If x and y are both prime, is x*y = 323?

Agreed. Just want to add: We can find the factors of 323 by realizing that 18^2 = 324, which is really close to 323. Start by checking the numbers around 18, namely, 17 and 19, to find if the product of these numbers is 323. Our first choice works.

In fact, this works for every number that is one less than a perfect square, since x^2 -1 = (x+1)(x-1). So 324 - 1 = (18+1)(18-1).

Hi All,

This DS question has some subtle Number Property patterns in it that can help you to avoid some of the math involved.

We're told that X and Y are both PRIME. We're asked if (X)(Y) = 323. This is a YES/NO question.

While it might be tempting to 'play around' with the 323, it's not necessary to do that at the start (and having the extra information from each of the two Facts will save you time).

Fact 1: X is the first prime number after 18

This is a relatively easy Fact to work with. X is 19.

When 323 is divided by 19, we get 17....
IF....Y = 17, then the answer to the question is YES
IF....Y = any OTHER prime, then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: Y is the last prime number before 180

We don't have to figure out the exact value of Y to deal with Fact 2 (since we already know form the prompt that X is ALSO prime).

Whatever Y is, it MUST be relatively close to 180 (For example, we know that 90 is NOT prime, and there must be at least one prime between 90 and 180, even if we don't know exactly what it is).

Now we can talk about what X could be....
Since 323 is NOT divisible by 2, IF....X = 2 then the answer to the question is NO (and it doesn't matter what Y is).
Since 323 is NOT divisible by 3, IF....X = 3 then the answer to the question is NO (and it doesn't matter what Y is).
Since 323 is NOT divisible by 5, IF....X = 5 then the answer to the question is NO (and it doesn't matter what Y is).

At this point, we know that X would have to be AT LEAST 7. For the product of (X)(Y) to equal 323, Y would have to be less than 50. From Fact 2, we know that it's far GREATER than 50, so there is NO CHANCE that (X)(Y) = 323. The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.

Final Answer:
GMAT assassins aren't born, they're made,
Rich

\(323 = 324 - 1 = 18^2 - 1 = 17*19\) - the only way you can present 323 as a product of primes.
Option 1 says that X is 19, but it says nothing about Y, which prevents us from answering the question, thus insufficient
Option 2 says that Y = 179 which is so big that any product of 179 and a prime number X will be bigger than 323 thus the answer to the question is NO and thus option 2 is sufficient.
B it is then.

VERITAS PREP OFFICIAL SOLUTION:

So the first thing that came to my mind is “Wow, that’s random”. The premise seems so arbitrary that it makes many approaches seem irrelevant. Even knowing that the two numbers are prime, we cannot quickly determine whether they must multiply to 323 without some more analysis and manipulation. Luckily, this is a Data Sufficiency question, so we have two additional statements that can help guide our analysis.

It’s important to note that in Data Sufficiency, we are trying to determine whether we can say with certainty that the two numbers multiply together to 323. This also means that if we can determine with certainty that the two numbers cannot multiply to 323, we have sufficient data. The uncertainty arises when we don’t know either way (i.e. maybe), so that provides a good framework for our analysis.

The first statement gives us a big hint, telling us that x is the first prime number after 18. This very quickly implies that x must be 19. We now have a hint as to why the number 323 was chosen (perhaps the author drove a Mazda in the ‘90s). If 323 is not a multiple of 19, then statement 1 will provide definitive evidence that x*y cannot possibly equal 323. Short of using a calculator, we can find multiples of 19 that are nearby and iterate manually until we find the correct answer. 19 x 20 would be easy to calculate as we can consider it as 19 x 2 x 10, or 38 x 10, or 380. From there, we can drop 19s until we get in the correct range.
380 – 19 is 361
361 – 19 is 342
342 – 19 is 323

You might be able to get there faster than by using this strategy, but after a few seconds of calculations, you can determine that 19 * 17 yields exactly 323. The question indicated that x and y would both be prime numbers, and 17 is indeed a prime number, so the possibility exists. However, it’s important to note that we know nothing (John Snow) about the value of y, other than it is a prime number. It could just as easily be 2, or 7, or 30203 (yes that’s a prime; I like palindromes). Since y could have any prime value, there’s insufficient evidence to determine that the product of x and y must be 323. Statement 1 is insufficient, and we can eliminate answer choices A and D.

Statement 2 indicates that y is the last prime number before 180, but it is important to remember that we must evaluate this statement alone. We now have no information about the value of x, other than it is a prime number. Statement 2 gives us a specific value of y, even if we’re not exactly sure what it is. We could do a little math and check to see if 179 (the number right before 180) is a prime, and in this case it is. The verification process is somewhat tedious, you have to check to see if it’s divisible by any prime number smaller than the square root of the number, so once you check 2, 3, 5, 7, 11 and 13, you’re confident than 179 is a prime number.

Knowing only that x is a prime number, we must now try and determine whether 179 and any prime could yield a product of 323, and the answer is very quickly no. The smallest prime number is 2, and 179 * 2 is already 358. You can also visually determine that 179 is more than half of 323, so there’s no need to even formally calculate the result. This statement on its own guarantees that x * y can never be 323, and thus is sufficient information to answer the question. The correct selection is answer choice B, as this statement alone is sufficient.

It is important to point out that these statements, taken together, give very clear numbers for both x and y. When this happens, you know that you can combine the statements and get only one value. That value may or may not be 323 (in this case it’s really, really not), but either way it provides sufficient information to definitively answer the question. However, it is almost always going to be the wrong answer, as it simply provides too much information. There’s no mystery or intrigue left, everything is laid out on the sheet in front of you. In business, as in life, if something seems too good to be true, it usually is.

Indeed, this question is essentially testing to see whether you’ll overpay for information on Data Sufficiency. However, at first blush, it just seems like an arbitrary collection of numbers with a question attached. When faced with similar head-scratchers, keep in mind that the statements (and/or answer choices) will provide hints. Trying to factor out 323 without any hints is a challenging endeavour, so look for hints and exploit them as much as possible. Hopefully, on test day, the only head scratching you’ll do is wondering which school you’ll go to with your outstanding score.

Rich, great reasoning! I actually started playing with 323.

Hi shasadou,

With more practice, you'll come to develop a better sense of whether you should 'play around' with the given information/question or not. As a general rule, I look for 'complexity' (or a lack of it). If I can quickly manipulate the given information, then I'll typically do it (a few extra seconds spent there might create a big shortcut later). However, if the work is NOT something that can be done quickly or requires too much effort, then I'll often leave it for later (when I can combine it with whatever information each of the 2 Facts provides).

This is yet another way that DS questions 'test' your overall thoroughness of thinking - flexible thinking is a character trait that Business Schools want you to have - which is why it's a built in 'measure' of the GMAT.

GMAT assassins aren't born, they're made,
Rich

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 x and y are both prime, is x*y = 323?

(1) x is the first prime number after 18
(2) y is the last prime number before 180

In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. For 1) 1equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), it becomes x=19, y=179. Since x*y=/323, it is no and sufficient. However, the question is an integer question which is one of the key questions. So, apply 4(A) of the mistake type. For 1), you don’t know y and it is not sufficient. For 2), when y=179, it becomes x*y=/323=19*17, which is 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.

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