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# P1 and P2 are both prime

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P1 and P2 are both prime [#permalink]

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11 Oct 2007, 07:33
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Can any on pls explain why the answer is C. Thanks.

P1 and P2 are both prime. Determine p1

1. p2 - p1 = 2
2. (p2)^2 - (P1)^2 = 120
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11 Oct 2007, 07:54
Welcome to GMAT Club !

Yes... (C) it is

Stat1
p2-p1 = 2

o If p2 = 7 then p1 = 5
o If p2 = 5 then p1 = 3

INSUFF.

Stat2
(p2)^2 - (P1)^2 = 120

That implies,
o (p2 - p1)*(p2 + p1) = 6 * 20 => p2 = 13 and p1 = 7
or
o (p2 - p1)*(p2 + p1) = 4 * 30 => p2 = 17 and p1 = 13
or
o (p2 - p1)*(p2 + p1) = 2 * 60 => p2 = 31 and p1 = 29

INSUFF

Both 1 and 2
2*(p2+p1) = 120
<=> p2+p1 = 60
<=> p2=31 and p1=29

SUFF.
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11 Oct 2007, 08:05
skyjuice wrote:
Can any on pls explain why the answer is C. Thanks.

P1 and P2 are both prime. Determine p1

1. p2 - p1 = 2
2. (p2)^2 - (P1)^2 = 120

1.There are many primes with difference 2, e.g. 3 and 5, 5 and 7. Therefore, 1 in INSUFF.

2. There are only two primes that satisfy this equation and differ by 2.

In fact, I was not sure whether there were more than two primes that satisfied just (2). 120 is not much, and if we try to put some numbers, we will see that difference between p1^2 and p2^2 becomes larger and larger after 29 and 31. However, then I tried 11 and 1. It is C.
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11 Oct 2007, 08:38
JingChan wrote:
Note: 1 is not a prime number ;P

Eeerr... Yes, that is right. It is an exception (found that in an old notebook). Then who can find another 2 primes that satisfy the second equation?
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12 Oct 2007, 08:59
Fig

Do I have to try and eliminate all possibilities (or consider those multiple poss) when I solve st 2 bcos I wudnt even remember and knock st2 when I see

(p2 + p1)(p2-p1) = 120
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12 Oct 2007, 09:08
lnaik wrote:
Fig

Do I have to try and eliminate all possibilities (or consider those multiple poss) when I solve st 2 bcos I wudnt even remember and knock st2 when I see

(p2 + p1)(p2-p1) = 120

To me, we just need to be sure that the statment 2 is valid or not.... So finding 2 cases that bring 2 different answers is what we need here
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13 Oct 2007, 08:01
OlgaN wrote:
Fig wrote:
Welcome to GMAT Club !

Yes... (C) it is

Stat1
p2-p1 = 2

o If p2 = 7 then p1 = 5
o If p2 = 5 then p1 = 3

INSUFF.

Stat2
(p2)^2 - (P1)^2 = 120

That implies,
o (p2 - p1)*(p2 + p1) = 6 * 20 => p2 = 13 and p1 = 7
or
o (p2 - p1)*(p2 + p1) = 4 * 30 => p2 = 17 and p1 = 13
or
o (p2 - p1)*(p2 + p1) = 2 * 60 => p2 = 31 and p1 = 29

INSUFF

Both 1 and 2
2*(p2+p1) = 120
<=> p2+p1 = 60
<=> p2=31 and p1=29

SUFF.

Can be p1 and p2 for example 37 and 23, 17 and 47 etc? Why exactly 31 and 29?
Thanks.

it has to satisfy either both statements:
1)p2-p1 = 2
31-29 = 2
all the other primes you listed does not

2) (p2)^2 - (P1)^2 = 120
(p2 - p1)*(p2 + p1) = 120
same as above.. again your examples does not hold true for this stmt
13 Oct 2007, 08:01
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