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If 1 ≤ n ≤ 100,
[#permalink]
21 Feb 2020, 11:14

Expert Reply

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Question Stats:

If \(1 ≤ n ≤ 100\), and \(\frac{n+7}{2}\) is a multiple of 4 but not a multiple of 3, then which of the following could be true?

Indicate all such statements.

A. n is even

B. n is odd

C. n is prime

D. n is a multiple of 3

E. n is a multiple of 4

Kudos for the right answer and explanation

_________________

Indicate all such statements.

A. n is even

B. n is odd

C. n is prime

D. n is a multiple of 3

E. n is a multiple of 4

Kudos for the right answer and explanation

_________________

Re: If 1 ≤ n ≤ 100,
[#permalink]
05 Mar 2020, 18:19

1

For this question, when n is even (n+7) is always odd, so it is no divisible by 2 and not mutiple of 4 as well.

when n is odd, choose easy n=1..

when n is prime, choose n =73..

and for multiple of 3, n= 9.

when n is odd, choose easy n=1..

when n is prime, choose n =73..

and for multiple of 3, n= 9.

Re: If 1 ≤ n ≤ 100,
[#permalink]
10 Mar 2020, 08:25

1

1

Bookmarks

If (n+7)/2 is a multiple of 4, then n+7 is a multiple of 8.

All multiples of 8 are even, and the sum of two numbers is even only if both are odd or both are even. Since 7 is odd, n is odd too.

n can be prime. To check this easily, start with multiples of 8. If n+7=8, n=1. If n+7=16, n=9. If n+7=24, n=17, which is a prime number.

Also, as seen above, if n+7=16, n=9, which is a multiple of 3.

All multiples of 8 are even, and the sum of two numbers is even only if both are odd or both are even. Since 7 is odd, n is odd too.

n can be prime. To check this easily, start with multiples of 8. If n+7=8, n=1. If n+7=16, n=9. If n+7=24, n=17, which is a prime number.

Also, as seen above, if n+7=16, n=9, which is a multiple of 3.

Re: If 1 ≤ n ≤ 100,
[#permalink]
10 Mar 2020, 09:13

What if n=33 ? It satisfies D and E, but not C. It is multiple of 3.

Re: If 1 ≤ n ≤ 100,
[#permalink]
10 Mar 2020, 09:25

1

sukrut96 wrote:

What if n=33 ? It satisfies D and E, but not C. It is multiple of 3.

It's asking for any possible values of n satisfying the given conditions. n isn't a fixed number.

Re: If 1 ≤ n ≤ 100,
[#permalink]
26 Oct 2021, 14:28

1

only B is right

1 is not prime number

and is unable to divided by 3

1 is not prime number

and is unable to divided by 3

If 1 n 100,
[#permalink]
Updated on: 05 Sep 2022, 07:13

1

n+7 is a multiple of 8

also n+7 is NOT a multiple of 6

List the multiples of 8 and corresponding "n."

Put an x next to any that are also multiples of 6, because we can't use those

multiples of 8 | n (subtract 7)

----------------------

8 ------------> 1

16 -----------> 9 - multiple of 3

24x

32 -----------> 25

40 -----------> 33

48x

56 -----------> 49

64 -----------> 57

72x

80 -----------> 73 - prime

88 -----------> 81

96x

Let's take the answer choices one at a time:

We can see n is always odd, never even. We could have deduced this anyway, since a multiple of 8 is even, and subtracting 7 will always produce an odd. Thus A is false, B is true.

For C, we can see that 73 is prime.

For D, we can see that 9 is a multiple of 3.

For E, since all values are odd, we know they will not be multiples of 4.

Thus, the correct answers are B, C, D.

also n+7 is NOT a multiple of 6

List the multiples of 8 and corresponding "n."

Put an x next to any that are also multiples of 6, because we can't use those

multiples of 8 | n (subtract 7)

----------------------

8 ------------> 1

16 -----------> 9 - multiple of 3

24x

32 -----------> 25

40 -----------> 33

48x

56 -----------> 49

64 -----------> 57

72x

80 -----------> 73 - prime

88 -----------> 81

96x

Let's take the answer choices one at a time:

We can see n is always odd, never even. We could have deduced this anyway, since a multiple of 8 is even, and subtracting 7 will always produce an odd. Thus A is false, B is true.

For C, we can see that 73 is prime.

For D, we can see that 9 is a multiple of 3.

For E, since all values are odd, we know they will not be multiples of 4.

Thus, the correct answers are B, C, D.

Re: If 1 n 100,
[#permalink]
05 Sep 2022, 07:12

punindya wrote:

If (n+7)/2 is a multiple of 4, then n+7 is a multiple of 8.

All multiples of 8 are even, and the sum of two numbers is even only if both are odd or both are even. Since 7 is odd, n is odd too.

n can be prime. To check this easily, start with multiples of 8. If n+7=8, n=1. If n+7=16, n=9. If n+7=24, n=17, which is a prime number.

Also, as seen above, if n+7=16, n=9, which is a multiple of 3.

All multiples of 8 are even, and the sum of two numbers is even only if both are odd or both are even. Since 7 is odd, n is odd too.

n can be prime. To check this easily, start with multiples of 8. If n+7=8, n=1. If n+7=16, n=9. If n+7=24, n=17, which is a prime number.

Also, as seen above, if n+7=16, n=9, which is a multiple of 3.

You cannot use n=17 as your prime, since if n=17, 17+7 = 24, which is divisible by 6. The prompt states that n+7 is not divisible by 6. Luckily, later in the list, we see n=73 IS a prime, so the answer is still that primes are possible.

gmatclubot

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