[Trickytests]

How many positive integers less than 10,000 are such that the product of their digits is 210?

A. 24

B. 30

C. 48

D. 54

E. 72

 

 

Correct Answer – D  – (click and drag your mouse to see the answer)

[Trickytests]

Question type: Counting

Case 1: 4 places integer less than 10000

—> 1st  210=1*2*3*5*7

—-> 2nd 210 =1*6*5*7. (Only 2*3 makes the single digit 6).

So, four digit numbers with combinations of the digits (1,6,5,7) and (2,3,5,7)

{1,6,5,7} # of combinations 4!=24

{2,3,5,7} # of combinations 4!=24

Case 2:  3 digit number= three digit numbers with combinations of digits {6,5,7}

will have the product of their digits equal to 210.

{6,5,7} # of combinations 3!=6

Total=24+24+6= 54

24+24+6=54.

Answer: D.

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