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Q #16
:

Directions: Read the following information to answer the question.

Baiju wants to do organic farming and decides to start of by planting mango, jackfruit and coconut trees. He gets 48 mango trees, 144 jackfruit trees and 264 coconut trees. His partner Manoj, an expert in drip irrigation, decides that they will have to plant the trees in rows such that each row should have the same kind of tree and that all rows should have equal number of trees What is the minimum number of rows Baiju is looking at?

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Answer:38 Explanation: hcf of 48,144 and 264 is 12 . For mango 48/12=4,for jackfruit 144/12=12,for coconut 264/12=22 So 4+12+22=38 Hence proved

Q #17
:

Directions: Read the following information to answer the question.

What is the highest power of 2 that will exactly divide 18!?

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Answer:16 Explanation:formula is: (X!/prime no.)+(X/prime no^2)……..continued till prime no. don’t get bigger than X NOTE: take the whole value you get ondividing So here (18/2+18/4+18/8+18/16)=9+4+2+1=16 Hence proved.

Q #18
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Directions: Read the following information to answer the question.

What will be the highest power of 3 that will exactly divide 83!?

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Answer: 40 Explanation: formula is: (X!/prime no.)+(X/prime no^2)……..continued till prime no. don’t get bigger than X NOTE: take the whole value you get ondividing. 83/3+83/9+83/27+83/81=27+9+3+1=40 Hence proved.

Q #19
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Directions: Read the following information to answer the question.

How many zeroes will 130! end in?

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Answer:32 Explanation:the no. of zeros at the end of n!=[n/5]+[n/5^2]+[n/5^3]+….. So,[130/5]+[130/25]+[130/125]+…..=26+5+1+0…=32 Hence proved.

Q #20
:

Directions: Read the following information to answer the question.

What is the last digit or units’ digit of 244?



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Answer:6 Explanation: cyclicity of 2 is 4.so power 44 when divided by 4 gives remaionder 0 . Note:If the remainder comes out 0 in any case then the unit digit will be the last digit of a cyclicity number. Here last digit of cyclicity of 2 is 6. Hence proved.