pq

Question

pq < 70, where both P and Q are distinct odd primes. Determine PQ.

Statement (1): PQ is one greater than a power of two.

Statement (2): The sum of the digits of PQ is a prime number.

satya2029 · Answer

From 1
PQ=32+1=33=3*11
PQ=64+1=65=5*13
NOT SUFFICIENT
From 2
PQ=65
PQ=41
Not sufficient
FROM 1 AND 2
PQ=65=64+1=5*13 and 6+5=11 a prime
Sufficient
C

Posted from my mobile device

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 •  p*q < 70 
 o p and q are distinct odd primes  
We need to find the value of  p*q 
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  PQ is one greater than a power of 2
 •  PQ = 2^x+1 , for some integer x
•  2^x + 1 < 70 
 o There are two possible values of x
  Case 1: If  x = 5 , then  2^5 + 1 = 33 = 3*11 < 70 
 • 11 and 5 both are odd primes 
 Case 2: If  x = 6 , then  2^6 + 1 = 65 = 5*13 
 • 5 and 13 both are odd primes.   
o We are not getting unique answer. 
Hence, statement 1 is not sufficient, we can eliminate answer option A and D.
 Statement 2:  The Sum of the digits of the PQ is a prime number.
 •  PQ < 70 
 o Case 1: If  p = 7  and  q = 3 , p and q are odd primes and  pq=21 < 70 
   2+1 = 3 , which is a prime number. 
o Case 2: If  p = 5  and  q = 13 , p and q are odd primes and pq =65 < 70
   6 + 5 = 11 , which is a prime number.  
• We are not getting unique answer. 
Hence, statement 2 is also not sufficient, we can eliminate options B.
 Step 3: Analyse Statements by combining. 
From statement 1: pq is either 33 or 65
From statement 2: The Sum of the digits of the PQ is a prime number.
 • If  pq = 33 , then  3 + 3 = 6 , which is not a prime number
• If  pq = 65 , then  6 + 5 = 11 , which is a prime number
 o  pq = 65   
Hence, the correct answer is  Option C.

GMATWhizTeam · Answer

Hey,
The solution given by you is good. However, there's just one small mistake. In statement 2,  PQ = 41 is not a valid case .  P*Q = 41*1  and we know that P and Q are prime numbers, so P or Q cannot be 1.

minustark · Answer

Odd primes : 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.. we don't need further as PQ will exceed 70. In fact PQ can be highest (19*3)= 57.

1) PQ can assume values like 9, 17, 33, 65. Among them 33(3*11) and 65(5*13) both meets the criteria given. Not sufficient
2) PQ can be 21 or 65. Not sufficient.
Togrther, PQ is 65. Suff.

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pq < 70, where both P and Q are distinct odd primes. Determine PQ.

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GMAT Data Sufficiency (DS) Questions

pq < 70, where both P and Q are distinct odd primes. Determine PQ.

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