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Bunuel
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How many positive integers· less than 20 are equal to the sum of a pos 07 Mar 2019, 00:05
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

65% (02:15) correct 35% (02:06) wrong based on 656 sessions

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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
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D
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How many positive integers· less than 20 are equal to the sum of a pos Updated on: 01 Apr 2019, 00:39
Originally posted by Archit3110 on 07 Mar 2019, 04:10.
Last edited by Archit3110 on 01 Apr 2019, 00:39, edited 2 times in total.
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Bunuel
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
Show more

Shreya9816 and danish07
question has asked +ve integers<20 are equal to sum of multiples of 3 & 4
step 1 : determine multiple of 3 & 4 which are <20
multiple of 3 ; 3,6,9,12,15,18 = 6
multiple of 4 ; 4,8,12,16,20 = 5 ;
now we got to add the multiples of 3 & 4 and determine pairs which are <20
pairs will be (4,3),(4,6)(4,9)(4,12),(4,15) ; (8,3),(8,6),(8,9); (12,3),(12,6) ; (16,3); total 11 pairs
but (4,15 ) & (16,3) give same sum viz 19 so only 1 pair to be considered
total pairs left 10
IMO D
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BrentGMATPrepNow
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How many positive integers· less than 20 are equal to the sum of a pos 08 Aug 2020, 06:34
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Bunuel
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
Show more

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

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How many positive integers· less than 20 are equal to the sum of a pos 09 Aug 2020, 04:58
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Bunuel
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

Shreya9816 and danish07
question has asked +ve integers<20 are equal to sum of multiples of 3 & 4
step 1 : determine multiple of 3 & 4 which are <20
multiple of 3 ; 3,6,9,12,15,18 = 6
multiple of 4 ; 4,8,12,16,20 = 5 ;
now we got to add the multiples of 3 & 4 and determine pairs which are <20
pairs will be (4,3),(4,6)(4,9)(4,12),(4,15) ; (8,3),(8,6),(8,9); (12,3),(12,6) ; (16,3); total 11 pairs
but (4,15 ) & (16,3) give same sum viz 19 so only 1 pair to be considered
total pairs left 10
IMO D
Show more


Hi,

But they haven't asked unique pairs. So why will the pair which gives same sum will be eliminated.?


Thank you.

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How many positive integers· less than 20 are equal to the sum of a pos 20 Sep 2020, 23:27
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10 Numbers less than 20 are Possible using a Positive Multiple of 3 + Positive Multiple of 4
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How many positive integers· less than 20 are equal to the sum of a pos 21 Sep 2020, 00:51
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Bunuel
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

]
question has asked +ve integers<20 are equal to sum of multiples of 3 & 4
step 1 : determine multiple of 3 & 4 which are <20
multiple of 3 ; 3,6,9,12,15,18 = 6
multiple of 4 ; 4,8,12,16,20 = 5 ;
now we got to add the multiples of 3 & 4 and determine pairs which are <20
pairs will be (4,3),(4,6)(4,9)(4,12),(4,15) ; (8,3),(8,6),(8,9); (12,3),(12,6) ; (16,3); total 11 pairs
but (4,15 ) & (16,3) give same sum viz 19 so only 1 pair to be considered
total pairs left 10
IMO D


Hi,

But they haven't asked unique pairs. So why will the pair which gives same sum will be eliminated.?


Thank you.


Posted from my mobile device
Show more


Pairs are not asked here. Only number of integers is asked. Since 19 is repeated but still we will count is as one.
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How many positive integers· less than 20 are equal to the sum of a pos 19 Dec 2020, 07:58
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Similar question : https://gmatclub.com/forum/how-many-pos ... %20numbers.
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How many positive integers· less than 20 are equal to the sum of a pos 07 Mar 2022, 08:30
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Bunuel
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
Show more



Since the answers have been given already. Ill just mention why we subtract one pair where the sum is 19.
Quite simply put, the question stem mentions clearly "How many positive integers" mening they are asking for the summed up value not the unique pairs of multiples. and as shown by my friends before, we get 19 in 2 pairs. so taking just the value once we subtract one of the pairs from 11 pairs in total giving the answer as 10 integers.
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How many positive integers· less than 20 are equal to the sum of a pos 09 Apr 2025, 23:06
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Why aren't we counting all the pairs involving 0, at the end of the day zero is a multiple of every number.
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How many positive integers· less than 20 are equal to the sum of a pos 09 Apr 2025, 23:32
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PietroCavallo
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

Why aren't we counting all the pairs involving 0, at the end of the day zero is a multiple of every number.
Show more

0 is not a positive number.


ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer.

3. Zero is neither positive nor negative (the only one of this kind)

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x)

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).



2. Properties of Integers



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
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