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Prob solving interesting qtns - doubts

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Prob solving interesting qtns - doubts

by wongee » Sun Sep 23, 2007 12:48 pm
First off, something really basic:

1. For a compound interest problem, I use the formula A=P(1+r/100)^n. I want to know how it works for a qtn that asks for interest compounded SEMI annually? Do you adjust r only or n as well?

2. Here's an interesting one. If you have the OG11th edition, it is on Pg 51, Q11. I really cannot understand this problem. any explanations would be very helpful.

3. OG Diag Pg 51, Q13:
If s and t are positive integers such tha s/t=64.12, which of the following could be the remainder when s is divided by t?
a.2
b.4
c. 8
d.20
e. 45

Can someone explain a not too long method to solve this?
Ans: E

4. Which of the foll is a product of 2 integers whose sum is 11?
a. -42, b. -28, c. 12, d. 26, e. 32

I got this question correctly since I actually used the info regarding the sum ofthe intergers and worked backwards figuring out that the numbers are 14 and -3. However, it seems it can be done using simultaneously eqns as well. i.e. x+y=11, xy= -42. How do you solve for this? Want ot know the other method in case the bulb doesnt strike on G-day.

5. When a square root sign is used on the GMAT, I read that we should use the POSITIVE root only. Is this true?
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by jsackmann » Thu Sep 27, 2007 6:57 am
Don't bother with the compound interest formula. The GMAT will never give you a question that requires you to compound more than 2 or 3 times.

But, in general terms, you need to adjust both r and n.

If you're compounding semi-annually at an annual rate of 8%, that's an interest rate (per compounding term) of 4%, and the number of compounds is twice the number of years.
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by wongee » Mon Oct 01, 2007 7:45 pm
OK got it, so basically implying:
Qtn 8% compounded semi annually for 2 years = (1+0.08/4)^4? or 0.08/2

Qtn:8% compounded semi annually for 1 year: (1-0.08/2)^2?

thanks.
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by ldoolitt » Tue Oct 02, 2007 1:39 pm
Heres how I would do 3.

s/t = 64.12 and s and t are integers
s/t = Whole + remainder/t

Thus

remainder/t = .12

OR

remainder / .12 = t

Since we know t must be an integer, we also know that the remainder / .12 = remainder * 25/3 must also be an integer. Plug in the numbers and viola!
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by ldoolitt » Tue Oct 02, 2007 1:49 pm
For 4 you could do two things

A) Factor trees, then try out all the possible combinations (its actually not that bad)

B) Simultaneous equations and quadratics. This one took me a bit longer than the first method (because I'm not good at large multiplications and square roots) but they are pretty much a toss up. If you are good with quadratics then do that.
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by wongee » Wed Oct 03, 2007 5:31 pm
Quadratics makes sense! I tried that one. Luckily for this one if you start from the top it works, but it is time consuming, espcially if you dont get it in the first two/three options.

Thanks though!
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by joshi.komal » Sun Oct 14, 2007 8:27 am
For the compound interest you have to adjust both rate and time.

You can make use of this formula instead:


A= P( 1 + r/n )^(nt)

where: P= principal
r = Annual rate of interest
(IMPORTANT) n = No of times the interest is compounded per year
t = No of years

so if interest is compounded quarterly then n=4

Thanks
Komal
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by wongee » Mon Oct 22, 2007 5:58 pm
Thanks Komal, so that means for a qtn, for e.g.

5000, compounded quarterly for 2 yrs, @8%

= P(1+r/4)^8 correct?

=5000(1+0.08/4)^8

I heard that the GMAT normally doesnt give high compounds (i.e. more than a year) but I just wanted to have the concept down correctly.
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