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Sat Math Question help

I just received my score report and I'm still stuck on this one question I encountered in May.
If x and n are positive integers and (x+n)/(4x+n) = 1/3, what is the smallest poissble value of x+n? The answer is 3. But how?

June 23, 2013

7 Comments • Newest first

Watermelon

Aren't you suppose to derivative these?

Reply June 23, 2013
Llamamamma

careful though if you get 2 questions wrong you drop to a 730

Reply June 23, 2013
AmyrIin

[quote=zilliro]EDIT: @amyriin

the method you're using is impractical. if the solution were (x+n)=30, what math would you do? guess at every permutation until you happen upon the correct answer?

(x+n)/(4x+n) = 1/3

3(x+n) = 1(4x+n)
3x+3n = 4x+n
2n = 1x
n = 1, x = 2 -> (x+n) = 3[/quote]

i'm sorry but you have a limited time on the SAT, and granted your method doesn't take THAT long, it seems much easier to guess and check. you don't really think at all that way and you get it done incredibly quickly.

perhaps it takes around the same time, but idk i would try to speed through it using whatever guerilla math i could. let's be honest the SAT math section requires really no real math.

Reply June 23, 2013
zilliro

[quote=jordan5663]Ahh thank you! I tried to solve for x+n using proportions but I didn't know what to do after that That's another burden lifted off my chest.[/quote]

EDIT: @amyriin

the method you're using is impractical. if the solution were (x+n)=30, what math would you do? guess at every permutation until you happen upon the correct answer?

(x+n)/(4x+n) = 1/3

3(x+n) = 1(4x+n)
3x+3n = 4x+n
2n = 1x
n = 1, x = 2 -> (x+n) = 3

Reply June 23, 2013 - edited
AmyrIin

[quote=jordan5663]Ahh thank you! I tried to solve for x+n using proportions but I didn't know what to do after that That's another burden lifted off my chest.[/quote]

that's just 1 question, although -1 in math prob yielded a 770. how'd you do in the end?

Reply June 23, 2013 - edited
jordan5663

[quote=AmyrIin]x+n = 1

Impossible
x and n have to both be positive
perhaps

x+n = 2?

x = 1 n = 1 doesnt work for bottom. bottom would = 5.

x + n = 3?

x = 1 n = 2?
3/6 --> nope.

x = 2 n = 1?
3/9 = 1/3.

yep![/quote]
Ahh thank you! I tried to solve for x+n using proportions but I didn't know what to do after that That's another burden lifted off my chest.

Reply June 23, 2013 - edited
AmyrIin

x+n = 1

Impossible
x and n have to both be positive
perhaps

x+n = 2?

x = 1 n = 1 doesnt work for bottom. bottom would = 5.

x + n = 3?

x = 1 n = 2?
3/6 --> nope.

x = 2 n = 1?
3/9 = 1/3.

yep!

Reply June 23, 2013 - edited