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Q #46
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Directions : These questions are based on the data given below.

Dr. Surya Rao is working on an experiment since the last four years. He is carrying out the experiment on guinea pigs and rats. The number of guinea pigs doubled every year while the rats quadrupled every year. In the last four years that Dr. Rao has been doing the experiments, he found that the mortality rat of both guinea pigs and rats was nil and their total population grew to 544. From the beginning the number of males and females had always been equal. How many female guinea pigs are there at present?

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Q #47
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Directions : These questions are based on the data given below.

If the sum of two numbers is 48 & their hcf is 6 , how many solutions exist for these two numbers.

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Solution : A + B = 48 hp + hq = 48 6(p +q)= 48 p + q =8 p,q -> (1,7) ,(2,6),(3,5),(4,4) only 2 solutions are correct as p & q needs to be co-prime .

Q #48
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Directions : These questions are based on the data given below.

There is a number of the format pqrpqr , where p q & r are the digits of the number . What is the least number of prime numbers it is certainly divisible by ?

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Solution : Pqrpqr= pqr x 1001 1001 = 7 x 11 X 13 234 X 1001 = 234234 23 X 1001 = 23023

Q #49
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Directions : These questions are based on the data given below.

What is the highest value of n for which numerator is exactly divisible by denominator 124!/63^n ?

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Q #50
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Directions : These questions are based on the data given below.

Find the least number which when divided by 20,25,35 and 40 leaves remainders 13,18,28 and 33 respectively.

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Solution : Here,(20-13) = 7,(25 – 18)=7,(35-28)=7 and (40-33)=7. So n + 7 = (L.C.M. of 20,25,35,40) =1400 N = 1400 -7 = 1393.