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A set S contains the following elements: {7, 11, 15, 19, 23, x}. What

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A set S contains the following elements: {7, 11, 15, 19, 23, x}. What [#permalink]

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A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?

(1) The elements are in arithmetic progression.
(2) x is prime.
[Reveal] Spoiler: OA

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Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What [#permalink]

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New post 14 Feb 2016, 12:28
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Set S {7, 11, 15, 19, 23, x}
(1) The elements are in arithmetic progression.
Common different in the set = 4
x can either be 3 or 27
Not sufficient
(2) x is prime
Not sufficient as x can be any prime number
Combining 1 and 2 , we get
x=3
Answer C
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Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What [#permalink]

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New post 14 Feb 2016, 23:59
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?

(1) The elements are in arithmetic progression.
(2) x is prime.


In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), x=3, 27, which is not unique and not sufficient.
For 2), x=3, 29,.. which is not unique and not sufficient.
When 1) & 2), x=3, which is unique and sufficient.
Therefore, the answer is C.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What [#permalink]

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New post 10 Sep 2017, 06:24
It is a tricky question that made me consider x is the greatest in the set

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Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What [#permalink]

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New post 28 Sep 2017, 09:17
Skywalker18 wrote:
Set S {7, 11, 15, 19, 23, x}
(1) The elements are in arithmetic progression.
Common different in the set = 4
x can either be 3 or 27
Not sufficient
(2) x is prime
Not sufficient as x can be any prime number
Combining 1 and 2 , we get
x=3
Answer C


How x can have the value of 3? since its an progression with the difference of the 4, ideally 23+4 = 27 should be the value right?
Can you please explain?

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Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What [#permalink]

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New post 30 Sep 2017, 03:49
Bunuel wrote:
A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?

(1) The elements are in arithmetic progression.
(2) x is prime.


Value based Qs
St-1 If the elements are in AP then x can be 3 or 27. not unique value. insufficient.
St-2 X is prime, then X can be any prime no.- insufficient
Combine- X is prime and set is in AP the X must be 3 unique ans. Sufficient
Ans is C

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Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What   [#permalink] 30 Sep 2017, 03:49
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A set S contains the following elements: {7, 11, 15, 19, 23, x}. What

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