Latest CAT Aptitude Question SOLUTION: The product of 3 natural number (N1,N2,N3) is 12 times their hcf. How many ordered triplets ( N1, N2, N3) are possible?

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(#M40157111) CAT Numerical Ability question number Keep an EYE

The product of 3 natural number (N1,N2,N3) is 12 times their hcf. How many ordered triplets ( N1, N2, N3) are possible?

Asked In CAT arun sawaiyan (7 years ago)

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Sitangshu Das  (7 years ago)

Let HCF be H
N1=Ha
N2=Hb
N3=Hc
Product of 3 numbers=>(H^3)(abc)=12H
So (H^2)(abc)=12
In this case H^2 will be either 1 or 4 because if its 9 or more than that then we wont get (H^2)(abc) as 12
So if H^2 = 1
then ordered triplets will be
(1,1,12)(1,2,6)(1,3,4)(1,4,3)(1,6,2)(1,12,1)(2,1,6)(2,2,3)(2,3,2)(2,6,1)(3,1,4)(3,2,2)(3,4,1)(4,1,3)(4,3,1)(6,1,2)(6,2,1)(12,1,1)
for H^2=4
The ordered triplets will be :
(1,1,3)(1,3,1)(3,1,1)

Hence total number of ordered triplets will be 21

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Abhishek Shaw  (7 years ago)

9 is the ans

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Sakshi Agarwal  (7 years ago)

suppose division is 2,2,3
__ __ __ filling these 3 places with 2,2,3 ways=3!/2!=3

division is 1,3,4
__ __ __ fill these places with 1,3,4 ways=3!=6

division is 1,2,6
__ __ __ fill these places with 1,2,6 ways=3!=6

division is 1,1,12
__ __ __ fill these places with 1,1,12 ways=3!/2!=3



Ans.18 ordered triplets possible

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Naresh Nani  (7 years ago)

how the answer is 9?

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