Num prp

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Fri Jan 28, 2011 11:05 pm

Is the prime number p equal to 31 ?
(1) p is equal to one less than twice the value of the square
of an integer.
(2) p is equal to four less than a multiple of Â…5

How do you evaluate the two statement together without listing a bunch of numbers?

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 28, 2011 11:05 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jan 29, 2011 12:18 am

yellowho wrote:Is the prime number p equal to 31 ?

(1) p is equal to one less than twice the value of the square of an integer.
(2) p is equal to four less than a multiple of Â…5

I can show you numbers, but if you know the fact that there is no particular formula or relation by which we can uniquely point out prime numbers, you can easily answer that both question together is NOT sufficient to answer the problem.

Because there will be infinite number of primes which will satisfy any bunch of properties at the same time unless the properties point to a particular prime. For example, if the property is like "p is 1 greater than LCM of 5 and 6", then it uniquely points to 31. But if the properties are general, i.e. like the ones given in the question, then they can never point to a particular prime.

The correct answer is E.

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diehard_gmat: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Fri Jan 28, 2011 12:36 am; Thanked: 1 times

by diehard_gmat » Sat Jan 29, 2011 3:32 am

Thanks Anurag!
This means we can answer any such questions just by looking at it!

Just being curious, can you show some numbers?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jan 29, 2011 3:41 am

diehard_gmat wrote:This means we can answer any such questions just by looking at it!

Yes, but be careful that the mentioned properties do not limit the range of primes. For example, here if it was mentioned that p is less than 50, then only such p is 31. If they are general properties, then you can always infer that there is more than one primes satisfying the properties.

diehard_gmat wrote:Just being curious, can you show some numbers?

p can be equal to 31 or 71.

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Sat Jan 29, 2011 11:10 am

St 1 gives P can be 7 or 17 or 31

Insufficient

St 2 : P can be 11 or 31 or 71.

Insufficient.

Pick E

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Jan 31, 2011 10:54 pm

Anurag,

Just to clarify the logic here, are we trying to find intersections of the two statements? To re-state, is there only one intersection (at 31) that the two statements below satisfy?

I did this by listing numbers and identifying overlaps. I think 1, 31, 71 works for both. I actually stopped at 1 and 31. I could be wrong here, but isn't statement 1 a parabola and statement two linear? Why is there more than 2 intersections, as you noted 71 also works.

[quote="Anurag@Gurome"][quote="yellowho"]Is the prime number p equal to 31 ?

(1) p is equal to one less than twice the value of the square of an integer.
(2) p is equal to four less than a multiple of Â…5[/quote]

I can show you numbers, but if you know the fact that there is no particular formula or relation by which we can uniquely point out prime numbers, you can easily answer that both question together is NOT sufficient to answer the problem.

Because there will be infinite number of primes which will satisfy any bunch of properties at the same time unless the properties point to a particular prime. For example, if the property is like "p is 1 greater than LCM of 5 and 6", then it uniquely points to 31. But if the properties are general, i.e. like the ones given in the question, then they can never point to a particular prime.

[spoiler]The correct answer is E.[/spoiler][/quote]

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Mon Jan 31, 2011 11:32 pm

yellowho wrote:I did this by listing numbers and identifying overlaps. I think 1, 31, 71 works for both. I actually stopped at 1 and 31. I could be wrong here, but isn't statement 1 a parabola and statement two linear? Why is there more than 2 intersections, as you noted 71 also works.

First, you can't consider 1 as a potential value for p as it violates the question stem itself. Question stem says p is a prime number, 1 is NOT a prime number.

Second, the statements do not represent parabola or straight lines. Integer functions are discrete in nature. Hence, they cannot be be represented by any continuous curve. Also you cannot plot the two statements in the same plane. This is because statement 1 says, p = (2mÂ² + 1) and statement 2 says p = (5n - 4), where m and n are some positive integer, not necessarily same. Hence the dependent variables (i.e. m and n) are different. Thus we cannot really establish a graphical "intersection" relation between them.

Logically we can say that the values of p are the "intersections" of the statements or properties, but graphically we can't.

As I have mentioned earlier, you cannot uniquely represent prime numbers by any general property. There will be infinite possible values of p satisfying these two relations. For example, 31, 71, 241, 881, 1151 etc.

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