SAT math question???

[BehindEnemyLines]

I've two questions I couldn't find answer in the Test Prep. I'm having trouble what the two questions are asking. Please give answers with explanations.

1. For all values of a, let < a > be defined as < a > = 4a - 4. Which of the following equals < 6 > - < 5 >?
A. < 2 >
B. < 3 >
C. < 4 >
D. < 5 >
E. < 6 >

2. If n is a postive integer, which of the following CANNOT be the units digits of 3^n?
A. 1
B. 3
C. 5
D. 7
E. 9

Thanks alot.

SORRY ABOUT THAT. I LOOKED AT THE WRONG ANSWER CHOICES. IT IS NOW CORRECTED.

Correct answer for #1 is A. <2>
Correct answer for #2 is C. 5
Those answers are from the back. I don't know how the book arrives at those answers. Can someone explain?

 

[IcemanJer]

1) answer is clearly 4.. might be a misprint in the question.
2) oops, nevermind.. didn't read the question close enough.

 

[GoodToGo]

Question is wrong. THe answer is 4 and its not on there. For #2, the answer is C(5).

3^1=3
3^2=9
3^3=27
3^4=81

but nothing has a last digit of 5. Hope this helps.

 

[ebaycj]

question 2 is C.

3^(1n) always ends in 3.
3^(2n) always ends in 9.
3^(3n) always ends in 1.
3^(4n) always ends in 7.
for all n > 1.

(this took about 5 seconds to figure out with a calculator, just do 3*3, then *3, then *3, then *3, then *3, and you will see a pattern).




question 1 should have an answer of 4.

<a> = ((4*a) - 4), or more simply 4*(a-1)

so then <6> - <5> would be :

[ (4*(6-1)) - (4*(5-1)) ]
then
[ (4*5) - (4*4) ]
then
[ (20) - (16) ]
then
[4]

done!


ebaycj

 

[Noriaki]

The way they've written q1, <> seems to be a "function".

And clearly this function applied to 6 subtract this function applied to 5 must be 4...

 

[BehindEnemyLines]

Sorry for the confusions.
The questions are NOT misprinted.
I correctED the possible answers for number 1 and 2.
Remember that the answers are from the back of the booklet and they're not mine.

 

[IcemanJer]

Originally posted by: Noriaki
The way they've written q1, <> seems to be a "function".

And clearly this function applied to 6 subtract this function applied to 5 must be 4...

misprints are not uncommon in prep books.

 

[Noriaki]

oh sure change the questions...hehehe

okay.

This is easy.

<a> = 4a - 4 = 4(a-1)

<6> - <5> = <x>
4(6-1) - 4(5-1) = 4(x-1)
(6-1) - (5-1) = (x-1)
5 - 4 = x - 1
1 = x - 1
2 = x

the answer is <2>

2 is already done.

 

[IcemanJer]

ahhhhh..... okay.

so 4 = 4*n - 4
n = 2

 

[Einz]

regarding question 2, the answer choices all have <> in them, meaning to apply the function also. I agree the answer to <6>-<5> is 4, but in the answer choices, only <2> equal 4 (2*4-4). Hence, the <2> answer choice is correct.

*EDIT* Gotta type faster

 

[satori]

Um guys, you aren't reading the question carefully enough .The answers for #1 is given as the <a> function...

So, <2> actually equals 4... the answer you guys were looking for...

edit: I gotta type quicker, too.

 

[Noriaki]

Originally posted by: satori
Um guys, you aren't reading the question carefully enough .The answers for #1 is given as the <a> function...

They weren't before He changed them on us

 

[IcemanJer]

Originally posted by: satori
Um guys, you aren't reading the question carefully enough.

In the original post, the < > in the answers were left out.

edit:\> I gotta type quicker too... hehe

 

[satori]

noriaka: Sorry, my bad. My faith in AT'ers is restored.

 

[BehindEnemyLines]

Thank you all for the help. Initially for #2, I didn't know what units digits meant - SAT wordings can be tricky. Now I understand #2.

I'm still not quite sure on #1 especially. "<> in them, meaning to apply the function also":

Einz :

regarding question 2, the answer choices all have <> in them, meaning to apply the function also. I agree the answer to <6>-<5> is 4, but in the answer choices, only <2> equal 4 (2*4-4). Hence, the <2> answer choice is correct

I do well in the verbal sections, but just stink on those math questions with hard rating and math in general. I will have more questions on math as I continue the prep books so I hope AT'ers here can help again.

Appreciate it.

 

[Noriaki]

Well..

4a - 4 is a function of a.

Instead of using the <a> notation they could say f(a) = 4a - 4.

Then the question woudl read f(6) - f(5) = ?

f(2) in this case.

Instead of the f(a) notation, they used the <a> notation. Assuming they mean that to be a function, it doesn't change anything.

You just take <6> and <5> and plug them into 4a-4 and get 24-4 and 20-4. No problems.

It's kind of an odd notation, but it works fine.

 

[IcemanJer]

in SAT math you'll see all sort of funky notations like that.

For example you'll get something like "If a [] b = (a*b + a^b)" or something like "Given a [] b, where [] is a mathmatical operation, solve for ....some..equation..."

It's quite annoying, but not hard.

 

[Noriaki]

Originally posted by: IcemanJer
in SAT math you'll see all sort of funky notations like that.

For example you'll get something like "If a [] b = (a*b + a^b)" or something like "Given a [] b, where [] is a mathmatical operation, solve for ....some..equation..."

It's quite annoying, but not hard.

Ahhhh

I'm Canadian going to a Canadian University, I have no reason to take an SAT. Canada doesn't use them, so Canadians only do them if we want to go to a US college.

I didn't realize they used odd notations like that.