Is the positive integer y a prime number?

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.

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

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: https://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

Answer = C

Cheers,
Brent

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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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.


Sent from my iPhone using GMAT Club Forum mobile app
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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


Sent from my iPhone using GMAT Club Forum mobile app

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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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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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

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

C

Given that y > 0 and y = k

Statement - 1:
If y = 81, then it is not prime (27 * 3 = 81)
If y = 89, then it is a prime
Insufficient

Statement - 2: y = 3x + 1
If x = 1, then y = 4 and not a prime
If x = 2, then y = 7 and a prime
Insufficient

Statement - 1 + 2:
80 < 3x + 1 < 95
Subtracting 1 from both the sides
79 < 3x < 94
79 < 81, 84, 87, 90, 93 < 94

As x is an integer all the numbers within the range are non-prime as these are multiples of 3. Hence we can say that y is not a prime integer.

Ans. C

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