Numbers -quant toughie

[hemant.maddineni]

If x is a prime number, what is the value of x?

(1) 2x + 2 is the cube of a positive integer.

(2) The average of any x consecutive integers is an integer.

The OA is E.

However I think that B is sufficient to answer this question.
Since x is a prime number x belongs to the set {2,3,5,7,11.....}

Now option (2) says that average of any x consecutive integers is a integer.
This property is true only for 3.

lets take 2 consecutive integers --- { 0 1 } -- average is not integer.
lets take 5 consecutive integers --- { -1 , 0 , 1 , 2, 3 } -- average is not an integer.
The same case hold for all other prime numbers except 3. => {0,1,2} {-1,0,1}... take any set , the average is always a integer.

[tpsharma2u]

Aans E..
SII can be satisfied by all odd nos ...just take the median to be the no of int ..and ull have the avg to be no itself..eg...
3...2,3,4...avg 3....
5...3,4,5,6,7..avg 5... and so on

[hemant.maddineni]

Aans E..
SII can be satisfied by all odd nos ...just take the median to be the no of int ..and ull have the avg to be no itself..eg...
3...2,3,4...avg 3....
5...3,4,5,6,7..avg 5... and so on

For 5 take the set { -1 , 0 , 1 , 2, 3 }. what you said doesn't hold true . Its not mentioned anywhere that only positive integers should be considered. If only positive integers should be considered then what you said holds true.

[tpsharma2u]

since for some values it holds true and for others it doesnt ...it is not sufficient and ans is E

[Kweku.Amoako]

i think the average of -1,0,1,2,3 is an integer(1)

average = sum/number of terms
sum = 5
number of terms = 5
average = 5/5 = 1

Likewise the average of -1,0,1 is 0/3 = 0(which is an integer and the middle #
For any set consecutive integers with an odd number of terms the average will always be an integer or the middle number.

Hence

statement (2) only implies x is odd...Obviously not Sufficient

[Kweku.Amoako]

Also for statement 1

2x + 2 = P^3 . Note that 2x + 2 implies P^3 is even hence possible values of P^3 include {8,64,216,512...etc}

Lets express these possible values in the form 2x +2

8 = 2(3) + 2, in which case x = 3 (prime number & odd )
64 = 2(31) + 2, in which case x = 31 (prime number & odd ) [editor: you should STOP HERE. as soon as you find two values, it's insufficient - end of story. you are wasting a lot of time if you keep finding more values.]
216 = 2(107) +2, in which case x = 107 (prime number & odd)
512 = 2(205) + 2, in which case x = 205(Not Prime) - this not a possible solution

Since X can be mutiple values this is Insufficient.

Also note that the possible solutions of x are all odd, which is exactly the information statement 2 provides(statement 2 implies x is odd). Hence statement 2 does not provide additional information to help figure out the value of x.

So the two statements combined do not provide sufficient information to solve the problem.

Answer should be E

[hemant.maddineni]

i think the average of -1,0,1,2,3 is an integer(1)

average = sum/number of terms
sum = 5
number of terms = 5
average = 5/5 = 1

Likewise the average of -1,0,1 is 0/3 = 0(which is an integer and the middle #
For any set consecutive integers with an odd number of terms the average will always be an integer or the middle number.

Hence

statement (2) only implies x is odd...Obviously not Sufficient

oops.. i missed the obvious point... i am not sure how i came to a conclusion that -1,0,1,2,3 is not an integer . Its blunder :( .

Thanks a lot.

[RonPurewal]

Also for statement 1

2x + 2 = P^3 . Note that 2x + 2 implies P^3 is even hence possible values of P^3 include {8,64,216,512...etc}

Lets express these possible values in the form 2x +2

8 = 2(3) + 2, in which case x = 3 (prime number & odd )
64 = 2(31) + 2, in which case x = 31 (prime number & odd ) [editor: you should STOP HERE. as soon as you find two values, it's insufficient - end of story. you are wasting a lot of time if you keep finding more values.]
216 = 2(107) +2, in which case x = 107 (prime number & odd)
512 = 2(205) + 2, in which case x = 205(Not Prime) - this not a possible solution

Since X can be mutiple values this is Insufficient.

Also note that the possible solutions of x are all odd, which is exactly the information statement 2 provides(statement 2 implies x is odd). Hence statement 2 does not provide additional information to help figure out the value of x.

So the two statements combined do not provide sufficient information to solve the problem.

Answer should be E

beautifully done.

[imanemekouar]

Can somebody explain it again . i did not get it.

[RonPurewal]

Can somebody explain it again . i did not get it.

where did you get stuck?