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If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 00:41
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Competition Mode Question If x is an integer and 0 < x < 67, what is the value of x? (1) x is divisible by at least two prime numbers greater than 2. (2) \(\sqrt{x+1} 1\) is prime. Are You Up For the Challenge: 700 Level Questions
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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 01:23
#1 x is divisible by at least two prime numbers greater than 2. we can have 15,35,55,39 insufficeint #2 √x+1−1 is prime x=8,63,35,15 insufficient from 1 & 2 x=63,35,15 insufficient IMO E
If x is an integer and 0 < x < 67, what is the value of x?
(1) x is divisible by at least two prime numbers greater than 2. (2) x+1‾‾‾‾‾√−1x+1−1 is prime.



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 01:23
(1) x is divisible by at least two prime numbers greater than 2. > Possible values of x = {15, 21, 33, 35, 39, 51, 55, 57, 63, 65} > Insufficient
(2) \(\sqrt{x+1}\)  1 is prime. > Possible values of x = {8, 15, 35, 63} > Insufficient
Combining (1) & (2), > Possible values of x = {15, 35, 63} > No Definite value > Insufficient
IMO Option E



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 04:13
Quote: If x is an integer and 0 < x < 67, what is the value of x?
(1) x is divisible by at least two prime numbers greater than 2. (2) \(\sqrt{x+1}−1\) is prime. (1) x is divisible by at least two prime numbers greater than 2. insufic\(x=(15,35,63)=(5*3,5*7,7*3^2)…\) (2) \(\sqrt{x+1}−1\) is prime. insufic\(\sqrt{x+1}−1=p…x+1=(p+1)^2=perf.square\) \(0<(p+1)^21<67…1<(p+1)^2<68…1<p+1≤8…0<p≤7\) \(p=(2,3,5,7)…(p+1)^2=(9,15,36,64)\) \(x+1=(9,15,36,64)…x=(8,14,35,63)\) (1&2) insufic\(x=(35,63)=(5*7,7*3^2)\) Ans (E)



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 07:52
If x is an integer and 0 < x < 67, what is the value of x? (1) x is divisible by at least two prime numbers greater than 2. x div. by 3 and 5. x = 15 or 45 .. OR x div. by 5 and 7. x = 35 INSUFFICIENT. (2) \(\sqrt{x+1}−1\) is prime. \(\sqrt{x+1}−1 = p\) \(\sqrt{x+1} = p + 1\) x + 1 = \(p^2 + 1 + 2p\) x = p * (p + 2) So, x = 2 * (2 + 2) = 8 OR x = 3 * (3 + 2) = 15 OR x = 5 * (5 + 2) = 35 INSUFFICIENT. Together 1 and 2 Two possibilities still exists, x = 15 or x = 35. Hence INSUFFICIENT. IMO Answer E.
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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 11:00
(1) x is divisible by at least two prime numbers greater than 2. There are many numbers b/w 0 and 67.... INSUFFICIENT
(2) √x+1−1 is prime.
√63+1 1 = 7 √35+1 1 = 5 √8+1 1 =3
So insufficient
Combining both only 35 is having two prime factors greater than 2
OA:C



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 12:21
(1) x is divisible by at least two prime numbers greater than 2.
The prime numbers could be 3,5,7,11,13 etc . Therefore numbers could be 15, 21,35,65 Insufficient.
(2) \sqrt{x+1}1 is prime.
Let the above expression equal to Y.
Y+1 = \sqrt{X+1}
(y+1)^2 = x+1
Since Y is any prime number 1,2,3,5,7, 11.. there could a multitude of values for x like 3, 8,15,35,63
Insufficient
Both statements together, we see X could be 15, 35,65 . Therefore insufficient
Answer is E



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 15:03
If x is an integer and 0 < x < 67, what is the value of x?
(1) x is divisible by at least two prime numbers greater than 2. (2)\(\sqrt{x+1}\)−1 is prime.
(1) x can be 15, 30, 45, 60 (divisible by 3 and 5 ), or 35 (divisible by 5 and 7) or 33,66 (divisible by 3 and 11), 55 (divisible by 5 and 11), 21, 42 (divisible by 3 and 7). So, Not sufficient.
(2) x can be 15 (3 is the resulting integer) or 35 (5 is the resulting integer). Not sufficient
Combining both, x can be either 15 or 35. Not sufficient. E is the answer.



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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15 Nov 2019, 21:10
We are given that x is divisible by at least two prime numbers greater than 2 and that 0<x<67.
Statement 1: x is divisible by at least two prime numbers greater than 2. Possible values of x: 15, 21, 30, 33, 35, etc. Statement 1 does not lead to a unique value of x, hence it is not sufficient.
Statement 2: √(x+1)1 is prime Possible values of x: 8, 15, 35, 63. Statement 2 does not lead to a unique value of x, hence it is not sufficient.
1+2 The numbers that satisfy conditions 1 and 2 are: 15, 35, and 63. Statements 1 and 2 when combined do not lead to a unique value of x. This means both statements even when combined are not sufficient.
The answer is, therefore, option E.



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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16 Nov 2019, 05:17
St 1 : clearly not sufficient.
St 2: Not sufficient.
Both : sufficient.
Considering that X is divisible by at least 2 primes >2, then we can test for values ..3,5,7 etc.
35 = 7×5 satisfies the condition.
√35+11 = 5. Prime no.
That's why (c)
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Re: If x is an integer and 0 < x < 67, what is the value of x?
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16 Nov 2019, 07:20
IMO E Statement 1 : x can be 15 / 21 / 35, both divisible by 3 & 5, 3 & 7 and 7 & 5 respectively. Not sufficient. Statement 2 : sqrt 35+1 = 6 1 = 5, which is a prime number or x = 15. sqrt 15+ 1 = 4 1 = 3 . Not sufficient. Combine both statements, we have x = 15 or 35.



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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16 Nov 2019, 12:12
Possible values for x are: x=3*5=15, x= 5*7=35, x=11*13=143, x=17*19=323, x=29*31=899, x=41*43=1763, x=59*61=3599.



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Re: If x is an integer and 0 < x < 67, what is the value of x?
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16 Nov 2019, 13:26
If x is an integer and 0 < x < 67, what is the value of x?
(Statement1): —> x could be 15(3*5 ), or 35( 5*7), or 63 (7*9) Insufficient
(Statement2): If x=8, then \((8+1)^{1/2} —1= 3–1=2\)(prime)
If x=15, then \((15+1)^{1/2}—1= 4–1=3\) (prime)
Insufficient
Taken together 1&2, x could be 15(3*5) —> \((15+1)^{1/2} —1= 4–1=3\) (prime)
x could be 35 (5*7) —> \((35+1)^{1/2}—1= 6–1=5\) (prime)
Also, x could be 63
Insufficient
The answer is E.
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Re: If x is an integer and 0 < x < 67, what is the value of x?
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16 Nov 2019, 13:26






