n is divisible by 14 and 3. Which of the following statements must be

Question

n is divisible by 14 and 3. Which of the following statements must be true?

I. 12 is a factor of n.
II. 21 is a factor of n.
III. n is a multiple of 42.

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

firas92 · Answer

n = 7*2*3*x = 21*2*x = 42*x

For 12 to be a factor of n, at least one more 2 must be there in its factors about which there is no mention

II and III must be true

Answer is  (D)

Hit Kudos if this helped!

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LevanKhukhunashvili · Answer

According to the stem, we know that n has 2, 3 and 7 as prime factors

I. 12=2^2*3; we only know that n is divisible by 2, nothing about 4  Not Valid 
II. 21=3*7;  Valid 
III. 42=2*3*7;  Valid

IMO
Ans:  D

m1033512 · Answer

IMO D

14 and 3 are co prime

so the LCM of 14 and 3 will be the value of n minimum can have

so n can be 42,and higher multiples

so 21 divides n

and n is multiple of 42

IMO D

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MathRevolution · Answer

n is divisible by 14 and 3: Possible numbers are 42, 84, 126, and so on

I. 12 is a factor of n:   NOT TRUE

II. 21 is a factor of n:   TRUE

III. n is a multiple of 42:   TRUE

Only options II and III are true.

Answer D

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem Series ↧↧↧

https://www.youtube.com/watch?v=d23Xj5jDaKk

n is divisible by 14 and 3

=> n = LCM(3,14)*k (where k is an integer) = 42k  Watch this video  to  MASTER LCM and GCD ]

I. 12 is a factor of n. 
n = 42k = 6*7k
Now, 12 will be a factor of n ONLY when k is even, which might not be true always
=>  FALSE  for MUST be true

II. 21 is a factor of n. 
n = 42k = 21*2k
=> 21 is a factor of n
=>  TRUE

III. n is a multiple of 42. 
n = 42k
=> n is a multiple of 42
=>  TRUE

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the basics of Factors and Multiples

https://www.youtube.com/watch?v=1rw-WLkavcM

n is divisible by 14 and 3. Which of the following statements must be

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GMAT Problem Solving (PS) Questions

n is divisible by 14 and 3. Which of the following statements must be

Prep Toolkit

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