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Q is less than 10

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by Ankur87 » Sat May 04, 2013 1:41 am
Q is less than 10. Is Q a prime number?
Q2 - 2 = P; P is prime and P < 10.
Q + 2 is NOT prime, but Q is a positive integer.
A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.


IMO : A
because:
Q^2 - 2 = P ( P = Prime, P < 10)
2^2 - 2 = 2 ( 2 is a Prime number and < 10 )
3^2 - 2 = 7 ( 7 is a Prime number and < 10 )

So Q is prime.
A is sufficient.

B is not sufficient as
(Q + 2 = 2+2 = not prime)
(Q + 2 = 4+2 = not prime)
2 is prime , 4 is not prime.
So we can't say if Q is prime or not.

But OA is C
Please explain.
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Source: — Data Sufficiency |
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by Atekihcan » Sat May 04, 2013 2:12 am
The question stem never said Q is an integer or Q is positive or negative. Only Q < 10.

From statement 1, (Q² - 2) is a prime number less than 10.
Possible values of (Q² - 2) are : 2, 3, 5, and 7
So, possible values of Q are : ±2, ±√5, ±√7, and ±3
Clearly, Q may or may not be prime number.
So, statement 1 alone is not sufficient.

From statement 1, Q is a positive integer less than 10 and (Q + 2) is not prime.
Possible values of (Q + 2) are : 4, 6, 8, 9, and 10
So, possible values of Q are : 2, 4, 6, 7, and 8
Clearly, Q may or may not be prime number.
So, statement 1 alone is not sufficient.

Now, both statements taken together, only possible value of Q is 2, i.e. Q is prime.
So, both statements together is sufficient.

Answer : C
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by Ankur87 » Sat May 04, 2013 2:21 am
sheh man..
my bad..
i think i was in a hurry or something..
how can i commit such a mistake..
Atekihcan wrote:The question stem never said Q is an integer or Q is positive or negative. Only Q < 10.

From statement 1, (Q² - 2) is a prime number less than 10.
Possible values of (Q² - 2) are : 2, 3, 5, and 7
So, possible values of Q are : ±2, ±√5, ±√7, and ±3
Clearly, Q may or may not be prime number.
So, statement 1 alone is not sufficient.

From statement 1, Q is a positive integer less than 10 and (Q + 2) is not prime.
Possible values of (Q + 2) are : 4, 6, 8, 9, and 10
So, possible values of Q are : 2, 4, 6, 7, and 8
Clearly, Q may or may not be prime number.
So, statement 1 alone is not sufficient.

Now, both statements taken together, only possible value of Q is 2, i.e. Q is prime.
So, both statements together is sufficient.

Answer : C
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by Blue_Skies » Tue May 07, 2013 12:12 pm
Q is less than 10. Is Q a prime number?
Q2 - 2 = P; P is prime and P < 10.
Q + 2 is NOT prime, but Q is a positive integer.

From 1 2(Q-1) is prime. Now this product is even and the only even prime number is 2. Hence Q-1 has to be 1. So , Q==2. Sufficient.

From 2 ) Their are multiple numbers which satisfy this condition. Ex : 6,7,8. Insufficient.

B
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