GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Nov 2018, 00:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50585
If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

06 Apr 2015, 06:29
1
7
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:07) correct 51% (02:07) wrong based on 191 sessions

### HideShow timer Statistics

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

Kudos for a correct solution.

_________________
Retired Moderator
Joined: 06 Jul 2014
Posts: 1241
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Re: If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

06 Apr 2015, 06:56
2
Bunuel wrote:
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

Kudos for a correct solution.

As we know that y and x are prime and if xy = 323 than we should have pair of integers 17 and 19

1) from this statement we know that x is 19 but know nothing about y so Insufficient
2) after a little checking we know that y = 179 and we know that product of 179 and another prime can't be equal 323 so Sufficient

_________________
Manager
Joined: 17 Mar 2014
Posts: 228
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.19
WE: Information Technology (Computer Software)
Re: If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

06 Apr 2015, 07:48
1
This is Yes/No type DS question. Our end answer should be Yes/No.

according to Statement 1 - X=19 but we dont know any thing about Y so insufficient
According to statement 2 - Y = 179 but 179*sny prime number is not equal to 323 , so we dont need to care about value of X here . So , X*Y is not equal to 323 - Sufficient

_________________

Press +1 Kudos if you find this Post helpful

Current Student
Joined: 23 May 2013
Posts: 188
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

06 Apr 2015, 09:40
4
Harley1980 wrote:
Bunuel wrote:
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

Kudos for a correct solution.

As we know that y and x are prime and if xy = 323 than we should have pair of integers 17 and 19

1) from this statement we know that x is 19 but know nothing about y so Insufficient
2) after a little checking we know that y = 179 and we know that product of 179 and another prime can't be equal 323 so Sufficient

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).
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12857
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

06 Apr 2015, 11:39
3
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.

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

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Manager Joined: 17 Mar 2015 Posts: 116 Re: If x and y are both prime, is x*y = 323? [#permalink] ### Show Tags 06 Apr 2015, 15:21 1 $$323 = 324 - 1 = 18^2 - 1 = 17*19$$ - 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. Math Expert Joined: 02 Sep 2009 Posts: 50585 Re: If x and y are both prime, is x*y = 323? [#permalink] ### Show Tags 13 Apr 2015, 06:41 Bunuel wrote: 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 Kudos for a correct solution. 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. _________________ Current Student Joined: 12 Aug 2015 Posts: 287 Concentration: General Management, Operations GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27 GPA: 3.3 WE: Management Consulting (Consulting) Re: If x and y are both prime, is x*y = 323? [#permalink] ### Show Tags 09 Jan 2016, 06:50 Rich, great reasoning! I actually started playing with 323. _________________ KUDO me plenty EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12857 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are both prime, is x*y = 323? [#permalink] ### Show Tags 09 Jan 2016, 10:43 2 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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6507
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

10 Jan 2016, 18:21
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
Joined: 09 Sep 2013
Posts: 8775
Re: If x and y are both prime, is x*y = 323?  [#permalink]

### Show Tags

21 Jul 2018, 05:51
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x and y are both prime, is x*y = 323? &nbs [#permalink] 21 Jul 2018, 05:51
Display posts from previous: Sort by