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Which of these must the factor of the product of four consecutive even

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Which of these must the factor of the product of four consecutive even  [#permalink]

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New post 05 Aug 2016, 20:43
1
8
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (02:38) correct 47% (02:08) wrong based on 83 sessions

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Which of these must the factor of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80

A) 1,2 only
B) 2,3 only
C) 1,2,3 only
D) 1,2,3,4 only
E) All of them

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Re: Which of these must the factor of the product of four consecutive even  [#permalink]

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New post 06 Aug 2016, 01:28
Product of every 4 even consecutive multiples will have atleast 2^3 and 3 as its prime factor.

There 1,2,3 and 4 satisfy the condition.

1) 48 --> 2^4 * 3
2) 64 --> 2^6
3) 96 -->2^5 * 3
4) 192 -->2^6 * 3
5) 80 --> 2^4 * 5

5 may or may not hold true. Consider 4 multiples as 2,4,6 and 8. Here we don't have any 5 as a factor for the product of these multiples but for 80 we need one 5 as a factor, hence, FALSE.
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Re: Which of these must the factor of the product of four consecutive even  [#permalink]

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New post 07 Aug 2016, 22:25
Let the four variables be a< b< c< d.

Assume a worst case scenario where the a equal to a prime number (hence odd).

therefore

a = divisible by 1
b = a + 1 (divisible by 2)
c = a + 3 (divisible by 3)
d = a + 4 (divisible by 4)

therefore

each answer choice must be divisible by 2 x 3 x 4 = 24

only 80 is not divisible. Therefore answer = D

stonecold wrote:
Which of these must the factor of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80

A) 1,2 only
B) 2,3 only
C) 1,2,3 only
D) 1,2,3,4 only
E) All of them
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Posts: 2638
Schools: Boston U '20 (M)
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Re: Which of these must the factor of the product of four consecutive even  [#permalink]

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New post 16 Jan 2017, 00:28
2
Here is what id did in this Question ->
Let the 4 consecutive evens be ->
2n
2n+2
2n+4
2n+6

Taking their product => 2n*(2n+2)*(2n+4)*(2n+6)=> 2^4 n(n+1)(n+2)(n+3)

Property in action -> Product of n consecutive integers is always divisible by n!

Hence => 2^4 n(n+1)(n+2)(n+3)=2^4*24k
For some integer k.
Clearly Options 1,2,3,4 must be factors of 2^4*24k
But 80 has a 5 in it so it may or may nor be the factor of 2^4*24k
Hence we ned to exclude E from the answer choice.

Hence D.

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Which of these must the factor of the product of four consecutive even  [#permalink]

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New post 12 Mar 2018, 12:46
stonecold wrote:
Which of these must the factor of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80

A) 1,2 only
B) 2,3 only
C) 1,2,3 only
D) 1,2,3,4 only
E) All of them


say 2*4*6*8
this gives us
6*8=48
2*4*8=64
2*6*8=96
4*6*8=192
but not 5, so not 80
1,2,3,4 only
D
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Which of these must the factor of the product of four consecutive even &nbs [#permalink] 12 Mar 2018, 12:46
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Which of these must the factor of the product of four consecutive even

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