The product of digits of a positive three-digit integer k is 120. Is k

Question

The product of digits of a positive three-digit integer k is 120. Is k a multiple of 5?

(1) k is a multiple of 3.
(2) If we switch any digits in k, it will decrease.

BrentGMATPrepNow · Answer

Given : The product of digits of a positive three-digit integer k is 120.  
Since there aren't that many three digit integers that satisfy this information, I find it useful to take the time out front to identify the possible cases. 
First recognize that k = (2)(2)(2)(3)(5)
So, the three digits could be  4, 5 and 6  OR  3, 5 and 8 .

Target question :    Is k a multiple of 5?

Statement 1 : k is a multiple of 3  
If k is a multiple of 3, then the sum of the digits of k must be divisible by 3
 4 + 5 + 6  =  15 , which is divisible by 3, so the three digits of k could be  4, 5 and 6  
 3 + 5 + 8  =  16 , which is NOT divisible by 3, so the three digits of k can't be  3, 5 and 8

So, it could be the case that k = 465, in which case  k is a multiple of 5. 
It could also be the case that k = 456, in which case  k is a NOT multiple of 5. 
Since we can’t answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : If we switch any digits in k, it will decrease. 
This means the digits of k are such that the value of k is  maximized . 
Since the three digits could be  4, 5 and 6  OR  3, 5 and 8 , there are two possible values of k:  k = 654  or  k = 853  
If k = 654, then  k is NOT a multiple of 5. 
If k = 853, then  k is NOT a multiple of 5. 
This means there is only one possible answer to be target question.
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

hientranzx · Answer

The product of digits of a positive three-digit integer k is 120. Is k a multiple of 5?
k = abc: a*b*c = 120
120 =12*10 = 3*2*2*5*2
Since abc has 3 digits --> abc should contain: 5 3 8 (8 = 2*2*2) or 5 4 6 (4=2*2, 6=2*3).

k is a multiple of 5 only when it is 385, 835, 465, 645

(1) k is a multiple of 3. --> k contains 4, 5, 6.
If k is 465, 645 --> Sufficient
If 5 is not in the unit place --> Not sufficient (ex: 546, 546...)

(2) If we switch any digits in k, it will decrease.
The highest number will be 853, 654 --> These numbers are not a multiple of 5 --> sufficient.

Answer B

JerryAtDreamScore · Answer

Breaking Down the Info:   
> We first need to break 120 down into three digits. 
> We only have two ways to do this:  120 = 8*15 = 8*3*5 , and observe we may move a 2 over from 8 to get  120 = 4*6*5 . 
> Thus k has 12 possible candidates, and there are 6 possible numbers from each scenario.

Rephrase the question:   
> Does k have a unit digit of 0 or 5? Note we cannot have a unit digit of 0 given the product of digits must be 120, therefore we may even go one step further:
>  Does k have a unit digit of 5?

Statement 1 Alone:   
> The first case  120 = 8*3*5  has a sum of digits  8 + 3 + 5 = 16 , which is not a multiple of 3; so k itself is not a multiple of 3. 
> Then by elimination, we confirmed we must have the second case, which indeed has a sum of digits that is a multiple of 3. 
> However, this only confirms which scenario we fall in, and we do not know if 5 is the unit digit. Thus this statement is insufficient.

Statement 2 Alone:   
> This gives us the formation of the digits, we must have either 853 or 654. 
> Both options answer the question " Does k have a unit digit of 5? " with NO.
> Thus this statement is sufficient.

Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The product of digits of a positive three-digit integer k is 120. Is k

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 Data Sufficiency (DS) Questions

The product of digits of a positive three-digit integer k is 120. Is k

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