Latest TCS Aptitude Question SOLUTION: in how many possible ways you can write 3240 as product of 3 positive integers a, b, c . a 450 b 420 c 350 d 320

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in how many possible ways you can write 3240 as product of 3 positive integers a, b, c .
a 450
b 420
c 350
d 320

Asked In TCS sahitya (9 years ago)

Solved Saraswathy Read Solution (11)

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Saraswathy  (9 years ago) Best Solution

3240 => 2^3 * 3^4 * 5^1
a => 2^x1 * 3^y1 * 5^z1
b => 2^x2 * 3^y2 * 5^z2
c => 2^x3 * 3^y3 * 5^z3
a * b * c = 3240
x1 + x2 + x3 = 3 => 5C2
y1 + y2 + y3 = 4 => 6C2
z1 + z2 + z3 = 1 => 3C2
5C2 * 6C2 * 3C2 = 10 * 15 * 3 = 450

Ans : (A) 450

Is this solution Helpfull? Yes (27) | No (9)  

Arpit goel  (9 years ago)

X1+X2+X3=3=>5C2
because x1+x2+x3----xr=n =>(n+r-1)C(r-1),
Here n=3 and r=3
so, put n and r in formula,we get 5C2.
Is it clear now??

Is this solution Helpfull? Yes (21) | No (4)  

raviteja  (9 years ago)

how u got 5c2,6c2,3c2 @SARASWATHI

Is this solution Helpfull? Yes (6) | No (1)  

mounika  (9 years ago)

hw can u write 5c2, x1+x2+x3=3 k explain plz

Is this solution Helpfull? Yes (2) | No (4)  

Lalithya Maheswaram  (9 years ago)

Continuation of saraswathi
we get x1+x2+x3=3=>this can be satisfied in 10 ways,similarly the other two can be satisfied in 12 and 3 ways.so intotal the answer is 10*15*3=450

Is this solution Helpfull? Yes (2) | No   

rahul garg  (9 years ago)

no of positive solns for a some nos ie x1+x2+x3=3 is given by a formula.this formula gives the non neg sols for such kind of eqns....
formula (3+3-1)c(3-1)this gives 5c2...this is actually done by this saraswati...
this is the key for those who dont know the formula

Is this solution Helpfull? Yes (2) | No   

harti  (9 years ago)

3240=2*2*2*5*3*3*3*3

so, the answer is 8!/(3!*4!)

Is this solution Helpfull? Yes (1) | No (9)  

harti  (9 years ago)

sorry the above one is the wrong solution.

Is this solution Helpfull? Yes (1) | No (2)  

swetha  (9 years ago)

how did u get 6c2 and 3c2
make it clear @saraswathy

Is this solution Helpfull? Yes (1) | No (1)  

vijay kumar  (9 years ago)

2^3*3^4*5^1=3240.....1/2(3+1)(1+1)(4+1)=20

Is this solution Helpfull? Yes | No (3)  

NAVADURU CHANDRA SEKHAR  (8 years ago)

By lcm, we calculate 3240=2^3 * 3^4 * 5
as a product of 3 integers a*b*c
we arrange 2^3 in 10 ways
and 3^4 in 15 ways
nd 5 in 3 ways
totally 10*15*3 = 450 ways

Is this solution Helpfull? Yes | No (1)  

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