If integer p is a factor of 42, is p a prime number?

Question

(1) p > 6
(2) p < 21

DS21228

BrentGMATPrepNow · Answer

Given : Integer p is a factor of 42  
The positive factors of 42 are:   1, 2, 3, 6, 7, 14, 21, 42

Target question :    Is p a prime number?

Statement 1 : p > 6  
So, p can equal any of the following values:   7, 14, 21, 42  
If n = 7, the answer to the target question is  YES, p is prime 
If n = 14, the answer to the target question is  NO, p is not prime 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : p < 21 
So, p can equal any of the following values:   1, 2, 3, 6, 7, 14  
If n = 7, the answer to the target question is  YES, p is prime 
If n = 14, the answer to the target question is  NO, p is not prime 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
We can already see that n = 7 and n = 14 satisfy BOTH statements. In other words: 
If n = 7, the answer to the target question is  YES, p is prime 
If n = 14, the answer to the target question is  NO, p is not prime 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

bM22 · Answer

Factors of 42: 1,2, 3, 6, 7, 14, 21, 42. Total of 8 factors. Statement 1: p > 6 The factors > 6 are 7, 14, 21, 42. p could be any one of the mentioned factors. Thus we cannot determine the value of p with certainty. => We cannot say whether p is prime or not. So Insufficient. Statement 2: p < 21 Again it could be any factor : 1, 2, 3, 6, 7, 14. We cannot calculate the specific value of p. => We cannot say whether p is prime or not. So Insufficient. Statement 1 + Statement 2: 6 < p < 21. => the factors that fall in this range are: 7, 14. One is prime and one is not. So we cannot say with certainty whether p is prime or not. So the 2 statements together are also Insufficient . Answer E.

GMATinsight · Answer

P is a factor of 42 Factors of 42 = {1, 2, 3, 6, 7, 12, 14, 21, 42} Prime factors of 42 = {2, 3, 7} Question: Is P = one of {2, 3, 7}? Statement 1 : p > 6 i.e. p could be 7 (YES) or 14 (NO) hence NOT SUFFICIENT Statement 2 : p < 21 i.e. p could be 7 (YES) or 14 (NO) hence NOT SUFFICIENT Combining the statements 6 < p < 21 Statement 1 : p > 6 i.e. p could be 7 (YES) or 14 (NO) hence NOT SUFFICIENT Answer: Option E

NitishJain · Answer

I marked this question wrong but thanks all for the explanation.

I wrote 42 as 2*3*7 (in multiples of prime number)
I missed the trick that factors could be a combination of prime factors as well (7, 14, 21) and considered only 7 and marked A as correct choice.

But I did consider 7, 6 (3*2), 14 (2*7) while rejecting B (p<21)

Silly mistake

Basshead · Answer

Factor pairs: 
 1, 42 
 2, 21 
 6, 7 
 14, 3

(1) If  p > 6 , then p can be  7, 14, 21, 42 . p can be non-prime or prime. INSUFFICIENT.

(2) If  p < 21 , p can be  1, 2, 3, 6, 7, 14 . p can be non-prime or prime. INSUFFICIENT.

(1&2) Combined, p can be 7 or 14. INSUFFICIENT.

Answer is E.

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If integer p is a factor of 42, is p a prime number?

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GMAT Data Sufficiency (DS) Questions

If integer p is a factor of 42, is p a prime number?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards