Problem Solving

Phil and Joe play a game of pattern recognition. Phil tells Joe to say any two numbers in sequence and he will form a pattern out of them. Joe say 12 and 15 and phil says 150 and 156. If phils response to Joe's 3rd number was 162, what was Joe's third number?

A. 17

B. 18

C. 20

D. 25.

E. 30

I think it should be B.) 18 since the above two numbers increase in steps of 3

- Deepak

Ian Stewart wrote:

dtweah wrote:Phil and Joe play a game of pattern recognition. Phil tells Joe to say any two numbers in sequence and he will form a pattern out of them. Joe say 12 and 15 and phil says 150 and 156. If phils response to Joe's 3rd number was 162, what was Joe's third number?

A. 17

B. 18

C. 20

D. 25.

E. 30

You will never see a GMAT question like this, since it's absolutely impossible to deduce the 'pattern' that Phil is using here. There's an infinite variety of 'patterns' that Phil could be using to get '150' when Joe says '12', and '156' when Joe says '15'. For example, Phil might take the number J that Joe gives him, and work out his own number P as follows:

P = J^2 - 25J + 306

Then, if P = 162, J could be 9 or 16. Or, it might be that Phil takes Joe's number J and works out his own number P as follows:

P = 2J + 126

Then if P = 162, J would be 18.

Since there is no single logically correct answer to a question in this format, it could never appear on a real GMAT. It seems to be a clumsy attempt to test linear functions, and I'd be nearly certain that the source intends for the answer to be 18, but it's not a well-designed question, and nothing like real GMAT questions. Where is it from?

You are over thinking Ian. Give it a second shot.

dtweah wrote:You are over thinking Ian. Give it a second shot.

No, he isn't.

Of course, the "simplest" (which is a relative term in mathematics) solution is B, 18, which is solved according to a linear pattern relating to the given numbers. But as Ian stated, there are an infinite number of "patterns" that will give rise to these two results, which is a horribly anemic data set to be working with anyway.

This question will never be seen on a GMAT exam, because the question is too vague and leaves the answer open to interpretation.

Feep wrote:

dtweah wrote:You are over thinking Ian. Give it a second shot.

No, he isn't.

Of course, the "simplest" (which is a relative term in mathematics) solution is B, 18, which is solved according to a linear pattern relating to the given numbers. But as Ian stated, there are an infinite number of "patterns" that will give rise to these two results, which is a horribly anemic data set to be working with anyway.

This question will never be seen on a GMAT exam, because the question is too vague and leaves the answer open to interpretation.

Yes it can. If the numbers in the above problem are changed to numbers such as Joe's 2, 4 and phil's 6, 8 you would withdraw the above comments, so that alone invalidates the comments. Would you say there is an infinite number of patterns that can generate joe's 2 ,4 and phils 6, 8? No. They are the set of even numbers begining with 2 so what ever Joe says phil adds 2. That set is unique. A similarly unique relationship exists between Phil's number's and Joe's numbers in the problem above. It need not be linear. This question is far below the range of Gmat's most difficult questions. If you assume a linear relationship and don't get the exact answer, try something else. Answer choices are exact not approximates.

dtwea wrote:Yes it can. If the numbers in the above problem are changed to numbers such as Joe's 2, 4 and phil's 6, 8 you would withdraw the above comments, so that alone invalidates the comments. Would you say there is an infinite number of patterns that can generate joe's 2 ,4 and phils 6, 8? No. They are the set of even numbers begining with 2 so what ever Joe says phil adds 2. That set is unique. A similarly unique relationship exists between Phil's number's and Joe's numbers in the problem above. It need not be linear. This question is far below the range of Gmat's most difficult questions. If you assume a linear relationship and don't get the exact answer, try something else. Answer choices are exact not approximates.

(sigh)

This is the last I'll say on the matter. This argument is a waste of time, and trust us, Ian Stewart is the closest thing this board has to a flowing wellspring of knowledge and wisdom. No offense, but his arguments have far more weight and thought behind them.

If those numbers were changed to 2, 4 (x-values) and 6, 8 (y-values), I would in no way withdraw my comments. Off the top of my head, let's list some patterns that might work here.

y = x + 4
y = x^2 - 4x + 8
y = x^3 - 5x^2 + 3x + 12

And so forth. There are an infinite number of these patterns in simple polynomial functions alone, and just because you think y = x + 4 looks the simplest to our human brains doesn't make it correct and the others wrong. Each one of these functions will yield different results for further entries in the series, and yet all satisfy the original conditions as listed by you.

This question is vague, ambiguous, and will never be found on any real GMAT test, ever. Trust Ian and me on this one, folks.

Feep wrote:

dtwea wrote:Yes it can. If the numbers in the above problem are changed to numbers such as Joe's 2, 4 and phil's 6, 8 you would withdraw the above comments, so that alone invalidates the comments. Would you say there is an infinite number of patterns that can generate joe's 2 ,4 and phils 6, 8? No. They are the set of even numbers begining with 2 so what ever Joe says phil adds 2. That set is unique. A similarly unique relationship exists between Phil's number's and Joe's numbers in the problem above. It need not be linear. This question is far below the range of Gmat's most difficult questions. If you assume a linear relationship and don't get the exact answer, try something else. Answer choices are exact not approximates.

(sigh)

This is the last I'll say on the matter. This argument is a waste of time, and trust us, Ian Stewart is the closest thing this board has to a flowing wellspring of knowledge and wisdom. No offense, but his arguments have far more weight and thought behind them.

If those numbers were changed to 2, 4 (x-values) and 6, 8 (y-values), I would in no way withdraw my comments. Off the top of my head, let's list some patterns that might work here.

y = x + 4
y = x^2 - 4x + 8
y = x^3 - 5x^2 + 3x + 12

And so forth. There are an infinite number of these patterns in simple polynomial functions alone, and just because you think y = x + 4 looks the simplest to our human brains doesn't make it correct and the others wrong. Each one of these functions will yield different results for further entries in the series, and yet all satisfy the original conditions as listed by you.

This question is vague, ambiguous, and will never be found on any real GMAT test, ever. Trust Ian and me on this one, folks.

Then find the pattern that produces the answer. If there are infinite, then all infinite will give the same answer, not approximation. There is only one relationship between Joe's number and PHil's number that produces an exact odd or or even number. The examples you give above are producing the series 2 4 6 8 , not approximations to them. . This is what you have to do for the problem in question. When I give the OA you will see the relationship. Until then discover it. Nice excange though. I am not contesting Ian's wisdom but because he says something doesn't make it. This is mathematics. It is an exact science and in the problem above there is only one unique pattern that makes phil to respond to ANY number Joe throws at him. Find it.

I agree with "Feep" and "Ian" if you come down to making polynomials there are more than one polyinomial hence more than one soln.

Talking of making those polynomial , not worth the time and effort

I couldn't find a free tut but for those interested https://www.stormingmedia.us/45/4527/0452746.html https://www.citeulike.org/user/sekhmet_m ... le/1118911

I am going to agree with the majority opinion over here. I have never come across a official GMAT question that appears remotely vague and this question does come across as vague. Like Ian said there are many possible combinations that can arrive at such a pattern and it is not possible to rule out such combinations during the real thing and hence I dont feel such a question will ever appear on GMAT.

dtweah wrote:Phil and Joe play a game of pattern recognition. Phil tells Joe to say any two numbers in sequence and he will form a pattern out of them. Joe say 12 and 15 and phil says 150 and 156. If phils response to Joe's 3rd number was 162, what was Joe's third number?

A. 17

B. 18

C. 20

D. 25.

E. 30

OA is C. Joe's number is the number of side of a regular polygon and Phil's is the measure of the interior angle of regular polygon
J= N P= (n-2)180/n

dtweah wrote:

dtweah wrote:Phil and Joe play a game of pattern recognition. Phil tells Joe to say any two numbers in sequence and he will form a pattern out of them. Joe say 12 and 15 and phil says 150 and 156. If phils response to Joe's 3rd number was 162, what was Joe's third number?

A. 17

B. 18

C. 20

D. 25.

E. 30

OA is C. Joe's number is the number of side of a regular polygon and Phil's is the measure of the interior angle of regular polygon
J= N P= (n-2)180/n

This makes the question even MORE vague, as it was not the simple linear relationship most of us made it out to be.

You say that your equation was correct, but so was Ian's "P = 2J + 126" and "P = J^2 - 25J + 306". There is absolutely no indication which one of these three (or any of the other infinite possibilities) is the actual relation, and each would yield a different "third number" for Joe.

I think you made up this question, and it's not bad, but merely vague. You'd need to include some sort of indication that it's related to interior angles of polygons.

dtweah wrote:

dtweah wrote:Phil and Joe play a game of pattern recognition. Phil tells Joe to say any two numbers in sequence and he will form a pattern out of them. Joe say 12 and 15 and phil says 150 and 156. If phils response to Joe's 3rd number was 162, what was Joe's third number?

A. 17

B. 18

C. 20

D. 25.

E. 30

OA is C. Joe's number is the number of side of a regular polygon and Phil's is the measure of the interior angle of regular polygon
J= N P= (n-2)180/n

dtweah

No offense please, but i think such stubbornness is annoying. We all make mistakes, and it's through humility that we can learn from our mistakes. Kindly put your mind into the excellent explanations given. Again, no offense.