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How many positive integers· less than 20 are equal to the su

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How many positive integers· less than 20 are equal to the su [#permalink] New post 03 Mar 2019, 10:44
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Question Stats:

46% (01:50) correct 53% (00:56) wrong based on 13 sessions
How many positive integers· less than 20 are equal to the sum of a positive multiple of 3 and a positive multiple of 4 ?

(A) Two

(B) Five

(C) Seven

(D) Ten

(E) Nineteen
[Reveal] Spoiler: OA

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Re: How many positive integers· less than 20 are equal to the su [#permalink] New post 04 Mar 2019, 07:01
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Carcass Array[WROTE]:
How many positive integers· less than 20 are equal to the sum of a positive multiple of 3 and a positive multiple of 4 ?

(A) Two

(B) Five

(C) Seven

(D) Ten

(E) Nineteen


We can list and count the possible outcomes

3 + 4 = 7
2(3) + 4 = 10
3(3) + 4 = 13
4(3) + 4 = 16
5(3) + 4 = 19
3 + 2(4) = 11
3 + 3(4) = 15
2(3) + 2(4) = 14
2(3) + 3(4) = 18
3(3) + 2(4) = 17

There are 10 possible outcomes.

Answer: D

Cheers,
Brent
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Re: How many positive integers· less than 20 are equal to the su [#permalink] New post 04 Mar 2019, 10:51
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Re: How many positive integers· less than 20 are equal to the su [#permalink] New post 09 Mar 2019, 12:07
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The positive multiples of 4 less than 20 are:

4, 8, 12, 16

Now we just add 3 to them until we can't anymore without going over 20.

For instance, we keep adding 3 to 4 and get: 7, 10, 13, 16, and 19.

We could also add 3 to 8 and get: 11, 14, and 17.

Next, adding to 12: 15, and 18.

And finally, add 3 to 16 to get 19. But we already counted that one, because 19 = 16 + 3 and 15 + 4.

Add them up and we get 10 in all.
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Re: How many positive integers· less than 20 are equal to the su [#permalink] New post 07 Nov 2019, 18:51
Hello

Please help me with the following
Since we are looking for positive integers· less than 20, that are equal to the sum of a positive multiple of 3 and a positive multiple of 4, Why 18+4 and 3+16 are not considered? The problem do not mention that the sum of the multiples has to be less than 20.
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Re: How many positive integers· less than 20 are equal to the su [#permalink] New post 08 Nov 2019, 04:13
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How many positive integers less than 20

Which means that the numbers MUST be under 20. Also the constraint is that they must be the sum of 3 and 4 or multiple of those but ALWAYS the resulkt to take into account must be under 20, excluded.

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Re: How many positive integers· less than 20 are equal to the su   [#permalink] 08 Nov 2019, 04:13
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