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If n is the product of three consecutive intergers, and n is divisible

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If n is the product of three consecutive intergers, and n is divisible  [#permalink]

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New post 12 Feb 2016, 03:51
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If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???
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Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

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New post 12 Feb 2016, 04:03
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tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


Hi,
first you have to see the minimum value and ways..
1) 5*6*7= 2*3*5*7
2) 6*7*8= 2^4*3*7
3) 7*8*9..=2^3*7*9..

what is the common in the three terms..
2*3*7..

lets find the choice which contains any term beyond these three..
(A) 6
2*3= so Always

(B) 14
2*7= again always

(C) 21
3*7= again always

(D) 28
2*2*7..
may be there, may not be there
CORRECT

(E) 42
2*3*7= again always

ans D
hope it helps
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Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

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New post 12 Feb 2016, 04:21
chetan2u wrote:
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


Hi,
first you have to see the minimum value and ways..
1) 5*6*7= 2*3*5*7
2) 6*7*8= 2^4*3*7
3) 7*8*9..=2^3*7*9..

what is the common in the three terms..
2*3*7..

lets find the choice which contains any term beyond these three..
(A) 6
2*3= so Always

(B) 14
2*7= again always

(C) 21
3*7= again always

(D) 28
2*2*7..
may be there, may not be there
CORRECT

(E) 42
2*3*7= again always

ans D
hope it helps


thx a lot I completely understand it !
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Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

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New post 12 Feb 2016, 04:23
2
2
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


The product of k consecutive integers is always divisible by k! (factorial of k).

So, according to the above, the product of 3 consecutive integers is divisible by 3! = 6. Since n is also divisible by 7, then it must be divisible by the LCM of 6 and 7, which is 42. Therefore n is divisible by 6, 14, 21 and 42. By POE the correct answer must be D.

Answer: D.
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Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

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New post 25 Mar 2017, 13:01
tjkim88 wrote:
If n is the product of three consecutive integers, and n is divisible by 7, which of the following is not necessarily a divisor of n ?


(A) 6

(B) 14

(C) 21

(D) 28

(E) 42

can you explain why???


28 divides only if the sequence includes a multiple of 4
it works for 6,7,8 and 7,8,9, but not for 5,6,7
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Re: If n is the product of three consecutive intergers, and n is divisible  [#permalink]

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New post 04 Nov 2018, 02:48
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Re: If n is the product of three consecutive intergers, and n is divisible   [#permalink] 04 Nov 2018, 02:48
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