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 2010 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.

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 · 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)

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) }

mkeshri185 · Answer

KarishmaB

I dont agree with the solution . if it says there is A% rise then it should be original value x (1+ A/100) and not original value x (1+A). Everywhere we do the same... if you i acceot your fact that new value will be OV * (1+A) for A% rise then tell me one thing... i have 100rs i want to increase it by 20% so my A =20% so what will be the new value? according to you 100*(1+20) and according to me 100*(1+ 20/100) now which one is correct>?

I dont know why there is a glitch in this concept that's simple and straightforward concept we all study from junior school. A% change means 1+A/100 or 1-A/100 that's it. If A was fractional change then it would make sense but not with % value

KarishmaB · Answer

As mentioned before: 
 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)

itachixuchiha · Answer

I also got had a similar confusion, but notice that " A and B represent the percent change  ", which means A = some x%  , by saying A% you are making it x%%. So yeah the terminology is confusing.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Two-part Analysis (TPA) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards