Question: How many positive integers less than 500 are divisible by 6, 8, or 10?

     A. 125
     B. 143
     C. 147
     D. 151
     E. 195

Answer: D

Approach Solution (1):
The question can be solved using venn diagram approach. The only catch in the question is that the factors are not prime. So while subtracting the overlapping part, we have To take the LCM unlike multiplication in prime numbers. Because 24 will also be divisible by both 6 and 8 it need not necessarily be 48.
So what we need to see is
Numbers divisible by 6
+ Numbers divisible by 8
+ Numbers divisible by 10
- Numbers divisible by 24
- Numbers divisible by 40
- Numbers divisible by 30
+ Numbers divisible by 120
That is
50 + 62 + 83 – 16 – 12 – 20 + 4 = 151
Correct option: D

Approach Solution (2):The only difference is when 10 is taken on it own, as shown:
When divided by 6: 83
When divided by 8: 62
When divided By 10: 50
When divided by LCM (6, 8): 20
When divided by LCM (8, 10): 12
When divided by LCM (6, 10): 16
When divided by LCM (6, 8, and 10): 4
Total = 83 + 62 + 50 – 20 – 12 – 16 + 4 + 1 = 151
Correct option: D

Approach Solution (3):
Numbers divisible by 6 + Numbers divisible by 8 + Numbers divisible by 10 - Numbers divisible by 24 - Numbers divisible by 40 - Numbers divisible by 30 + Numbers divisible by 120
That is
50 + 62 + 83 – 16 – 12 – 20 + 4 = 151
Correct option: D

“How many positive integers less than 500 are divisible by 6, 8, or 10?”- 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 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.

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