Which of the Following Represents the Largest 4 Digit Number GMAT Problem Solving

Question: Which of the following represents the largest 4 digit number that can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33 & 54.

1. 9123
2. 9383
3. 8727
4. 1067
5. None Of The Above

“Which of the following represents the largest 4 digit number”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

This question has only one approach.

We need to find the LCM of the given numbers 12, 14, 21, 33, and 54.
12= 2*2*3
14= 2*7
21= 3*7
33= 3*11
54= 3*2*3*3
So the maximum powers of all the prime numbers are:
2=2
3=3
7=1
11=1
Therefore LCM=2^2*3^3*7^1*11^1=8316
So, 8316-7249=1067. Thus, if we add 1067 to 7249, the number will be divisible by all the above-given numbers. As 1067 is not the greatest 4-digit number, so it does not satisfy the condition.
Taking the next number that will be divisible is:
1067+8316=9383
Therefore, adding 9383 to 7249 will give us a number that will be divisible by all the given numbers.
It can also be seen that 9383 is the greatest 4-digit number that satisfies this condition. 
Correct Answer: B

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