If a, b, and c are positive integers, is it true that ab is divisible

Question

If a, b, and c are positive integers, is it true that ab is divisible by 12?

(1) 6a = 2b
(2) 3b = 4c

Bunuel · Accepted Answer

If a, b, and c are positive integers, is it true that a·b is divisible by 12?

(1) 6a = 2b --> you have to reduce here: 3a = b --> b is a multiple of 3 --> if b=12, then ab is divisible by 12 but if b=3 and a=1, then ab is NOT divisible by 12. Not sufficient.

(2) 3b = 4c --> b/c = 4/3 --> b is a multiple of 4. Not sufficient.

(1)+(2) b is a multiple of both 3 and 4, so it must be a multiple of their LCM, which is 12, so ab =12a = a multiple of 12. Sufficient.

Answer: C.

Mona2019 · Answer

(1) 6a = 2b
 => 3a= b
 ab= 3a^2 
 ab can be 3, 12,27
Insufficient

(2) 3b = 4c
 b = 4/3c
 As B is an integer, c should be of the form 3n
So b can be 4, 8, 12...
Insufficient

Combining both, b = 3a and b= 4/3c
a=4/9c
=> C has to be of form 9m=9,18..etc
So b = 12,24

Sufficient 
IMO C

Posted from my mobile device

GMATinsight · Answer

Question: Is ab divisible by 12?

Note: A number is divisible by 12 when its divisible by 4 as well as 3

Statement 1 : 6a = 2b 
i.e. b = 3a
i.e. b is a multipe of 3 
but we don't know whether ab is a multiple of 4 or not 
Hence,  NOT SUFFICIENT

Statement 2 : 3b = 4c 
i.e. b is divisible by 4 and c is divisible by 3
a is still unknown hence
Hence,  NOT SUFFICIENT

Combining the statements

STatement 1: b is divisible by 3
STatement 2: b is divisible by 4
i.e. b is divisible by 12
i.e. ab is divisible by 12

Hence,  SUFFICIENT

Answer: Option C

sumitkrocks · Answer

If a, b, and c are positive integers, is it true that ab is divisible by 12?

Statement 1:
6a = 2b
or 3a = b
so b can be 3, 6, 9, 12 ...mutiple of 3 
a = b/3, since a is an integer a can be 1,2 , 3 ..etc 
ab can be 3, 6, 9, 12, etc multiple of 3 
Not sufficient

Statement 2: 
3b = 4c

b=4c/3 since a, b and c are integers

c has to be a multiple of 3 and b has to be a multiple of 4

b=4, 8 , 12, 16...
about a no info

Not sufficient

Combining statement 1 and 2 
a=b/3 and b is a multiple of 4; form the combined statement we can say to keep a an integer b has to be a multiple of 12( shall have 3 and 4 both as factors)

Hence sufficient 
Answer C

sumitkrocks · Answer

In statement 2 : I agree that b is divisible by 4 and c is divisible by 3, but how did you arrive at conclusion that ab is divisible by 12; i do not see any information about "a" in statement 2 
Please help me understand

mohammadfaraaz123 · Answer

Required: ab/2*2*3 = Integer

Statement (1) 6a = 2b

3a = b
a = b/3

Since they are integers. We know B is divisible by 3.

b/3 = Integer

But don't have information on A.  Insufficient.

Statement (2) 3b = 4c

b= 4c/3

C/3= Integer 
b/4 = Integer , for sure

But we don't have any information on A

Insufficient

Combining Statement 1 and 2

b/3 = Integer
b/4= Integer

b/3*4 = integer as well.

Hence, ab/12 = integer.

Answer choice C is sufficient.

TarunKumar1234 · Answer

If a, b, and c are positive integers, is it true that ab is divisible by 12?

Statement 1:
6a = 2b
or 3a = b
so b can be 3, 6, 9, 12 ...mutiple of 3
a = b/3, since a is an integer a can be 1,2 , 3 ..etc
ab can be 3, 6, 9, 12, etc multiple of 3
Not sufficient

Statement 2:
3b = 4c

b=4c/3 since a, b and c are integers

c has to be a multiple of 3 and b has to be a multiple of 4

b=4, 8 , 12, 16...
about a no info

Not sufficient

Combining statement 1 and 2
a=b/3 and b is a multiple of 4; form the combined statement we can say to keep a an integer b has to be a multiple of 12( shall have 3 and 4 both as factors)

Hence sufficient
Answer C

If a, b, and c are positive integers, is it true that ab is divisible

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If a, b, and c are positive integers, is it true that ab is divisible

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