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Need Help with xy-plane, power, and word problem questions

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Manager
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Need Help with xy-plane, power, and word problem questions [#permalink] New post 21 Apr 2007, 15:21
Hi everyone,
I am posting four questions which are from GMATPrep. So, if you know how to solve the following, please let me know by explaninng them.

Thank you very much


==================Questions====================
1) In the xy-plane, line k has positive slope and x-intercept 4. If the area of the triangle formed by line k and two axes is 12, what is the y-intercept of link k?

a)-6
b)-4
c)-3
d)3
e)6

------------------------------------------------------------------------------------
2) My question is what is the shortcut to solve question like this?

2 + 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

The correct answer is 2^9
-------------------------------------------------------------------------------------
3) If (3)^x - (3)^x-1 = 162, then x(x-1) =?

a)12
b)16
c)20
d)30
e)81

---------------------------------------------------------------------------
4) In a certain furniture store, each week Nancy earns s salary of $240 plus 5 percent of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week?

a)$2200
b)$3450
c)$4200
d)$4250
e)$5000

Here what I did:
450 тАУ 240 = 210
(x)(5/100) = 210 => x = 4200! But the correct answer is 5000 Why?
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 [#permalink] New post 21 Apr 2007, 19:34
hey i did the same thing as u for Nancy in the furniture store.. so i would have gotten it wrong.. but then i looked it over and it says she gets 5% for her sales that EXCEEDS 800.. so the first 800 doesnt count!!!

therefore, she has to sell ABOVE 800 to start getting commission.. and if she sells 5000bucks, then she gets comission on 4200 of it... so yes, the answer is 5Grand...

however, that was worded trickily!!!
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 [#permalink] New post 22 Apr 2007, 00:37
1) In the xy-plane, line k has positive slope and x-intercept 4. If the area of the triangle formed by line k and two axes is 12, what is the y-intercept of link k?

a)-6
b)-4
c)-3
d)3
e)6


(A) for me :)

Let b be the Y interceptor

As the X interceptor is positive and the slope is positive too, the y interceptor must be negative.

That said, (D) & (E) are ruled out.

Then,
Area of the triangle = (-b) * 4 / 2 = 12 (right triangle at 0(0,0))
<=> -b = 12/2 = 6
<=> b = -6
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Re: Need Help with xy-plane, power, and word problem questi [#permalink] New post 29 Apr 2007, 23:59
Question
----------
3) If (3)^x - (3)^x-1 = 162, then x(x-1) =?

a)12
b)16
c)20
d)30
e)81
----------


Lets caculate x.

First, I work on the left side of the equality:
(3)^x - (3)^x-1 = (3)^x (1 - (3)^-1) = (3)^x (1 - 1/3) = (3)^x (2/3)

Second, I work on the whole equality
(3)^x (2/3) = 162
(3)^x = 162 * 3/2 = 81 * 3 = 3^5

Finally, x = 5
And x(x-1) = 20

It is perhaps a bit time consuming. If someone has any shortcuts it will be interesting. :wink:
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 [#permalink] New post 30 Apr 2007, 00:26
1) If it's positive rising and has an x-intercept, then the y-intercept must be negative.

So |1/2(4)(-y)| = 12
y = -6 (A)
--------------------------------------------------------------------------------
3) 3^x - 3^x/3 = 162
3(3^x) - 3^x = 486
3^x(2) = 486
3^x = 243
x = 5
So x(x-1)= 20 (C)
---------------------------------------------------------------------------
4) So the extra 5% of total sales above 800 = 210

0.05(total sales above 800) = 4200

total sales above 800 = 4200

So grand total = 4200+800 = 5000 (e)


For question 2, can you recheck that you have posted the question correctly?
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 [#permalink] New post 30 Apr 2007, 00:59
Q 4:

240 + (1/20)(X-800) =450

X=5000
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Re: [#permalink] New post 18 Aug 2008, 14:37
ywilfred wrote:

For question 2, can you recheck that you have posted the question correctly?



It should have been only two single 2's:

2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

I too would like to know the shortcut to this.
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Re: Re: [#permalink] New post 18 Aug 2008, 15:00
konclen wrote:
ywilfred wrote:

For question 2, can you recheck that you have posted the question correctly?



It should have been only two single 2's:

2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) = ?

I too would like to know the shortcut to this.


Use the geometric Progression.
Any series that is of the form, a, ar, ar^2, ar^3..... a*r^(n-1) is in GP.
The formula for sum of the terms that are in GP is => a *(r^n -1 )/(r-1)
For the series, 2 + 2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8), re-align the series:
= [2 + (2^2) + (2^3) + (2^4) + (2^5) + (2^6) + (2^7) + (2^8) ] + 2
= [2*(2^8 -1)/(2-1)] +2
= [2(2^8 -1)] + 2
= 2^9 -2 +2
= 2^9
It is good to get familiarized with AP (Arithmetic Progression) and GP (Geometric Progression) for these kind of problems.
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Re: Need Help with xy-plane, power, and word problem questions [#permalink] New post 24 Aug 2008, 01:53
Thanks a lot for the reply.

I eventually saw that it was rather quickly to resolve via the following:

2+2 = 2^2, which leads to
2^2 * 2^2 = 2 * 2^2 = 2^3
2^3 * 2^3 = 2 * 2^3 = 2^4
So on and so forth...
This leads to:
2^8 * 2^8 = 2 * 2^8 = 2^9
Re: Need Help with xy-plane, power, and word problem questions   [#permalink] 24 Aug 2008, 01:53
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