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What is the value of integer x?

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Source: — Data Sufficiency |
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by mals24 » Wed Jan 28, 2009 6:04 am
St 1: X could be 15 (divisible by 3 and 5) or 35 (divisible by 7 and 5)
Insuff

St 2: Since the difference of sqrt(x+1)-1 is prime, this means its an integer.
Hence sqrt(x+1) is also an integer and (x+1) is a perfect square

That is: x+1 = Perfect Square
x = Perfect Square-1
X could be either 15 or 35
Insuff

Combining the 2 youll get x as 15 or 35

Answer: E
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by gaggleofgirls » Wed Jan 28, 2009 6:57 pm
mals24 wrote:St 1: X could be 15 (divisible by 3 and 5) or 35 (divisible by 7 and 5)
Insuff

St 2: Since the difference of sqrt(x+1)-1 is prime, this means its an integer.
Hence sqrt(x+1) is also an integer and (x+1) is a perfect square

That is: x+1 = Perfect Square
x = Perfect Square-1
X could be either 15 or 35
Insuff

Combining the 2 youll get x as 15 or 35

Answer: E
You did get the right answer, but you left out a number of things that could have made it wrong.

From the stem: 0 < x < 53
You seemed to stop at 35

You are right for 1), it is insufficient, but becuase there are lots of numbers between 0 and 53 that you can make by multiplying 2 primes greater than 2
3*5 = 15
3*7 = 21
3 * 11 = 33
3 * 13 = 39
3 * 17 = 51
5 * 7 = 35

For 2)

You got x = 15 and x = 35, but you missed x = 48

sqrt (x+1) is a perfect square = sqrt49 = 7
49-1 = 48, which is < 53

You now need to go back to the original statement in 2) to test your 3 possible values for x.

The original statement is sqrt(x+1) -1 is prime

If x = 15
sqrt (15+1) = sqrt 16 = 4
4 - 1 = 3
3 is prime

If x = 35
sqrt (35+1) = sqrt36 = 6
6-1 = 5
5 is prime

If x = 48
sqrt (48 +1) = sqrt 49 = 7
7-1 = 6
6 is NOT prime

Therefore, 2 is insufficient becuase it gave multiple answers.

Combined does not help us becuase it includes at least of our choices.

-Carrie
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by sanjay_dce » Thu Jan 29, 2009 8:11 am
E should be the ans.

from stmt 1 : 15, 20,35, etc are nos
from stmt 2: x= 15, 35 etc
using both also no absolute ans hence E
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