How Many Two-Digit Numbers Are Divisible By Both 5 and 6? GMAT Problem Solving

Question: How many two-digit numbers are divisible by both 5 and 6?

1. none
2. one
3. two
4. three
5. more than three

‘How many two-digit numbers are divisible by both 5 and 6?’ - 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 understanding. 

Solution and Explanation:

Approach Solution 1:

There is only one way to solve this problem.
Let the two-digit numbers be 10 to 99
The number divisible by 5 and 6 refers:
For 5, must end in 5 or 0
For 6: must be divisible by 2 and 3
Using the prime factors: 5, 2, and 3
LCM = (5 * 2 * 3) = 30
30 is one multiple. Multiply by increasing integers
(30 * 1 = 30)
30 * 2 = 60
30 * 3 = 90
The next multiple of 30 is 120. Too large
There are three two-digit numbers divisible by 5 and 6: 30, 60, and 90

Correct Answer: D

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