Powerprep problems

[synthia]

Hi,

por favor, el señor solve these for me![V]

1. When a positive integer 'n' is divided by '7', the quotient is 'q' and the remainder is 4. when '2n' is divided by 7 the remainder is one and the quotient in terms of 'q' is:

a. q/2
b. (q/2)+1
c. 2q
d. 2q+1
e. 2q+2

Ans: 2q+1

2. Let a1,a2,a3,.........an....... be a sequence of +ve nos. where a1=1 and for n>=1, a(n+1)=an + 4. Which of the foll. represents the nth term of the sequence?

a.4n-3
b.4n-1
c.4n
d.4n+1
e.4n+4

Ans: 4n-3

[xaero]

Hi Synthia,

I'd suggest writing out the equations on a paper to solve these probs:

1) According to the first statement, n = (7*q)+4; (EQN 1)

According to the second statement, 2n = (7*x)+1; (EQN 2)
where x = new quotient

Double the first equation, equate the RHS of both equations and then solve for x.

x = 2q+1;


As for your second problem, its a case of an arithmetic series, where the nth term of a sequence is given by:-

an = a1+(n-1)*d; where d = common difference between consecutive nos.

here d = a(n+1) - a(n) = 4, according to data.

therefore, an = 1+(n-1)*4, since a1 here is 1. That is an = 4n-3;

[synthia]

Hi Xaero,

thanks a lot! Hey, now that I know it, it seems really very simple!! Thanks again pal!BTW, do we have to know all the series formulae before we take GRE?

[xaero]

Hi Synthia,

It sure helps to brush up all your high school math formulae, esp those that havent be used too often, such as AP, GP, HP and all those stuff..

[Alexey_K(LexxRuss)]

Done, I mean I solve it myself
1) 2q+1
2) 4n-3

[pawanjsvn]

Another approach-
It always helps to just pick numbers to solve such questions. It saves a lot of time too.

1) Remainder of n/7 is 4.
Choose the nearest number which is n=11.
So, q = 1.

Now, 2n = 22, and 22/7 has q1=3 and remainder = 1.
Clearly the only true relation between q1 and q from the answer choices given is q1 = 2q+1

2) Given a1=1 => a2 = a1 +4 = 5.
Substitute n=2 in all given solutions,
'4n-3' is the only one that gives a 5.