Set S consists of n consecutive positive integers. If n 3, what is

Question

Set S consists of n consecutive positive integers. If n > 3, what is the value of n?

(1) The number of multiples of 2 contained in set S is equal to the number of multiples of 3 contained in set S.
(2) n is odd.

ArunSharma12 · Answer

statement 1: 
S =   or any other set starting with multiple of LCM of 2 and 3 and having four numbers satisfies #M(2)=#M(3).
this gives me n =4.

statement 2:
n is odd. 
not sufficient.

Ans: A

firas92 · Answer

I had a similar approach but assuming that this is a good quality question, we cannot have n=4 and n odd since the gmat does not give us contradicting statements.

S={3,4,5,6,7,8,9} (n=7)
S={5,6,7,8,9} (n=5)
S={6,7,8,9} (n=4)

Combining, n can take at least two value

So IMO the answer must be E

Posted from my mobile device

Archit3110 · Answer

given that n>3
#1
 The number of multiples of 2 contained in set S is equal to the number of multiples of 3 contained in set S.
two possiblities of n 
case 1; 3,4,5,6 ; n=4
case 2; 3,4,5,6,7,8,9 ; n= 7
insufficeint
#2
n is odd
clearly insufficient ; 
from 1 &2
for all values of n as odd ; we get differenct values of multiples of 2 and multiples of 3
IMOE ; sufficient

RahulHGGmat · Answer

Hi  Bunuel ,

Greetings of the day and Happy Diwali in advance.

I figured the correct answer option for this one. However, it took some extra time. Request you to share your line of thought as it might reduce the time taken to attempt this question.

Looking for your response ahead.

Bunuel · Answer

This question is a part of  Are You Up For the Challenge: 700 Level Questions  collection.

khumoyuns · Answer

try   and   
both of these sets satisfy both 1 and 2.

so E

RICHA1189 · Answer

Set S consists of n consecutive positive integers. If n > 3, what is the value of n?

(1) The number of multiples of 2 contained in set S is equal to the number of multiples of 3 contained in set S.
Multiples of any number are infinite, hence set is not defined. 
Insufficient

(2) n is odd.
No new information .. can be 5 , 7, 9,11 …. And so on
Insufficient

Combining A AND B = no new information .

Answer is E

jack_tay · Answer

How did you get "The number of multiples of 2 contained in set S is equal to the number of multiples of 3 contained in set S.
2 possiblities of n case 1; 3,4,5,6 ; n=4"?

5 is not a multiple of 2 or 3?

chetan2u · Answer

Here, the positive consecutive integers could start from anywhere and end anywhere.

(1) The number of multiples of 2 contained in set S is equal to the number of multiples of 3 contained in set S.
Every 2nd number is multiple of 2 and every 3rd number is a multiple of 3.
Lets take different cases:
n=4: First and third are multiple of 2 and First and Fourth are multiple of 3. The first will be even multiple of 3 => 6,7,8,9 or 18,19,20,21
n=5: second and fifth or First and Fourth are multiple of 3, while second and fourth are multiple of 2.=> 5,6,7,8,9 or 15,16,17,18,19
n=6: NOT possible as there will always be 3 multiples of 2 and 2 multiples of 3
n=7: 2nd, 4th and 6th are multiples of 2 while 1st, 4th and 7th are multiples of 3.=> 9,10,11,12,13,14,15 
No more possible values of n as we can see
n=8 Not possible as multiples of 2 are 4, while multiples of 3 will be 2 or 3.
n=9 Not possible as multiples of 2 are 4 or 5, while multiples of 3 will be 3.
Insuff

(2) n is odd
n could be anything
Insuff

Combined
n can be 5 or 7.
Insuff

E

bumpbot · Answer

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Set S consists of n consecutive positive integers. If n > 3, what is

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