Find the number of four-digit numbers, that have distinct

Question

Find the number of four-digit numbers, that have distinct digits whose product is 540.

(A) 24
(B) 6
(C) 48
(D) 30
(E) 14

divyadna · Answer

Factorise 540

1*540, product is 0
2*270, product is 0
3*180, product is 0
4*135, product is 540. Arrangements possible=4!=24

5*108, product is 0
6*90, product is 0
9*60, product is 0
10*54, product is 0
12*45, product is 540. Arrangements possible=4!=24

18*30, product is 0
20*27, product is 0

Total numbers possible= 24+24=48

Option C

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Archit3110 · Answer

540 = 3^3*2^2*5
4 digit possible pairs

6,9,2,5 and 4,9,3,5
Both these pairs can be arranged in 4! Ways each
(6925) 4! =24
(4935) 4!=24
Total 48 ways option C

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gmatophobia · Answer

540 = 3^3 * 2^2 * 5

Possible digits = {3,9,4,5}, {6,9,2,5}

Each set of 4 digits can be arranged in 4! ways. As we have two sets the number of four-digit numbers = 2*4! = 3*24 = 48

Option C

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