Problem Solving

1]A certain portfolio consisted of 5 stocks, priced at $20, $35,

$40, $45 and $70, respectively. On a given day, the price of

one stock increased by 15%, while the price of another

decreased by 35% and the prices of the remaining three

remained constant. If the average price of a stock in the

portfolio rose by approximately 2%, which of the following

could be the prices of the shares that remained constant?

A) 20, 35, 70

B) 20, 45, 70

C) 20, 35, 40

D) 35, 40, 70

E) 35, 40, 45


2] A guidance counselor is planning schedules for 30 students.
Sixteen students say they want to take French, 16 want to
take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish. How many students want French only?


3]If 4x - 3y = 24, then what is the value of 2y ? 8(x / 3)?
(1)-16
(2)-12
(3)-8
(4)-6
(5)-4

4]A natural number is divided into two positive unequal parts
such that the ratio of the original number to the larger (divided)
part is equal to the ratio of the larger part to the smaller part.
What is the value of this ratio?
(51/2 − 1)

(51/2 + 1) / 2

(51/2 + 1) / 4

(51/2 + 1) / (51/2 − 1)

(51/2 + 3) / (51/2 − 1)

5] A sequence of real numbers is defined by the rule:
a(n) = 4 − 3 a(2 −n).
What is the value of a(0)?
0

1

4/3

2

3

Please also provide the explanation also...

[/list]

I think sth is missing in the 3rd question.

Is it 2y * 8(x/3) or 2y/8(x/3)

Solution for 5th problem

a(0) = 4 - 3a(2) ------ 1

a(2) = 4 - 3a(0) -------2

Substitute equation 1 in 2

a(2) = 4 - 3(4 - 3a(2))
a(2) = 1

Substitute a(2) in 1
a(0) = 1

Answer for 2nd problem is 7

I can explain this if you can confirm the solution. This question can be easily done with Venn Daigrams

Hi,
Yup the answer of 2nd question is 7.
Sorry in the third question i missed out multiplication sign,the question is as
If 4x - 3y = 24, then what is the value of 2y*8(x / 3)?
And thanks yup the answer for question 5 is 1.I messed somewhere....
Thanks...

Are you sure it wasn't a subtraction sign that was left out in Question 3? In that case, the answer would be A) -16, since

4x-3y=24
(multiply by -1)
3y-4x=-24
(multiply by 2/3)
2y-(8/3)x=-16

If it was meant as a multiplication then I'm stumped...

Our main aim is to calculate "z"

Here are the equations you can use to solve for z

x+y+3+8 = 16
x+z+2+3 = 16
y+3+2+5 = 11

Asmita

Eric, Gabriel or Stacy should help us with the remaining problems.

Are you having solutions for these problems?

2] A guidance counselor is planning schedules for 30 students.
Sixteen students say they want to take French, 16 want to
take Spanish, and 11 want to take Latin. Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish. How many students want French only?

This question is best solved with the help of a Venn Diagram

Latin students total = 11
Only Latin = 5
Only French and Latin = 5-3=2
Latin + French + Spanish = 3
Therefore Latin + Spanish only = 11-(5+3+2)=1

Spanish Total = 16
Spanish + Latin only = 1
Latin+French+Spanish=3
Spanish only = 8
Therefore Spanish + French only = 16-(1+3+ 8 ) = 4

Total french = 16
Spanish + French only = 4
French + Latin only = 2
Spanish + French + Latin = 3
Therefore French only = 16-(4+2+3)=16-9=7

There is something missing in the third question...Please clarify

f2001290 wrote:Asmita

Eric, Gabriel or Stacy should help us with the remaining problems.

Are you having solutions for these problems?

@ f2001290 ... good work with the venn diagram ...

Now since the 2nd and 5th question have already been discussed ( also I agree with mschling the missing sign in the 3rd question shuld be the – sign and not the * sign … and he has also got the answer right .. so that takes care of the 3rd question)….. i am posting the method to solve the 4 question ...

let the larger part be a .. the smaller part be b .. so the number is a+b....

.. according to the given condition (a+b)/a= a/b .... subtracting 1 from both the sides of the eqn ..

we have (a+b)/a - 1= a/b –1 …
b/a= a/b – 1…
b/a-a/b = -1…

let b/a = x … so we have

x-1/x = -1 …
x^2 - 1= -x
x^2 + x – 1 = 0 ..

solving for x we have x = (5^1/2 - 1 )/2 .. but we want the ratio a/b … so a/b = 1/x (since x =b/a) … so we have a/b = 2 / (5^1/2-1) .. multiplying both the numerator and denominator with 5^1/2 + 1 … we have ( 2 (5^1/2+1))/((5^1/2-1)*(5^1/2+1)) .. which is equal to … 2 * (5^1/2+1)/4 = (5^1/2 + 1)/2 .. so the answer is B …

I have to tell that this is a tuff question and according to me out of the scope of the gmat … got to go ... will post the solution of the first q later .. btw the first question has already been discussed … somewhere in the PS forum … if u find it ... good .. or will post the solution later ….

The avg price of stock portfolio increased by 2%
ie total rise in value 2% (20+35+40+45+70) = 4.2
also the increase in 15% minus dectrease in 35% should be 4.2

so looking at options taking what remains from the options to calculate

A 15% of 45 - 35% of 40 is not equal to 4.2 is infact negative

B 15% of 40 - 35% of 35 is not equal to 4.2 is infact negative

C 15% of 70 - 35% of 45 is not equal to 4.2 is infact negative

D 15% of 45 - 35% of 20 is not equal to 4.2 is infact negative

E 15% of 70 - 35% of 20 is 10.5 - 7 is closer to the ans

It seems to be E though i am not sure