If x = 31! 18, then x is divisible by which of the following

Question

If x = 31! – 18, then x is divisible by which of the following

I. 6
II. 9
III. 12

A. I only
B. II only
C. III only
D. I and II
E. I, II and III

This is a  PS Butler Question

Check the links to other Butler Projects:

Data Sufficiency Butler  
  Critical Reasoning Butler

Sonatomar · Answer

⭐ Important trick

If:

A is divisible by n

then A−B is divisible by n only if B is also divisible by n.

So don't just see that 31! is divisible by 12 and automatically conclude 31!−18 is divisible by 12.

abhishekb1352 · Answer

Here x = 31! -18
31! had factors of 3, 6, 9 and 12 among others whereas 18 = 2*3*3
18 is divisible by both 6 and 9 but not by 12.

so in total x = 31! - 18 is also only divisible by both 6 and 9 but not by 12. Hence option D. I and II only.

dhart · Answer

In that case , 31! - 18 is divisible by 6 and 9
option D

onlyPlanA · Answer

This can also be easily calculated to avoid careless mistakes.

x = 31! - 18
x/6 = 31!/6 - 18/6 = zero remainder
x/9 = 31!/9 - 18/9 = zero remainder
x/12 = 31!/12 - 18/12 = remainder > zero

Hence, option D.

SS990 · Answer

x=31!-18= 18(31*30*29.....-1)

so above is divisible by 18, hence div by 6 and 9. for it to be div by 12, it needs 2^2 which is not possible since the bracket would be an odd number and 18 has only one power of 2

hence answer is D

If x = 31! 18, then x is divisible by which of the following

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 x = 31! 18, then x is divisible by which of the following

Prep Toolkit

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