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Re: If a is divisible by 5!, then a/4 must be [#permalink]

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03 Nov 2016, 02:23

Bunuel wrote:

If a is divisible by 5!, then a/4 must be

I. an odd integer II. a multiple of 3 III. a multiple of 10

A. I only B. II only C. III only D. I and III only E. II and III only

IMO E If a is divisible by 5! then a must be of the form 120*k when k is an integer 1, 2, 3 then a can be 120, 240, 360, 480.... a/4= 30, 60, 90, 120..... from this we can say a/4 satisfies E.

If a is divisible by 5!, then a/4 must be [#permalink]

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03 Nov 2016, 02:38

Nice Question. This is a must be true question. Statement 1 => a/4 must be odd Hmm Let a = 5! => clearly a/4 is even> Hence 1 must not be true. Statement 2 => of course it will be true as a must contain a 3 => a/4 must be a multiple of 3 statement 3 => Officourse the least value of a is 5! and 5!/4 is clearly divisibly by 10 Hence E
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Re: If a is divisible by 5!, then a/4 must be [#permalink]

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03 Nov 2016, 07:14

If a is divisible by 5! ie a is divisible by 2,3,4,5. So a/4 is divisible by 2,3,5.

I) Is it odd integer? No, as it is still divisible by 2 II) Is it multiple of 3? Yes, as it is divisible by 3 III) Is it multiple of 10? Yes, as it is divisible by 2 and 5

Re: If a is divisible by 5!, then a/4 must be [#permalink]

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03 Nov 2016, 07:22

Bunuel wrote:

If a is divisible by 5!, then a/4 must be

I. an odd integer II. a multiple of 3 III. a multiple of 10

A. I only B. II only C. III only D. I and III only E. II and III only

first of all, 5! = 1*2*3*4*5

a/4 = 1*2*3*5 - an even number. I is not true. A and D are out. II - we have a factor of 3, so yes, IT IS a multiple of 3. C is out. III - we have a factor of 2 and a factor of 5 - so yes, IT IS a multiple of 10. B is out.

I. an odd integer II. a multiple of 3 III. a multiple of 10

A. I only B. II only C. III only D. I and III only E. II and III only

Since 5! = 5 x 4 x 3 x 2 x 1 = 120, and a is divisible by 5!, we know that a is divisible by some multiple of 120. However since we are determining what MUST be true, we can set a equal to the smallest positive multiple of 120, which is 120.

Thus a/4 = 120/4 = 30.

Now we can analyze each Roman numeral.

I. a/4 is an odd integer

Since 120/4 = 30, a/4 does not have to result in an odd integer. Roman numeral one is not correct.

II. a/4 is a multiple of 3

Since 120/4 = 30, a/4 will always be a multiple of 3, Roman numeral II is correct.

III. a/4 is a multiple of 10

Since 120/4 = 30, a/4 will always be a multiple of 10, Roman numeral III is correct.

Answer: E
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I. an odd integer II. a multiple of 3 III. a multiple of 10

A. I only B. II only C. III only D. I and III only E. II and III only

a is divisible by 5! i.e. a is a multiple of 120

i.e. then a/4 must be a multiple of 120/4 = multiple of 30 Which is Even, a multiple of 3 and a multiple of 10 as well

Hence Answer: Option E
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