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# few DS and PS questions..

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Manager
Joined: 18 Apr 2007
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few DS and PS questions.. [#permalink]  20 Aug 2007, 10:18
hey guys! thanks soo much for looking at this post.. i know these questions are easy for you guys, but i would really REALLY appreciate help! i feel i am lacking the basics.. lol

For every integer K from 1 to 10 inclusive, the Kth term of a sequence is given by:
(-1)^k+1 (1/2^k)
If T is the sum of the first 10 terms in the sequence, then T is:

OK so i plugged in 1 and got 1/4.. but i dont understand why the answer is between 1/4 and 1/2.. bc if I plug in 10.. doesnt (-1)^11 give us -1??

What function is f(a+b)=f(a)+f(b) for all positive numbers a+b?

I just really forget how functions work! so if someone could help me out here, that be wonderful! the answer is F(x)=-3x

If the speed of X meters/sec. is equivalent to the speed of Y km/hr. what is Y in terms of X?

3600000x

18x/5

5x/18

6x/5

60x

Just confused as to the best approach to set this question up.

Thanks again for all your help!! i have the GMAT in 7 days.. and i am mildly stressing! LOL!
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Manager
Joined: 18 Apr 2007
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ohhh! i have one more problem.

2^x - 2^x-2 = 3(2)^13
What is the value of X?

9
11
13
15
17

thanks again!
VP
Joined: 10 Jun 2007
Posts: 1464
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andrealittrell wrote:
ohhh! i have one more problem.

2^x - 2^x-2 = 3(2)^13
What is the value of X?

9
11
13
15
17

thanks again!

(2^x) - (2^(x-2)) = (2^x) - (2^x)/(2^2) = (2^x)*(1-1/4)
= (2^x)*(3/4) = (2^(x-2)) * 3

so, x-2 = 13 => x=15
Manager
Joined: 18 Jun 2007
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2^x - 2^(x- 2) = 3.2 ^13

2^x - 2^x * 1/ 4 = 3.2^13
2^x * (1- 1/4) = 3 * 2^13

2^x *3 / 4 = 3.2^13

2^x = 3 * 2^13 * 4/3

2^x = 2 ^ 15

X = 15
Manager
Joined: 18 Apr 2007
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hey, ok i totally get that! (thanx for the help!)
but.. i am just confused as to where the 1 in 1-1/4 comes from?!?

2^x-2^x(1/4)

why do u put a 1 in front of 1/4????
VP
Joined: 10 Jun 2007
Posts: 1464
Followers: 6

Kudos [?]: 142 [0], given: 0

andrealittrell wrote:
hey, ok i totally get that! (thanx for the help!)
but.. i am just confused as to where the 1 in 1-1/4 comes from?!?

2^x-2^x(1/4)

why do u put a 1 in front of 1/4????

Here is what you have:
((2^x) - (2^x)/4)
Factor out 2^x, you get
(2^x)*(1-1/4)
GMAT Club Legend
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For every integer K from 1 to 10 inclusive, the Kth term of a sequence is given by:
(-1)^k+1 (1/2^k)
If T is the sum of the first 10 terms in the sequence, then T is:

The first term is (-1)^2(1/2) = 1/2
The second term is (-1)^3(1/2) = -1/4
The third term is (-1)^4(1/8) = 1/8
The fourth term is (-1)^5(1/16) =-1/16

So we have on our hands a geometric progression with sum of term given as S =a(1-r^n)/(1-r)

So a = 1/2, r = -1/2, n = 10. S = 1/2(1-(-1/2)^10)/(1+1/2). The term (-1/2)^10 is going to be very big, so the S is close to (1/2)/(2/3) = 1/3 which is between 1/2 and 1/4.
GMAT Club Legend
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Posts: 5068
Location: Singapore
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Kudos [?]: 194 [0], given: 0

If the speed of X meters/sec. is equivalent to the speed of Y km/hr. what is Y in terms of X?

3600000x

18x/5

5x/18

6x/5

60x

1km = 1000m
y km = 1000y metres

So 1000y metres in 1 hour = 1000y/60*60 metres/sec = 5y/18 m/s

So x m/s = 5y/18 m/s
y = 18x/5 m/s --> Ans B
Manager
Joined: 18 Apr 2007
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BHK -- thank you so so so much! hugee help!

and thanks guys for helping me out with the other questions, i really appreciate it!
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