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

1. 9000
2. 9400
3. 9600
4. 9800
5. 9999

Correct Answer: C
Solution and Explanation:
Approach Solution 1:
The problem statement asks to find out the greatest number of four digits which is divisible by 15, 25, 40 and 75.
Since the 4-digit number is divisible by 15, 25, 40 and 75.
Hence, the number must be divisible by LCM of 15, 25, 40, 75
Therefore, the LCM of 15, 25, 40 and 75 = 600.
We know that the greatest 4-digit number in the number system is 9999.
To get the required number, we need to subtract the number 9999 from the remainder of 9999 divided by the LCM 15, 25, 40 and 75 i.e 600.
Therefore, the required number = 9999 – Remainder of (9999/600)
= 9999 – 399
= 9600
Hence, the greatest number of four digits divisible by 15, 25, 40 and 75 = 9600.

Approach Solution 2:
The problem statement asks to find out the greatest number of four digits which is divisible by 15, 25, 40 and 75.
We can solve the problem by analysing each of the options.
The number has to be a multiple of 5 and 2.
Therefore, the number has to have 0 as a unit digit. Hence, option E gets eliminated.
The number is also a multiple of 3.
Therefore, the sum of the digits of the number must be divisible by 3.
Option D: 9800 = 9 + 8 + 0 + 0 = 17 - NOT divisible by 3 so eliminate D
Option C: 9600 = 9 + 6 + 0 + 0 = 15 - divisible by 3. Hence, this option satisfies all the conditions. Therefore, option C is the answer.
Hence, the greatest number of four digits divisible by 15, 25, 40 and 75 = 9600.

Approach Solution 3:
The problem statement asks to find out the greatest number of four digits which is divisible by 15, 25, 40 and 75.
Therefore, the question is basically asking for multiple of the LCM of 15, 25, 40 and 75.
Let’s resolve the LCM of 15, 25, 40, and 75 to get the answer:
We know that the factors of 15 = 3 x 5
We know that the factors of 25 = 5^2
We know that the factors of 40 = 2^3 x 5
We know that the factors of 75 = 5^2 x 3
Therefore, the LCM 15, 25, 40, and 75 is 2^3 x 3 x 5^2 = 8 x 3 x 25 = 600.
The largest 4-digit number that is a multiple of 600 is 9600.
Hence, the greatest number of four digits divisible by 15, 25, 40 and 75 = 9600.

“The greatest number of four digits which is divisible by 15, 25, 40 and 75” - is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide Quantitative Review 2018”. The candidates must have a solid knowledge of mathematics in order to solve GMAT Problem Solving questions. The candidates can go through GMAT Quant practice papers to analyse varieties of questions that will enable them to achieve better ranking in the exam.

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