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M31-11

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M31-11  [#permalink]

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New post 09 Jun 2015, 06:49
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A
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D
E

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  35% (medium)

Question Stats:

75% (00:50) correct 25% (00:33) wrong based on 32 sessions

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Re M31-11  [#permalink]

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New post 09 Jun 2015, 06:50
Official Solution:

What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64


We need such number which is not a factor of 30! and is not a prime number.

The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is therefore 2*31=62. Notice that all numbers between 30 and 62, are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all their primes in higher powers). For example:

31 is a prime, hence x cannot be 31.

\(32 = 2^5\). 30! will for sure have 2 in higher power than 5, hence 32 IS a factor of 30!.

\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!

...

\(64= 2^6\). 30! will for sure have 2 in higher power than 6, hence 64 IS a factor of 30!.


Answer: D
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Re: M31-11  [#permalink]

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New post 29 Dec 2017, 14:35
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Re: M31-11  [#permalink]

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New post 17 Jun 2018, 19:04
Bunuel wrote:
Official Solution:

What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64


We need such number which is not a factor of 30! and is not a prime number.

The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is therefore 2*31=62. Notice that all numbers between 30 and 62, are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all their primes in higher powers). For example:

31 is a prime, hence x cannot be 31.

\(32 = 2^5\). 30! will for sure have 2 in higher power than 5, hence 32 IS a factor of 30!.

\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!

...

\(64= 2^6\). 30! will for sure have 2 in higher power than 6, hence 64 IS a factor of 30!.


Answer: D


I somehow did not understand this explanation.
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Re: M31-11  [#permalink]

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New post 17 Jun 2018, 19:07
Cbirole wrote:
Bunuel wrote:
Official Solution:

What is the least positive integer that is not a factor of 30! and is not a prime number?

A. 31
B. 32
C. 33
D. 62
E. 64


We need such number which is not a factor of 30! and is not a prime number.

The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is therefore 2*31=62. Notice that all numbers between 30 and 62, are either primes (and we know that x is NOT a prime) or factors of 30! (because 30! has all their primes in higher powers). For example:

31 is a prime, hence x cannot be 31.

\(32 = 2^5\). 30! will for sure have 2 in higher power than 5, hence 32 IS a factor of 30!.

\(33 = 3*11\). Both 3 and 11 are factors of 30!, hence 33 IS a factor of 30!

...

\(64= 2^6\). 30! will for sure have 2 in higher power than 6, hence 64 IS a factor of 30!.


Answer: D


I somehow did not understand this explanation.


We need such number which is not a factor of 30! and is not a prime number.

The smallest prime which is not a factor of 30! is obviously 31. So, the smallest positive integer that is not a factor of 30! and is not a prime number is 2*31=62.

Answer: D.

Check more solutions here: https://gmatclub.com/forum/what-is-the- ... 98237.html

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M31-11  [#permalink]

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New post 27 Sep 2018, 02:59
The fact that we are directly told to look for a none prime number does give us the key to solving this question.

As we know 31 is a prime number, we can look for the next smallest answer choice that does contain a prime factor which is not part of 30!.
Once we see that 62 = 2x31 we know we have found our right answer.

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Re: M31-11 &nbs [#permalink] 27 Sep 2018, 02:59
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