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# New Set: Number Properties!!!

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Intern
Joined: 25 Jan 2019
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27 Feb 2019, 01:57
Hi Bunuel,

In 2) it says 2√x^2 is a prime number. Does that not mean that x is a 1 since -2 cannot be a prime number. I think answer is B
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Re: New Set: Number Properties!!!  [#permalink]

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27 Feb 2019, 02:01
abhishekbhat wrote:
Hi Bunuel,

In 2) it says 2√x^2 is a prime number. Does that not mean that x is a 1 since -2 cannot be a prime number. I think answer is B

If x = -1, then $$2\sqrt{x^2}=2*1=2$$, not -2.

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20 Mar 2019, 18:14
caioguima wrote:
8] Since we have an even number of elements in the set, the median will be the average of the two central numbers. Therefore, the median will be of type: (1/p + 1/q)/2 = (q+p)/(2.p.q), where p and q are primes.

(1) The reciprocal of the median, X = 2pq/(p+q) , is prime. So, pq/(p+q) = 1 (let me know if this passage was not trivial for you). Therefore: pq = p + q , which means p = q = 2. Since 1/2 is also the largest possibility of an element for S, we must have all numbers of the set equal to 1/2. Therefore, Sufficient

(2) The only terminating decimals of type 1/n, where n is a prime number are: 1/2 and 1/5. Set S has to have only elements equal to 1/2 and 1/5, which means the median can be equal to 1/2, 1/5 or something between 1/2 and 1/5. Therefore, the median is always greater than 1/5. Sufficient

if all the numbers were 1/5 , the median would have been (1/5 + 1/5)/2= 1/5.
the reciprocal of 1/5 is 5 a prime number. so we can have all 1/2 or all 1/5 . in both the cases the numbers are not less than 1/5.Please correct me where I am going wrong. option A is sufficient.
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Re: New Set: Number Properties!!!  [#permalink]

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02 Apr 2019, 22:20
Bunuel wrote:
6. Set S consists of more than two integers. Are all the integers in set S negative?

(1) The product of any three integers in the set is negative. If the set consists of only 3 terms, then the set could be either {negative, negative, negative} or {negative, positive, positive}. If the set consists of more than 3 terms, then the set can only have negative numbers. Not sufficient.

(2) The product of the smallest and largest integers in the set is a prime number. Since only positive numbers can be primes, then the smallest and largest integers in the set must be of the same sign. Thus the set consists of only negative or only positive integers. Not sufficient.

(1)+(2) Since the second statement rules out {negative, positive, positive} case which we had from (1), then we have that the set must have only negative integers. Sufficient.

HI Bunuel,
Agree with the analysis about (2) , max and min numbers shall have the same sign. However, for case of positive signs, the max and min can only be 2 and 1, with information of set consists of more than 2 integers, we can eliminate the case of both are positive signs, thus the sets have all negative integers. Ans : B

Thanks!
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Re: New Set: Number Properties!!!  [#permalink]

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02 Apr 2019, 22:58
1
greenbear wrote:
Bunuel wrote:
6. Set S consists of more than two integers. Are all the integers in set S negative?

(1) The product of any three integers in the set is negative. If the set consists of only 3 terms, then the set could be either {negative, negative, negative} or {negative, positive, positive}. If the set consists of more than 3 terms, then the set can only have negative numbers. Not sufficient.

(2) The product of the smallest and largest integers in the set is a prime number. Since only positive numbers can be primes, then the smallest and largest integers in the set must be of the same sign. Thus the set consists of only negative or only positive integers. Not sufficient.

(1)+(2) Since the second statement rules out {negative, positive, positive} case which we had from (1), then we have that the set must have only negative integers. Sufficient.

HI Bunuel,
Agree with the analysis about (2) , max and min numbers shall have the same sign. However, for case of positive signs, the max and min can only be 2 and 1, with information of set consists of more than 2 integers, we can eliminate the case of both are positive signs, thus the sets have all negative integers. Ans : B

Thanks!

Cannot a set be say {1, 2, 3, 4, 5, 7} --> the product of the smallest and largest = 1*7 = 7 = prime.
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Re: New Set: Number Properties!!!  [#permalink]

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12 Apr 2019, 06:48
Bunuel wrote:
2. If a positive integer n has exactly two positive factors what is the value of n?

Notice that, n has exactly two positive factors simply means that n is a prime number, so its factors are 1 and n itself.

(1) n/2 is one of the factors of n. Since n/2 cannot equal to n, then n/2=1, thus n=2. Sufficient.

(2) The lowest common multiple of n and n + 10 is an even number. If n is an odd prime, then n+10 is also odd. The LCM of two odd numbers cannot be even, therefore n is an even prime, so 2. Sufficient.

With respect to this question, are we making an assumption that n doesn't have any negative factors? The question stem is silent on the negative factors of n.
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Re: New Set: Number Properties!!!  [#permalink]

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12 Apr 2019, 07:06
tejasvis7 wrote:
Bunuel wrote:
2. If a positive integer n has exactly two positive factors what is the value of n?

Notice that, n has exactly two positive factors simply means that n is a prime number, so its factors are 1 and n itself.

(1) n/2 is one of the factors of n. Since n/2 cannot equal to n, then n/2=1, thus n=2. Sufficient.

(2) The lowest common multiple of n and n + 10 is an even number. If n is an odd prime, then n+10 is also odd. The LCM of two odd numbers cannot be even, therefore n is an even prime, so 2. Sufficient.

With respect to this question, are we making an assumption that n doesn't have any negative factors? The question stem is silent on the negative factors of n.

Factors (at least on GMAT) are positive divisors.
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Re: New Set: Number Properties!!!   [#permalink] 12 Apr 2019, 07:06

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