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

Question

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

KarishmaB · Accepted Answer

You have x and y are prime. You need to find whether xy = 323.

(1) x is the first prime after 18.

This means x is 19. But what is y? We don't know. So should we move on right away that this statement alone is not sufficient? No. What if 19 is not a factor of 323? Since both x and y are integers, if 19 were not a factor of 323, it would be sufficient to say that xy is not 323. 
323/19 = 17. So if y is 17, xy will be 323. If y is any other value, xy will not be 323. 
Not sufficient alone.

(2) y is the last prime before 180.
We don't need to find the last prime before 180 as long as we know that it would be 179 or 173 etc. We don't really need to find it exactly. What we do know is that last prime before 180 is certainly not 19. y is something like 179/173 etc and since 323 does not have 2 as a factor, xy will certainly not be 323. Hence this statement alone is sufficient to say that xy is NOT 323.

Answer (B)

utkmittal1 · Answer

323 = 19 x 17. There are only four factors of 323...1, 17, 19, 323.

Statement 1: x is the first prime after 18. It means X=19. For xy = 323, y should be 17. But y can take any prime value ....2, 3, 5 etc. Not sufficient

Statement 2: y is the last prime before 180. It means y=179. Now x can take any prime value but product of 179 and any other number cannot be 323. Therefor, xy cannot be 323. Sufficient

Answer is B

rahul16singh28 · Answer

Statement I:

x = 19 ,  y can be 2,3,5,7,11,17,....  etc. So, Insufficient.

Statement II:

y = 179 . When we factorize  323  we have  323 = 17*19 . So, one number has to be either of them. But as this statement one number is 179. Hence, their product wont be equal to 323.

So, Sufficient.

varun4s · Answer

Factors of 323 are: {1, 17 ,19 ,323}

(1) x= 19 and and y can be any prime number{2,3,5,7,11,13,17...}
 If x= 19 and y=17 then  
 If x=19 and y= 2 then  
 We need confirm answer either yes or no

(2)Y=180 and x can be any prime number{2,3,5,7,11,13,17....}
In all these cases, product of xy can never be 323

So we have confirmed no answer.

Answer: B.

dcummins · Answer

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

(1) x is the first prime after 18.

x=19
simple division will reveal that for xy to equal 323, y must be 17 (nothing else)

Y may equal 17, or it may be something else as there are no restrictions.

(2) y is the last prime before 180.
the last prime = 179

Think,  if x is also prime then what is the smallest prime we can start with? X=2
  2*179 = 358
358>323 so NO, xy is not equal to 323

minustark · Answer

1) x = 19. So, xy can be 38, 57, or any product of a prime no and 19. Not suff.
2) We don't need to find the last prime before 180 as 323 =3*11^2. So in no way the product of the last prime before 180 can make such a small product with another prime. Suff.

B is the CA.

BhaveshGMAT · Answer

Does not 'last prime before 180' mean last in number prime working backwards from 180?

Therefore I took last prime as 2 and not 179.

I thought if the value is 179, the question should be 'first prime before 180'?

VeritasKarishma   Bunuel  please clarify!

KarishmaB · Answer

'last prime before 180' means 'the last prime you get before you reach 180'. 
The sequence (first, last etc) would go from left to right on the number line by default (unless mentioned otherwise).
Though if our metrics show that too many people get confused here, we might use "the greatest prime less than 180" or something similar.

rvgmat12 · Answer

OE:

Statement (1) tells us that x = 19. If x = 19, then xy = 19y. If y = 17, then xy does equal 323. If y = any other prime, then xy does not equal 323; INSUFFICIENT. Statement (2) tells us that y is 179 (you don’t necessarily have to pinpoint this one, you can determine the answer by assuming that some number in the 170’s is prime) and 179 times any other prime is greater than 323. (179 * 2 = 358, and any prime greater than 2 will just increase the product.) So xy CANNOT equal 323; (B)

This is a good problem to practice "construct thinking" - by far, most students who answer incorrectly choose answer choice C, and often they do so quite quickly. But consider how relatively "easy" it is to use both statements to get an answer - statement (1) tells you (albeit in code) the value of x, and statement (2) tells you the value of y. So with both statements together it's pretty clear that you'll get the exact value of xy and be able to answer the question. This should be your clue that it's worth investing a little bit of extra time trying to Leverage Assets - trying to squeeze a little extra value out of either of the statements individually, since it's likely that the GMAT is setting up C as a trap answer and rewarding those who can derive more value from a single statement alone.

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

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

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