The Greatest 6-Digit Number When Divided by 6, 7 ,8 , 9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8 Respectively GMAT Problem Solving

Question: What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 8 respectively?

1. 456780
2. 678910
3. 997479
4. 997918
5. 997920

“The Greatest 6-Digit Number When Divided by 6,7,8,9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8 Respectively GMAT Problem Solving” - 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. 

Correct Answer: D

Approach Solution:

There is only one approach to solve the problem statement

Find out:

• The greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 8 respectively.

When a positive integer is divided by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so D is the only possible answer.

Or we could use the remainder by 9 -- if we want to know a large number's remainder when we divide by 9. We can sum its digits, and then take the remainder of that sum when we divide by 9.

First we will calculate the LCM of the given numbers.
The LCM of (6, 7, 8, 9, 10) = 2520

Now, we will check one option within the provided 5.

Options A, B and E are divisible by 10 i.e remainder is Zero.
C gives a remainder of 9 when divided by 10.
Only D gives a remainder of 8 when divided by 10
Hence, we will check option D first.

Dividing 999999 by 2520, we get 2079 as remainder.

Applying the common difference:
The common difference for remainders is 2;
6 - 4 = 2
7 - 5 = 2

Therefore the required number is:
= 999999 - 2079 - 2
= 997918.

Correct Answer: D

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