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Devil's Dozen!!!

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Re: Devil's Dozen!!!  [#permalink]

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New post 04 Jun 2017, 06:16
goalMBA1990 wrote:
Bunuel wrote:
6. Is the perimeter of triangle with the sides a, b and c greater than 30?

700+ question.

(1) a-b=15. Must know for the GMAT: the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides. So, a+b>c>15 --> a+b+c>30. Sufficient.

(2) The area of the triangle is 50. For a given perimeter equilateral triangle has the largest area. Now, if the perimeter were equal to 30 then it would have the largest area if it were equilateral. Let's find what this area would be: \(Area_{equilateral}=s^2*\frac{\sqrt{3}}{4}=(\frac{30}{3})^2*\frac{\sqrt{3}}{4}=25*\sqrt{3}<50\). Since even equilateral triangle with perimeter of 30 can not produce the area of 50, then the perimeter must be more that 30. Sufficient.

Answer: D.


hi Bunuel,
I didn't get your point mentioned in "For a given perimeter equilateral triangle has the largest area." because in statement B nothing is mentioned about type of triangle. Also please correct me if I am wrong for the statement "can't we do like this if we are assuming triangle as equilateral: (50= sqrt of 3 * a^2 ) / 4 and find what is a? Then a+a+a will give definite answer. So B is also sufficient to answer this question."

Thanks.


From (2) we have that if even an equilateral triangle with perimeter of 30 cannot have the area of 50, then the perimeter must be more that 30. So, if even an equilateral triangle with perimeter of 30 cannot have the area of 50, then the perimeter must be more that 30.
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Devil's Dozen!!!  [#permalink]

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New post 27 Oct 2018, 14:08
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Hi Bunuel! I am a bit confused for the case n=1.

If n=1 then statement one equates to 5 and statement 2 equates to 6. Hence the possible values of P are 5,2,3. none of which is a factor of 1?

If each statement is true, then P should then be a prime factor of 5 and either 2 or 3, but that's impossible?

Will be grateful if you could clarify. Thank you.

Bunuel wrote:
2. If n is a positive integer and p is a prime number, is p a factor of n!?

(1) p is a factor of (n+2)!-n! --> if \(n=2\) then \((n+2)!-n!=22\) and for \(p=2\) then answer will be YES but for \(p=11\) the answer will be NO. Not sufficient.

(2) p is a factor of (n+2)!/n! --> \(\frac{(n+2)!}{n!}=(n+1)(n+2)\) --> if \(n=2\) then \((n+1)(n+2)=12\) and for \(p=2\) then answer will be YES but for \(p=3\) the answer will be NO. Not sufficient.

(1)+(2) \((n+2)!-n!=n!((n+1)(n+2)-1)\). Now, \((n+1)(n+2)-1\) and \((n+1)(n+2)\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1. So, as from (2) \(p\) is a factor of \((n+1)(n+2)\) then it can not be a factor of \((n+1)(n+2)-1\), thus in order \(p\) to be a factor of \(n!*((n+1)(n+2)-1)\), from (1), then it should be a factor of the first multiple of this expression: \(n!\). Sufficient.

Answer: C.
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Re: Devil's Dozen!!!  [#permalink]

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New post 21 Feb 2019, 03:52
Hi, If someone could explain the 13th question in more detail it would be helpful
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Re: Devil's Dozen!!!  [#permalink]

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New post 31 Jul 2019, 02:06
Selection of n numbers from K numbers is kCn, isn't it?
And of kCn ways, only one way will be such that all numbers are in ascending order.
Therefore, the probability is = 1/kCn

Shouldn't answer be C?

Bunuel wrote:
7. Set A consists of k distinct numbers. If n numbers are selected from the set one-by-one, where n<=k, what is the probability that numbers will be selected in ascending order?

(1) Set A consists of 12 even consecutive integers;
(2) n=5.

We should understand following two things:
1. The probability of selecting any n numbers from the set is the same. Why should any subset of n numbers have higher or lower probability of being selected than some other subset of n numbers? Probability doesn't favor any particular subset.

2. Now, consider that the subset selected is \(\{x_1, \ x_2, \ ..., \ x_n\}\), where \(x_1<x_2<...<x_n\). We can select this subset of numbers in \(n!\) # of ways and out of these n! ways only one, namely \(\{x_1, \ x_2, \ ..., \ x_n\}\) will be in ascending order. So 1 out of n!. \(P=\frac{1}{n!}\).

Hence, according to the above the only thing we need to know to answer the question is the size of the subset (n) we are selecting from set A.

Answer: B.
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Re: Devil's Dozen!!!  [#permalink]

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New post 31 Jul 2019, 02:12
gvij2017 wrote:
Selection of n numbers from K numbers is kCn, isn't it?
And of kCn ways, only one way will be such that all numbers are in ascending order.
Therefore, the probability is = 1/kCn

Shouldn't answer be C?

Bunuel wrote:
7. Set A consists of k distinct numbers. If n numbers are selected from the set one-by-one, where n<=k, what is the probability that numbers will be selected in ascending order?

(1) Set A consists of 12 even consecutive integers;
(2) n=5.

We should understand following two things:
1. The probability of selecting any n numbers from the set is the same. Why should any subset of n numbers have higher or lower probability of being selected than some other subset of n numbers? Probability doesn't favor any particular subset.

2. Now, consider that the subset selected is \(\{x_1, \ x_2, \ ..., \ x_n\}\), where \(x_1<x_2<...<x_n\). We can select this subset of numbers in \(n!\) # of ways and out of these n! ways only one, namely \(\{x_1, \ x_2, \ ..., \ x_n\}\) will be in ascending order. So 1 out of n!. \(P=\frac{1}{n!}\).

Hence, according to the above the only thing we need to know to answer the question is the size of the subset (n) we are selecting from set A.

Answer: B.


I tried to elaborate a bit here: https://gmatclub.com/forum/m27-184482.html
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New post 12 Oct 2019, 16:03
Bunuel wrote:
10. There is at least one viper and at least one cobra in Pandora's box. How many cobras are there?

Quite tricky.

(1) There are total 99 snakes in Pandora's box. Clearly insufficient.

(2) From any two snakes from Pandora's box at least one is a viper. Since from ANY two snakes one is a viper then there can not be 2 (or more) cobras and since there is at least one cobra then there must be exactly one cobra in the box. Sufficient.

Answer: B.


What if there are two pairs of VC VC, then you would have two cobras? Question is asking for absolute number of cobras, but you could have infinite pair of vipre cobras right? thus E.. Maybe I am missing something.. thank you
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New post 13 Oct 2019, 00:48
DanielMx wrote:
Bunuel wrote:
10. There is at least one viper and at least one cobra in Pandora's box. How many cobras are there?

Quite tricky.

(1) There are total 99 snakes in Pandora's box. Clearly insufficient.

(2) From any two snakes from Pandora's box at least one is a viper. Since from ANY two snakes one is a viper then there can not be 2 (or more) cobras and since there is at least one cobra then there must be exactly one cobra in the box. Sufficient.

Answer: B.


What if there are two pairs of VC VC, then you would have two cobras? Question is asking for absolute number of cobras, but you could have infinite pair of vipre cobras right? thus E.. Maybe I am missing something.. thank you


We cannot have more than 1 cobra. If there are 2 cobras and 2 vipers then the second statement will NOT hold. (2) says from ANY two snakes from Pandora's box at least one is a viper. If there are 2 cobras and 2 vipers then we could have two snakes from which BOTH are cobras.
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Re: Devil's Dozen!!!   [#permalink] 13 Oct 2019, 00:48

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