M31-16

Question

If  \frac{x}{11p}  is an odd prime number, where  x  is a positive integer and  p  is a prime number, what is the least value of  x ?

A. 22
B. 33
C. 44
D. 66
E. 99

Bunuel · Accepted Answer

Official Solution:

If  \frac{x}{11p}  is an odd prime number, where  x  is a positive integer and  p  is a prime number, what is the least value of  x ?

A. 22
B. 33
C. 44
D. 66
E. 99

Given:  \frac{x}{11p} = (odd \ prime) ;
 
This implies  x = 11p*(odd \ prime) .
 
We need to minimize  x , so we should minimize  p  and  (odd prime) . Since  p  is a prime, then the least value of  p  is 2 and the least possible value of  (odd prime)  is 3. Therefore  x_{min}=11p*(odd \ prime)=11*2*3=66 .

Answer: D

kin2win · Answer

I think this is a  high-quality  question and I agree with explanation.

Mehemmed · Answer

I think this is a  high-quality  question and I agree with explanation.

Shubhgarg · Answer

is 1 a prime number?

gmatophobia · Answer

No. The smallest prime number is 2.

bb · Answer

Sounds like you may want to get a property numbers book or chapter covered and refresh these grade school rules before jumping into practice questions.

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Bunuel · Answer

1 is NOT a prime number. A Prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. The smallest prime (and the only even prime) is therefore 2.

To elaborate more (you don't really need this for the GMAT but still if interested):

By definition  a prime number is a  positive integer greater than 1  that has no positive integer divisors other than 1 and itself.

The main reason 1 is not conceded as prime is because of  the fundamental theorem of arithmetic  (unique prime factorization theorem), which states that  every integer greater than 1 can be represented  uniquely  as a product of prime numbers .

For example,  60 = 2^2*3*5  (the order of the primes does not matter here). Now, if we allow 1 to be a prime then we can represent 60 as  1*2^2*3*5  or as  1^2*2^2*3*5  or as  1^3*2^2*3*5  as  1^4*2^2*3*5  ... As you can see the representation is no longer unique and thus the fundamental theorem of arithmetic is no longer correct, which is a problem because the  fundamental  theorem of arithmetic is called  fundamental  for a reason.

2. Properties of Integers  
     Theory   
 Math: Number Theory 
 Number Properties: Tips and hints 
 Advanced Number Properties on GMAT (All 5 parts) 
 Do you make these 3 mistakes in GMAT Even-Odd Questions?  
 Everything about Factorials on the GMAT 
 Solving Complex Problems Using Number Line 
     Questions   
 Tough New Set: Number Properties Set 
 Power of a Number in a Factorial Problems 
 Number Properties Ability Quiz 
 Special Numbers and Sequences Problems 
 The E-GMAT Number Properties Knockout: 10 Great 700+ Ques for you! 
 Trailing Zeros Problems 
 DS Questions 
 PS Questions

For other subjects:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

ruchirk · Answer

I think this is a  high-quality  question and I agree with explanation.

sssdd1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

odd_major · Answer

I think this is a  high-quality  question and I agree with explanation.

Premkungg · Answer

I like the solution - it’s helpful.

Rashmi96 · Answer

I like the solution - it’s helpful. on the forum discussion, only ads are coming

bot00078 · Answer

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M31-16

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