Latest CAT Aptitude Question SOLUTION: The number of positive integers which divide 2004 to leave a remainder of 24 ?

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The number of positive integers which divide 2004 to leave a remainder of 24 ?

Asked In CAT Devendra Marghade (12 years ago)

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chaitanya  (12 years ago)

Since 2004 - 36 = 1980, any number which divides 1980 but does not divide 24 will leave a remainder of 24. Since 1980 = 2^2*3^2*5*11, there are 36 divisors of 1980; of those, 1, 2, 3, 4, 6, and 12 also divide 24, so there are 36 - 6 = 30 numbers which leave a remainder of 24 when dividing 2004

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Aman  (12 years ago)

22

2004 -24 = 1980
1980 = 2^2*3^2*5*11

there are 36 divisors of 1980.
out of which 1, 2, 3 ,4 ,5 ,6, 9, 10, 11, 12, 15, 18, 20, 22 are less than 24.
so they can not leave remainder more than 24.

so 36-14=22 integers are there which divide 2004 to leave a remainder of 24.

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jyotish r  (12 years ago)

the answer is 22. we know a number a=(x1^(k1))*(x2^(k2))*.....has (k1+1)*(k2+2)...factors. here 1980=2^2*3^2*11*5. therefore 3*3*2*2=36 factors. but we need to take into account those greater than 24. 1 2 3 4 5 6 9 10 11 12 15 18 20 22 are

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phani  (12 years ago)

AS PER PRINCIPLE OF DIVISION,
2004=Q*D+24
=>Q*D=1980
WE HAVE TO FIND NUMBER OF FACTORS FOR IT AND THAT IS ANSWER:
36
1980=2*2*3*3*5*11
WE HAVE TO LOOK FOR DIFFERENT COMBINATIONS OUT OF IT........
WE HAVE TWO 2'S,TWO 3'S,ONE 5 AND 11.
NUMBER OF COMBINATIONS=(2+1)(2+1)(1+1)(1+1)-1=35
1 IS ALSO FACTOR,SO ANSWER IS 36

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