What is the Largest Five-Digit Number which is Divisible by 17? GMAT Problem Solving

Question: What is the largest five-digit number which is divisible by 17?

1.  99,999
2. 99,994
3. 99,993
4. 99,992
5. 99,991

‘What is the largest five-digit number which is divisible by 17?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

Breaking the five-digit numbers into multiples of 17, we get that 99,999 is the highest five-digit which is divisible by 17.
So to get five-digit numbers we can get the multiples of 17:
Therefore, 5000 * 17 = 85,000. [As 6 * 17 = 102]
Case 1: We get 99,999 - 85,000 = 14,999 (smaller number)
So the closest number in this case will be 17 * 8 = 136.}
That implies 17 * 800 = 13,600
Case 2: Now to get another smaller number, we can 14,999 - 13,600 = 1,399. So the next Closer number will be 17 * 8 = 136
That implies 17 * 80 = 1,360
Case 3: Now to get an even smaller number, we can 1,399-1,360= 39.So the next Closer number 39 will be divisible by 17 is 34.
Now that we have an excess of 5 and so, 99,999 - 5 = 99,994. This is the largest number divisible by 17. Hence option B is the correct answer.

Correct Answer: B

Approach Solution 2:

We can find the greatest number of 5-digit numbers by multiplying with 17.
So, the largest 5-digit number is 99999
Then, 99999= 17 x 5882 + 5
99994 = 17 x 5882
This shows that 99994 is divisible by 17 and the next number that is divisible by 17 will be a 6-digit number. Therefore 99994 is the highest 5-digit number that is divisible by 17. Hence option B is the correct answer.

Correct Answer: B

Approach Solution 3:

Largest 5 digit number = 99999
Now,
99999 = 17 × 5882 + 5
99994 = 17 × 5882
It shows that 99994 is divisible by 17 and the next number divisible by 17
6 digit number
So, 99994 is the highest 5 digit number divisible by 17.

Correct Answer: B

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