Why do Both A=3 and A=6 work for divisibility by 3 and 6?

[dnt]

i saw this in a SAT prep book and i cannot figure out what's going on here:

it says: "2A is divisible by both 3 and 6. If A is a digit, what is the value of A?"

seems simple enough but the choices are 1, 2, 3, 4, and 6. don't both 3 and 6 work?

if A is 3, then 2A is 6, and that is divisible by both 3 and 6.

if A is 6, then 2A is 12 and that is divisible by both 3 and 6.

what am i missing?

 

[NateTG]

Then mean "2A=2*10+A". (A is 4)

 

[dnt]

i don't understand. how did you get that equation and how did you even solve it?

2A=2*10+A?

wouldnt that mean A = 20? and i still have no ieda how you got that from the info i provided. please help.

 

[chroot]

dnt,

The question means "the digit 2 followed by some digit A," NOT 2*A.

- Warren

 

[konartist]

It's the SAT questions like these that kill me.

 

[AlphaNumeric]

Any number divisible by 6 is divisible by 3, so it's somewhat superfulous to ask 'divisible by 3 and 6'.

 

[Curious3141]

i saw this in a SAT prep book and i cannot figure out what's going on here:

it says: "2A is divisible by both 3 and 6. If A is a digit, what is the value of A?"

seems simple enough but the choices are 1, 2, 3, 4, and 6. don't both 3 and 6 work?

if A is 3, then 2A is 6, and that is divisible by both 3 and 6.

if A is 6, then 2A is 12 and that is divisible by both 3 and 6.

what am i missing?

They meant "2A" as it is written down, not "two times A".

E.g. If "27" is "2A" then "A" is 7. Getit ?

 

[Markjdb]

Any number divisible by 6 is divisible by 3, so it's somewhat superfulous to ask 'divisible by 3 and 6'.

Every number divisible by 6 is obviously divisible by 3, but not every number divisible by 3 is divisible by 6 (eg.27). That's why the syntax of the question is the way it is: 'divisible by 3 and 6' not 'divisible by 6 and 3'

 

[Curious3141]

That's why the syntax of the question is the way it is: 'divisible by 3 and 6' not 'divisible by 6 and 3'

That makes no sense at all, the order of the conditions has no bearing when "and" is the conjoiner. The question could simply have stated. "2A is divisible by six", and that would've had the same meaning without the redundancy.

 

[Hootenanny]

Indeed, I wonder how much time the person(s) who set the question thought about it . Probably not aslong as we've been discussing it.

 

[dnt]

thanks for the explanations - i do understand it now but i think its a poorly worded question, especially for anyone whos taken algebra (who is probably everyone if you are taking the SAT).

2A means 2 times A (usually) when in math class.