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Need Help with xy-plane, power, and word problem questions [#permalink]
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

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

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?

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...

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

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. _________________

To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton