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Math Expert V
Joined: 02 Sep 2009
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Is the positive integer y a prime number?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 54% (02:01) correct 46% (01:50) wrong based on 266 sessions

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Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

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Joined: 26 Nov 2012
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Re: Is the positive integer y a prime number?  [#permalink]

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Bunuel wrote:
Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

Stat 1: We get 83 and 89 as primes...Insufficient.

Stat 2: y-1 = 3x, the result must be multiple of y..we are not sure of y ..Insufficient.

both 82 = 3x, 88 = 3x...Not sufficient..

IMO option E.
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Re: Is the positive integer y a prime number?  [#permalink]

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Stat 1: 80 < y < 95, We get both prime and nonprime numbers =Insufficient.

Stat 2: y= 3x + 1, the result must be multiple of y, and x is positive integer, X and y are unknown =Insufficient.

both statements
the result must be multiple of y , and x is positive integer, possible values of y for x to be integer are 82,85,88,91,94, all are nonprimes= sufficient condition to answer the question,

IMO , answer = C
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Joined: 12 Sep 2015
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Re: Is the positive integer y a prime number?  [#permalink]

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Top Contributor
2
Bunuel wrote:
Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

Target question: Is y a prime number?

Given: y is a positive integer

Statement 1: 80 < y < 95
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of y that satisfy statement 1. Here are two:
Case a: y = 81, in which case y is NOT prime
Case b: y = 83, in which case y IS prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: y = 3x + 1, where x is a positive integer
There are several values of y that satisfy statement 2. Here are two:
Case a: y = (3)(1) + 1 = 4, in which case y is NOT prime
Case b: y = (3)(2) + 1 = 7, in which case y IS prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let's list ALL possible values of y.
y = (3)(27) + 1 = 82 (82 is NOT prime)
y = (3)(28) + 1 = 85 (85 is NOT prime)
y = (3)(29) + 1 = 88 (88 is NOT prime)
y = (3)(30) + 1 = 91 (91 is NOT prime)(91 = 13 times 7)
y = (3)(31) + 1 = 94 (94 is NOT prime)
So, we can conclude that y is NOT prime
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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Re: Is the positive integer y a prime number?  [#permalink]

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msk0657 wrote:
Bunuel wrote:
Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

Stat 1: We get 83 and 89 as primes...Insufficient.

Stat 2: y-1 = 3x, the result must be multiple of y..we are not sure of y ..Insufficient.

both 82 = 3x, 88 = 3x...Not sufficient..

IMO option E.

In the highlighted line above, you are actually getting a definite answer that y is NOT a prime. Hence, answer should be C not E.
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Re: Is the positive integer y a prime number?  [#permalink]

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Statement 1 - Not Sufficient
Statement 2 - X can be any positive integer therefore, not sufficient.

Statement 1 & 2 combined

Y=3x + 1
And 80<y<95

Insert values of x that satisfy the combined equation and all numbers are not prime.

We can sufficiently answer the question.

Therefore C is the answer.

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Re: Is the positive integer y a prime number?  [#permalink]

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Answer should be both statements together are sufficient to get the answer . From first statement you are getting many prime numbers not a definite value , but if you use y=3x+1 then the only prime number between 80 and 95 is 91 when X=30 which will give you 91 , hence addresses first statement as well

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Re: Is the positive integer y a prime number?  [#permalink]

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Answer should be both statements together are sufficient to get the answer . From first statement you are getting many prime numbers not a definite value , but if you use y=3x+1 then the only prime number between 80 and 95 is 91 when X=30 which will give you 91 , hence addresses first statement as well

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That is incorrect mate.
If you use both statements together, it proves none of the numbers are prime. If you get even one number as prime, you're getting 2 answers hence, insufficient.

In this case, all the numbers are not prime, and that's why the 1) & 2) are sufficient together and C is the answer. Be careful with this when solving DS questions.

91 is not a prime number. It's a multiple of 7.

Hope this helps.
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Re: Is the positive integer y a prime number?  [#permalink]

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Question has a question mark - it is asking that whether y is prime number or not? So not is also an answer . It is simple case of putting number in second equation and testing -

1- 3*27 (X=27)+1= 82
2- 3*28 (X=28)+1 =85
3- 3*29 (X=29) + 1 = 88
4- 3*30 (X=30) +1 = 91
5- 3*31 (X=31)+1 =94

We can not test further as that will not comply with first statement

Out of above 5 numbers no one is prime number . So you get the answer which is NO ,Y will not be prime number

And thanks for above that 91 is not prime number ( simple negligence ) to cause error but yes we never want answer in DS , so still got saved

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Re: Is the positive integer y a prime number?  [#permalink]

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Bunuel wrote:
Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

Anybody please tell how C is the correct answer. As per me, E is the correct answer
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Re: Is the positive integer y a prime number?  [#permalink]

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sukeshap wrote:
Bunuel wrote:
Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

Anybody please tell how C is the correct answer. As per me, E is the correct answer

To demonstrate that the correct answer is E, you must show that there are two possible values for y that satisfy BOTH statements AND yield conflicting answer choices to the target question (is y prime?).
When we combine the statements, we can see that y can equal 82 or 85 or 88 or 91 or 94
In all 5 possible cases, the answer to the target question is the same; y is not prime.
In other words, we can be CERTAIN that the answer to the target question is NO - y is not prime.

Cheers,
Brent
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Re: Is the positive integer y a prime number?  [#permalink]

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Bunuel wrote:
Is the positive integer y a prime number?

(1) 80 < y < 95
(2) y = 3x + 1, where x is a positive integer

each alone is obviously insuff

both together

the min value of x in y = 3x+1 is 27.... to satisfy 80<y<95 , all primes >3 are in the form 6n+1 or 6n-1 , i.e. before or after a multiple of 6

in the given range multiples of 6 are 84 , 90 , check around 84 and 90 ( 83,85) and (89,91) ... of which only 85 and 91 satisfy the form (3x+1)both of which are non prime .... suff

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Re: Is the positive integer y a prime number?  [#permalink]

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