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(#M40010393) TCS Numerical Ability question Keep an EYE

How many 3-digit numbers have even number of factors?(a) 22 (b) 879 (c) 21 (d) 878

Asked In TCS trisha sinha (11 years ago)

Solved Garima Read Solution (9)

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abhishek kumar verma  (11 years ago)

Every factor of a number has a pair, so there ought to be an even number of factors for every number. However, if a pair of the factors are the same number, then there will be an odd number of factors, that is if the number is a perfect square.

Assuming three digit numbers are 100 to 999:

From 100 to 999, the perfect squares are 10^2 = 100 to 31^2 = 961, a total of 31-10+1 = 22 numbers.

So of the 999-100+1 = 900 three digit numbers, 22 have an odd number of factors, so 900-22 = 878 have an even number of factors.

Is this solution Helpfull? Yes (20) | No (2)  

abhishek kumar verma  (11 years ago)

Every factor of a number has a pair, so there ought to be an even number of factors for every number. However, if a pair of the factors are the same number, then there will be an odd number of factors, that is if the number is a perfect square.

Assuming three digit numbers are 100 to 999:

From 100 to 999, the perfect squares are 102 = 100 to 312 = 961, a total of 31-10+1 = 22 numbers.

So of the 999-100+1 = 900 three digit numbers, 22 have an odd number of factors, so 900-22 = 878 have an even number of factors.

Is this solution Helpfull? Yes (9) | No (3)  

Garima  (11 years ago)

option (d )........878 ( 900-22).... 3-digit numbers have even number of factors.
Because there are 22 perfect squares between 100-999.

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trisha sinha  (11 years ago)

plz plz explain it

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trisha sinha  (11 years ago)

please explain the logic clearly...how is 22 perfect squares and why did u subtracted from 900

Is this solution Helpfull? Yes (3) | No (2)  

diptangshu paul  (11 years ago)

perfect sq always have odd no of factor..
like 36
36=6^2 = 2^2*3^2
so, no of factors = [ 2+1]*[2+1] =9
which is odd.. chechk others if u want...
answer is 900-22= 878

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Chandra Sekar V  (11 years ago)

Hell No! Only the prime numbers have even number of factors so the answer is (a)22 (from 10^2 to 31^2)

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Chandra Sekar V  (11 years ago)

Sorry for my previous answer the correct answer is 878 because i've counted 1 as a factor

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Anuj Katiyal  (11 years ago)

nice one...agree with abhishek verma

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