The greatest number of four digits which is divisible by 15, 25, 40 an

Question

The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:

A. 9000
B. 9400
C. 9600
D. 9800
E. 9999

PKN · Answer

Since the 4-digit number is divisible by 15, 25, 40 and 75. So, the number must be divisible by LCM( 15, 25, 40 ,75)=600.

The greatest 4-digit number in number system is 9999.

So, the required number=9999-Rem( \frac{9999}{600} )=9999-399=9600

Ans. (C)

chetan2u · Answer

the choices straight away give you the answer.. 
the number has to be multiple of 5 and 2, so has to have 0 as units digit... eliminate E
the number is also a multiple of 3, so the sum of digits of number must be divisible by 3...
9800=9+8+0+0=17.. NOT divisible by 3 so eliminate D
9600 = 9+6+0+0=15...div by 3, so our answer
C

Also the question is basically asking for multiple of the LCM of 15,25,40 and 75
 15=3*5...........
25=5^2...............
40=2^3*5...........
75=3*5^2 
LCM =  2^3*3*5^2=600 
in choices 9600 is the largest multiple of 6...

Mansoor50 · Answer

I solved this by looking at the GCF ... which is 15 in this case.....
then i looked at each number which was divisible by 15 ... turned out to be C.

I wonder if my logic is correct?

Md231 · Answer

I would solve this by elimination.

B, D are not multiples of 3 whereas 15, 75 are. So these can be eliminated.

E is odd.

A is too small so I would test 9600 and I see that it is divisible by all.

C it is.

ScottTargetTestPrep · Answer

Let’s determine the LCM of 15, 25, 40, and 75:

15 = 3 x 5

25 = 5^2

40 = 2^3 x 5

75 = 5^2 x 3

So the LCM is 2^3 x 3 x 5^2 = 8 x 3 x 25 = 600, and the largest 4-digit number that is a multiple of 600 is 9600.

Answer: C

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The greatest number of four digits which is divisible by 15, 25, 40 an

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