Over a period of 2 years from 2010 to 2012, Stock A and Stock B have

Question

Over a period of 2 years from 2010 to 2012, Stock A and Stock B have changed in value. In 2010, a share of Stock A and a share of Stock B were, together, worth a total of N dollars. Also, in 2010, the ratio of the price of Stock A to Stock B was 0.8. A and B represent the percent change in value of stocks A and B, respectively from 2012 to 2012. The percent change in a quantity X is calculated using the formula:

100∗\frac{X_{new}−X_{old}}{X_{old}}

In the table, select the expression that represents the value of Stock B in 2010 and the expression that represents the ratio of Stock A to Stock B in 2012. Make only two selections, one in each column.

Franzhel · Accepted Answer

For the first column:
Let the value of stock A and the value of stock B be SA and SB.
We know that  SA+SB= N  and that  SA/SB=0.8 . Therefore  SB+0.8SB=N  ->  SB=N/1.8

For the second column, we are asked SA/SB in year 2012. Since the increase in percentage is A and B, SA in 2012 will be equal to  SA*(1+A)  and SB will be  SB*(1+B) .
Then,  SA/SB (in 2012) = \frac{SA*(1+A)}{SB*(1+B)} . Since we know that SA/SB is 0.8, the answer is  \frac{0.8*(1+A)}{(1+B)}

Sajjad1994 · Answer

Official Explanation

Because of all of the variables in the answer choices, this problem provides an excellent opportunity to pick numbers. Considering the parameters, you know that Stock A in 2010 must be 4/5 the value of Stock B, and you will need to take percent changes for each. So choose numbers that will provide easy calculations, such as: Stock A = 80 and Stock B = 100, and the % increase for A is 25 and for B is 20. This also means that N is 180.

With this, you can see that the value of stock B, 100, can be obtained by using N/1.8, so that is the correct answer in the left-hand column.

For the right-hand column, recognize that the percent changes must be involved, so you only need to test the last three choices. And you will find that the new ratio should be 100, Stock A plus 25%, to 120, Stock B plus 20%. This is 5/6, which checks out with the fifth answer choice, 0.8 ((1+A)/(1+B).

Answer: Value of Stock B in 2010: N/1.8

Ratio in 2012: 0.8((1+A)/(1+B))

kevMat000 · Answer

1st part:

Price A = P.A so P.A + P.B = N also P.A/P.B = .8 (in 2010)

P.A = N - P.B --> (N - P.B) / P.B = .8 --> P.B = N / 1.8

2nd part: 
P.Ai = initial price A
P.Af = final price A

given formula: A = (P.Af - P.Ai) / P.Ai

Solve for P.Af because the question asks for the ratio ( P.Af / P.Bf )

P.Af = P.Ai * (A + 1)
P.Bf = P.Bi * (B + 1)

P.Af / P.Bf =   /   and we know P.A/P.B from 2010 is the initial so it's .8

P.Af / P.Bf = (.8 * (A+1)) / (B+1)

ahddhah · Answer

language is not very clear as it says 2012 to 2012

ridbag · Answer

Hi! I did not understand have we taken % increase in 2012 for A as 25 and for B as 20? Can you please elaborate? Thanks!

SirSanguine · Answer

Hi Sajjad!
Why no division by 100?

Apeksha2101 · Answer

How are we calculating new percentage increase at 2012 year, how do we know the value of A and B in year 2012.
??

sayan640 · Answer

In 2010 , let , X+ Y = N ; X/Y = .8 ; X is the price of stock A and Y is the price of stock B
In 2012 , they become X(1+A) and Y(1+B)

Y = N - X
Y = N - .8Y
Y = N/1.8

That's the answer. And the ratio is , X/Y * (1+A)/(1+B) = .8 *(1+A)/(1+B)

Would you like to provide any other smart approach ?  KarishmaB   chetan2u   GMATinsight

KarishmaB · Answer

In 2010, ratio of price of A:B = 0.8:1 = 4:5
 Value Of B = \frac{5}{9} * N = \frac{N}{1.8}

Percent change in value is given as A and B. This will be values like 20%, 25% etc i.e. 0.2, 0.25 etc. So the multiplier factor is 1.2 or 1.25 etc i.e. (1 +A) and (1+B)

Ratio of new values =  \frac{4(1+A)}{5(1+B)} = \frac{0.8(1+A)}{(1+B) }

ANSWER:
 \frac{N}{1.8}

\frac{0.8(1+A)}{(1+B) }

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Value of Stock B in 2010	Ratio in 2012	Values
		N/0.8
		N/1.2
		N/1.8
		A/0.8+B/1.25N
		0.8((1+A)/(1+B))
		1.25((1+A)/(1+B))

Over a period of 2 years from 2010 to 2012, Stock A and Stock B have

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