If a and b are non-negative integers, is ab prime?

Question

1) a = 17
2) b = 91

OptimusPrepJanielle · Answer

Statement 1 : This tells us only about a.
If b were 1, then product ab = 17 and it would be prime.
If b were 2 (or any other number), then product ab = 34 and it would not be prime.
Hence insufficient

Statement 2 : This tells us only about b
But it says that b = 91 and this is not a prime.

So if we multiply a non prime number with any other number, we will get a non prime number.
Hence product ab is not prime.
Hence Sufficient

Option B

MathRevolution · Answer

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.

If a and b are non-negative integers, is ab prime?

1) a = 17
2) b = 91

In the original condition, there are 2 variables, which should match with the number of equations. So, you need 2 equations. However, for 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), ab=17*91=/ prime, which is no and sufficient. Therefore, the answer is C. However, since this is an integer question, one of the key questions, apply the mistake type 4(A). For 1), a=17, b=1 -> yes, a=17, b=18 -> no, which is not sufficient.
For 2), b=91=7*13 -> ab=/ prime, which is always no and sufficient.
Therefore, the answer is B.

-> For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

nramirez · Answer

Hi.
I've just solved this problem, from a Veritas Prep test.
My question is, given the non-negative phrase, can't a or b be zero? In that case, S1 a = 17*b=0 = 0, not prime. S2 a=0 * b=91 equals zero, not prime. That's why I think both statements are necessary (C).
Appreciate comments.

Thanks!

chetan2u · Answer

Hi,
 you are correct in your assumption that one of the numbers can be 0 also, but it will still not make a difference to the answer..
Statement 2 tells us that ab can not be prime, since b=91, and a can be prime,2 , or 0 or 9 etc the product will never be PRIME 
suff

priyer111 · Answer

I came across this Data Sufficiency question on one of the Veritas Tests.

If a and b are non-negative integers, is ab prime?

a = 17
b = 91

The solution appears to be B, according to Veritas. Because b=91, it is obvious that anything multiplied with a non-prime number is a non-prime number. But what about 0? Zero is a non-negative integer. It's not sufficient to know that b=91 because if a=0, then ab is neither prime nor composite. I selected E as my answer which is incorrect, according to the solution key.

Please clarify! Thanks!

KarishmaB · Answer

Yes, a can be 0. In that case, using statement 2 alone, we get that ab = 0*91 = 0.
0 is not prime.

So if the question is: Is ab prime? 
You answer "No."

If a has any other non negative integer value, ab = 91a and will not be prime. Again, you answer "No" to the question.

So in every case, your answer will be "No." and hence statement 2 is sufficient.

Note that we don't care whether ab is 0 or a composite number. The point is that it will not be prime.

Basshead · Answer

(1) 17 is clearly prime; we need to know the value of b. If b = 1, then ab is prime. If b =2, then ab is not prime. INSUFFICIENT.

(2) 91 is not prime. Therefore ab is not prime. SUFFICIENT.

It's helpful to memorize the prime numbers up to 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

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If a and b are non-negative integers, is ab prime?

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