,multiples of 2 ,remaining. So we have 1+2+4+8+16+32+64+31 = 158. Hence minimum no. of bags required is 8. 

why the bag of 31 ?

Akhilesh Singh · Answer

A bag of 31 is needed to cover for the values above 127. 1+2+4...+64 = 127, so if somebody asks you for say 155 coins, How would you give him?
64+32+31+16+8+4. So we need a bag of 31 to cover the values between 127 and 158.
Thanks

aasish m · Answer

You cannot get a sum of 128 by using a bag with 31 coins

Suri Gangula · Answer

Akhilesh answered it very well, Download Number Systems formulas and Progression formulas to learn more concepts and tips.

Shikhar Gupta · Answer

8 bags can be 1,2,3,7,14,28,56,47

Shikhar Gupta · Answer

128= 64+31+28+4+1

Avinash Nair · Answer

17

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