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Re: If 1 ≤ n ≤ 100, [#permalink]
What if n=33 ? It satisfies D and E, but not C. It is multiple of 3.
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Re: If 1 ≤ n ≤ 100, [#permalink]
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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.
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Re: If 1 ≤ n ≤ 100, [#permalink]
1
only B is right
1 is not prime number
and is unable to divided by 3
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If 1 n 100, [#permalink]
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.

Originally posted by KC15 on 05 Sep 2022, 07:10.
Last edited by KC15 on 05 Sep 2022, 07:13, edited 1 time in total.
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Re: If 1 n 100, [#permalink]
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.




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.
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Re: If 1 n 100, [#permalink]
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