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# M25 #29

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09 Oct 2008, 06:34
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$$X$$ and $$Y$$ are prime integers. What is $$X + Y$$ ?

1. $$X - Y$$ is a prime integer
2. $$Y \lt X \lt 6$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Is 1 considered a prime number? I selected C but was wrong. According to the answer:
S2 is not sufficient. Consider $$X = 5$$ , $$Y = 3$$ and $$X = 3$$ , $$Y = 2$$ which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?
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09 Oct 2008, 08:56
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sharmar wrote:
$$X$$ and $$Y$$ are prime integers. What is $$X + Y$$ ?

1. $$X - Y$$ is a prime integer
2. $$Y \lt X \lt 6$$

(C) 2008 GMAT Club - m25#29

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

Is 1 considered a prime number? I selected C but was wrong. According to the answer:
S2 is not sufficient. Consider $$X = 5$$ , $$Y = 3$$ and $$X = 3$$ , $$Y = 2$$ which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

1) X - Y is prime
case 1: 5 - 2 = 3
5 + 2 = 7

case 2: 7 - 5 = 2
7 + 5 = 13

2) Y < X < 6
Possible value for Y = {2, 3}
Possible value for X = {3, 5}

1) & 2)
Case 1: 2 < 3 < 6
3 - 2 = 1 ----- Not Prime
Drop this case

Case 2: 2 < 5 < 6
5 - 2 = 3 ----- Prime
5 + 2 = 7

Case 3: 3 < 5 < 6
5 - 3 = 2 ----- Prime
5 + 3 = 8

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09 Oct 2008, 09:11
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[quote="sharmar"]$$X$$ and $$Y$$ are prime integers. What is $$X + Y$$ ?

1. $$X - Y$$ is a prime integer
2. $$Y \lt X \lt 6$$

the difference between consecutive primes = /2/ except 2,3 = /1/

from 1

x,y could be any prime >3....insuff

from 2

obviously not suff

both

no idea if they are consec or not ...insuff

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09 Oct 2008, 10:14
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sharmar wrote:
Nevermind... I think I figured it out... I didn't consider 5-2 = 3

ALSO CONSIDER 7-2 = 5 OR 7-5 = 2

SOME MORE 13 - 2 = 11 AND 13 - 2 = 11
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02 Jul 2010, 05:05
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No, 1 is not considered a prime. A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

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05 Jul 2010, 19:53
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X and Y are prime integers. What is X+Y ?

1. X-Y is a prime integer
2. Y<X<6

Case 1: X-Y is prime number
Set (X,Y) : (5,2), (5,3),(7,2),(7,5),(13,2)(13,11).
No Unique Soln.

Case 2. Y<X<6
Set (X,Y) : (5,3),(5,2)(3,2)
No Unique Soln.

Combining Case 1 & Case 2 : no Unique Soln.

Thus E: Stmt 1 & Stmt 2 Together are not sufficient.
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27 Mar 2012, 01:09
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Expert's post
sharmar wrote:
$$X$$ and $$Y$$ are prime integers. What is $$X + Y$$ ?

1. $$X - Y$$ is a prime integer
2. $$Y \lt X \lt 6$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Is 1 considered a prime number? I selected C but was wrong. According to the answer:
S2 is not sufficient. Consider $$X = 5$$ , $$Y = 3$$ and $$X = 3$$ , $$Y = 2$$ which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

If $$x$$ and $$y$$ are prime numbers, what is the value of $$x+y$$ ?

(1) $$x-y$$ is a prime number --> if $$x=5$$ and $$y=2$$ (notice that in this case $$x-y=3=prime$$) then $$x+y=7$$ but if $$x=5$$ and $$y=3$$ (notice that in this case $$x-y=2=prime$$) then $$x+y=8$$. Not sufficient.

(2) $$y<x<6$$ --> the same example as above is valid for this statement also. Not sufficient.

(1)+(2) Again, the example from statement (1) is still valid and gives two different values for $$x+y$$. Not sufficient.

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10 Jul 2013, 05:13
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Expert's post
knightofdelta wrote:
Bunuel wrote:
sharmar wrote:
$$X$$ and $$Y$$ are prime integers. What is $$X + Y$$ ?

1. $$X - Y$$ is a prime integer
2. $$Y \lt X \lt 6$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Is 1 considered a prime number? I selected C but was wrong. According to the answer:
S2 is not sufficient. Consider $$X = 5$$ , $$Y = 3$$ and $$X = 3$$ , $$Y = 2$$ which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

If $$x$$ and $$y$$ are prime numbers, what is the value of $$x+y$$ ?

(1) $$x-y$$ is a prime number --> if $$x=5$$ and $$y=2$$ (notice that in this case $$x-y=3=prime$$) then $$x+y=7$$ but if $$x=5$$ and $$y=3$$ (notice that in this case $$x-y=2=prime$$) then $$x+y=8$$. Not sufficient.

(2) $$y<x<6$$ --> the same example as above is valid for this statement also. Not sufficient.

(1)+(2) Again, the example from statement (1) is still valid and gives two different values for $$x+y$$. Not sufficient.

Can we also consider negative cases of these integers, since the question did not explicitly state that the integers were positive?

No, we cannot. "If $$x$$ and $$y$$ are prime numbers..." Only positive numbers can be primes.

Hope it helps.
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02 Jul 2010, 04:19
isnt 1 a prime number ?
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06 Jul 2011, 13:38
1 simple question : are negative prime numbers considered in GMAT ?

If yes, this question can be solved in 30 sec....else the 3,2 explanation is correct
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14 Jul 2011, 07:30
Prime number is an integer number P$$>=$$2, divisible by only itself and 1.
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29 Jul 2011, 23:44
Some folks here say 1 is not a prime. But it is.
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27 Mar 2012, 03:18
petrifiedbutstanding wrote:
Some folks here say 1 is not a prime. But it is.

1 is DEFINITELY not a prime number. The smallest prime is 2.

For more on Number Properties check: math-number-theory-88376.html

Hope it helps.
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11 Jul 2012, 22:17
Question can be answered by using both the statements together

x=5
y=3
x-y=2 which is a prime number

and yes 1 is not prime..
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31 Aug 2012, 20:08
Good question. I am particularly happy that I did end up solving this one is about a min and half.

Followed the plugging in of values approach with values as 5,2,3 for statement (ii) and for statement (i) there are a whole number of possible options.

Both statements together as well fail to give a concrete answer for the values 2,3,5. Hence chose E.
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18 Sep 2012, 05:16
Picking up on bunnels statement re: 1 being a prime....

If you have trouble remembering in the heat of battle, think: a prime number has 2 factors, 1 and itself. Although 1 has factors of 1 and iteslf, these are one and the same and therefore it doesn't have 2 (intiger) factors.
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10 Jul 2013, 04:11
Bunuel wrote:
sharmar wrote:
$$X$$ and $$Y$$ are prime integers. What is $$X + Y$$ ?

1. $$X - Y$$ is a prime integer
2. $$Y \lt X \lt 6$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Is 1 considered a prime number? I selected C but was wrong. According to the answer:
S2 is not sufficient. Consider $$X = 5$$ , $$Y = 3$$ and $$X = 3$$ , $$Y = 2$$ which is true...

edit: but if you take both together... the only possible answer is X=5 and Y=3 and not X=3 and Y=2. The only way S2 and S1 is not sufficient is if we consider 1 a prime number... am I missing something?

If $$x$$ and $$y$$ are prime numbers, what is the value of $$x+y$$ ?

(1) $$x-y$$ is a prime number --> if $$x=5$$ and $$y=2$$ (notice that in this case $$x-y=3=prime$$) then $$x+y=7$$ but if $$x=5$$ and $$y=3$$ (notice that in this case $$x-y=2=prime$$) then $$x+y=8$$. Not sufficient.

(2) $$y<x<6$$ --> the same example as above is valid for this statement also. Not sufficient.

(1)+(2) Again, the example from statement (1) is still valid and gives two different values for $$x+y$$. Not sufficient.

Can we also consider negative cases of these integers, since the question did not explicitly state that the integers were positive?
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10 Jul 2013, 06:25
petrifiedbutstanding wrote:
Some folks here say 1 is not a prime. But it is.

Natural numbers that have EXACTLY two factors are called prime numbers. Obviously, the number "1" has exactly 1 factor, so it is neither prime nor composite.. Yeah, this number is a different breed !!
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10 Jul 2013, 06:27
heartbeats1987 wrote:
petrifiedbutstanding wrote:
Some folks here say 1 is not a prime. But it is.

Natural numbers that have EXACTLY two factors are called prime numbers. Obviously, the number "1" has exactly 1 factor, so it is neither prime nor composite.. Yeah, this number is a different breed !!

Right. So if I see "different breed" on a GMAT DS, I should think "1" right?
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10 Jul 2013, 06:30
knightofdelta wrote:
heartbeats1987 wrote:
petrifiedbutstanding wrote:
Some folks here say 1 is not a prime. But it is.

Natural numbers that have EXACTLY two factors are called prime numbers. Obviously, the number "1" has exactly 1 factor, so it is neither prime nor composite.. Yeah, this number is a different breed !!

Right. So if I see "different breed" on a GMAT DS, I should think "1" right?

1 is NOT a prime number. The smallest prime is 2. And this is not only for the GMAT but generally.

For more check Number Theory chapter of our Math Book: math-number-theory-88376.html

Hope it helps.
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# M25 #29

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