Is x a multiple of 4?

Question

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x

Mohammadmo · Answer

Dear! This question is for data sufficiency section.

Posted from my mobile device

Bunuel · Answer

Moved to DS forum. Thank you for noticing.

EncounterGMAT · Answer

\frac{x}{4} =integer?

(1) x + 2 is divisible by 2

\frac{x+2}{2} =integer =>x=2, 4, 6, 8....(all multiples of 2)

If x=2, is  \frac{2}{4} =integer? NO

If x=4, is  \frac{4}{4} =integer? YES

If x=6, is  \frac{6}{4} =integer? NO

INSUFFICIENT!

(2) 6 is a factor of 3x

\frac{3x}{6} = integer =>  \frac{x}{2}  = integer =>x=2, 4, 6, 8....(all multiples of 2)

If x=2, is  \frac{2}{4} =integer? NO

If x=4, is  \frac{4}{4} =integer? YES

If x=6, is  \frac{6}{4} =integer? NO

INSUFFICIENT!

(1) + (2)

\frac{x+2}{2} =integer and  \frac{x}{2}  = integer.........Same as individual statements...no extra information
INSUFFICIENT!

Hence, answer is  option E .

P.S:  Please check the OA since it says the answer is  option C

Bunuel  please help confirm the OA

Bunuel · Answer

You are right. Correct answer is E. Edited. Thank you.

WM88 · Answer

Can somebody explain to me why if 6 is a factor of 3x, than x must be divisible by 2?

TheNightKing · Answer

whollymoses 
Well, if 6 is a factor of 3x then the least value x can take is 2. Because then 3x becomes 6 and 6 is a factor of 6. The next value x can take is 4, which gives us 12 and 6 is a factor of 12. And So on.

I hope that helps!

minustark · Answer

(1) X could be 0 or 2, in this case X will not be a multiple of 4. X could be 4 or 8, which are multiples of 4. Not sufficient.

(2) 3x/6 = an integer. x can be 2, 4 or 6, so it may or may not be a multiple of 4. Not sufficient.

Together, X can be 6 or 10, or 4 or 8. Not sufficient.

E is the answer.

CAMANISHPARMAR · Answer

The individual statements are not enough and give the same information that x is divisible by 2. If x is divisible by 2, it does not mean that it is also divisible by 4; it may or may not be the case.

Hence the correct answer is option E

Sabby · Answer

Is x a multiple of 4?

Let's choose 2 numbers to test : x= 2 and x = 8

(1) x + 2 is divisible by 2

For x= 2
x+2= 2+2 = 4 which is a divisible by 2 and a multiple of 4

For x = 8
x+2 = 8+2 = 10 which is divisible by 2 but is not a multiple of 4

=> sometimes yes, sometimes no = insufficient

(2) 6 is a factor of 3x

For x = 2 
3x= 3*2= 6 which is a factor of 6 but not a multiple of 4

For x=8
3x= 3*8 = 24 which is a factor of 6 and a multiple of 4

=> sometimes yes, sometimes no = insufficient
 
TOGETHER INSUFFICIENT

Answer E

v12345 · Answer

Statement 1 : Insufficient 
If x=6, x+2=8,divisible by 2 and multiple of 4
If x=8, x+2=10,divisible by 2 but not multiple of 4

Statement 2 : Insufficient 
If x=6, 3x=18,6 is factor but not multiple of 4
If x=8, 3x=24,6 is factor and multiple of 4
 
Combining both, also insufficient.
Hence, OA is (E).

bumpbot · Answer

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Is x a multiple of 4?

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GMAT Data Sufficiency (DS) Questions

Is x a multiple of 4?

Prep Toolkit

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