If a*b*c*d = 390, where a, b, c and d are positive integers, and a

Question

If a*b*c*d = 390, where a, b, c and d are positive integers, and a < b < c < d, which of the following could be the value of d − a?

A. 9
B. 10
C. 11
D. 13
E. 15

This is a  PS Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Critical Reasoning Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

GMATinsight · Answer

a*b*c*d = 390 = 2*3*5*13 OR 1*5*6*13 OR 1*6*10*13 OR 1*5*6*23

i.e. d-1 = 13-2 = 11 POSSIBLE

Answer: Option C

chetan2u · Answer

390=1*2*3*5*13  and a<b<c<d
1*2*3*5*13 can be written as 1*5*6*13 or 2*3*5*13 or 1*2*3*65 and so on. 
Thus a can take only two values, 1 and 2, while d would be a multiple of 13
Least value of d-a: When d is least and a the maximum. 
 d\geq 13  and a can be only 1 or 2.
Thus, least value of d-a = 13-2 = 11, and next is 13-1 = 12
 11 is in the options.

Other values => 13*2-1 or 25 and 13*3-1 or 38 and 13*5-1 or 64.

athena97 · Answer

Nice question! Looks simple but showed me I need more practice with maximizing and minimizing. Are there any posts specifically on that topics please?

Posted from my mobile device

Bunuel · Answer

14. Min/Max Problems 
     Theory   
 Maximizing/Minimizing Strategies on the GMAT - All in One Topic! 
     Questions   
 Worst Case Scenario Questions  
 DS Questions 
 PS Questions

For more check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

If abc*d = 390, where a, b, c and d are positive integers, and a < b

Prep Toolkit

Top 5 GMAT Debrief Videos

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

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a*b*c*d = 390, where a, b, c and d are positive integers, and a < b