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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A set S contains the following elements: {7, 11, 15, 19, 23, x}. What

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

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Difficulty:   55% (hard)

Question Stats: 46% (00:51) correct 54% (00:52) wrong based on 138 sessions

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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.

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

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

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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.

 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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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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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

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

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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]

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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.

S = [7,11,15,19,23,x]. To know the value of x, we should 1st know the position of x and second check, if the elements are in any sequence or not. We see, difference between two elements is 4.

Option 1 says, the elements are in AP. Difference between two elements is 4. So x must be either 27 or 3. INSUFFICIENT.
Option 2 says, x is prime. However we dont know its position.
Option 1+2, the element must be 3.

Thus correct option is 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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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.

I am learning this technique but I am still far from being good at it.

Statement 1: The elements are in AP. So we think x is 27. Great.

Statement 2: x is prime. Well, At first you think what do I do with this? But then why will they say x is prime? Also. 27 is not Prime. That means x can be 3 too. And in this case you need both to realize x is 3.
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You are missing on great learning if you don't know what this is: Project SC Butler Re: A set S contains the following elements: {7, 11, 15, 19, 23, x}. What   [#permalink] 12 Nov 2019, 14:00
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