Big Book Question - Incorrect Options?

GRE Quant Problem Solving
1

Hello! Please see the attached screenshot where Greg explains that the answer is 10.
However, when I brute force it I am getting an answer that is different and is not available in the options:

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Here is my explanation:

Multiples of 3: 3, 6, 9, 12, 15, 18
Multiples of 4: 4, 8, 12, 16

Possible combinations:

  1. 3 + 4 = 7
  2. 3 + 8 = 11
  3. 3 + 12 = 15
  4. 3 + 16 = 19
  5. 6 + 4 = 10
  6. 6 + 8 = 14
  7. 6 + 12 = 18
  8. 9 + 4 = 13
  9. 9 + 8 = 17
  10. 12 + 4 = 16
  11. 15 + 4 = 19

Can you tell me where I am going wrong? I am getting 11 answers and the option has 10. Greg in the video doesn’t go further than 8 selections since its obvious that nothing below 8 works and 19 is too big, so the answer is option D - 10.

2

we’ll count 19 only once

3

Could you please explain why? Its two different combination of digits that are forming 19.
Maybe I am making a reading mistake, here.

4

Its two different combination of digits that are forming 19.

The question is asking the number of positive integers, not combinations.

5

Ah got it! I see where I made the mistake.
Thank you so much!