Samantha's investment portfolio consists of three stocks

Question

Samantha's investment portfolio consists of three stocks: an airline, a bank, and a computer
company. In the month of February, the price of the airline's stock rose by 10%, that of the bank
decreased by 15% and that of the computer company also decreased by 15%, but the overall value of
her portfolio increased. If Samantha owns equal amounts of all three stocks, which of the following
could be the initial prices of the three stocks in the order airline, bank, and computer company
respectively?

A.$55, $85, $40
B.$65, $60, $60
C.$65, $55, $90
D.$85, $25, $20
E.$25, $60, $70

A. $55, $85, $40
B. $65, $60, $60
C. $65, $55, $90
D. $85, $25, $20
E. $25, $60, $70

MacFauz · Accepted Answer

Since Samantha owns equal amounts of stocks, the 10% increase alone should set off the 15% decrease in each of the other two stocks. i.e The stock which increased should have a substantially higher value than the two stocks which decreased. Between B & D, D is obviously the safer bet and is the right answer.

Answer is D.

PareshGmat · Answer

Can someone please explain how D is the answer?

Bunuel · Answer

Perfect solution by MacFauz here: samantha-s-investment-portfolio-consists-of-three-stocks-142973.html#p1147009 Hint: the question asks for which option is the expression (A*1.1+B*0.85+C*0.85)-(A+B+C) positive.

Solenja · Answer

i know this is not the best way to answer this question ,but if you read the question and understand the first stock should be much higher in value compared to the other two.

pusansen99 · Answer

Let initial price be, A(Airline) -> x, B(Bank) -> y, C(Computer) -> z
In Feb, A -> 1.1x, B -> 0.85y, C -> 0.85z

As given in the statement, in February, the portfolio value was higher than the initial value.
So,
(1.1x + 0.85y + 0.85z) - (x + y + z) > 0

Only  Option D  will satisfy this condition.

Sarvam · Answer

Let initial prices be:
Airline = A
Bank = B
Computer = C

Samantha owns equal amounts (same number of shares)

After changes:

Airline → +10% → 1.10A
Bank → −15% → 0.85B
Computer → −15% → 0.85C

Total initial value = A + B + C
Total new value = 1.10A + 0.85B + 0.85C

Given:
New value > Initial value

So:
1.10A + 0.85B + 0.85C > A + B + C

Simplify:

(1.10A − A) + (0.85B − B) + (0.85C − C) > 0

0.10A − 0.15B − 0.15C > 0

Rearrange:

0.10A > 0.15(B + C)

Multiply by 10:

A > 1.5(B + C)

Check options:

A. 55 > 1.5(85 + 40) = 187.5 ❌
B. 65 > 1.5(60 + 60) = 180 ❌
C. 65 > 1.5(55 + 90) = 217.5 ❌
D. 85 > 1.5(25 + 20) = 67.5 ✅
E. 25 > 1.5(60 + 70) = 195 ❌

Final Answer:

D. 85, 25, 20

Ishaan30 · Answer

This is a ratio question once you take off the disguise of it being a percentage question.
Let Airlines be a, Bank be b and Computer be c.
 
   a 
 b 
 c 
 Total 
 
  100%a 
 100%b 
 100%c 
 Overall  
 
  110%a 
 85%b 
 85%c 
 Increased overall

This means that 110%a > 85%b + 85%c. By which we can also conclude that 10% > 15%b +15%c.
I always convert % in fractions because they work out pretty easily as fractions. a/10 > 3b/20 + 3c/20
Working it out gives us 2a/3 > b + c
Now we know that about 60% of a should be bigger than b + c.

Looking at options -

Indeed, an approximation before all this calculation would probably have been correct. But I solve to show the basic process one must understand to get wiser at GMAT.
Hope this helps.

OnyxGum · Answer

Initial portfolio value = A + B + C

Later: Portfolio value changes = 0.1A - 0.15B - 0.15C

Value of portfolio increased, meaning:
0.1A - 0.15B - 0.15C > 0
0.1A - 0.15 (B+C) > 0
2A - 3 (B+C) > 0
2A > 3 (B+C)

Quick check:
A. $55, $85, $40 -> 2 x 55 < 3 x 85 ❌
B. $65, $60, $60 -> 2 x 65 < 3 x 60 ❌
C. $65, $55, $90 -> 2 x 65 < 3 x 90 ❌
D. $85, $25, $20
E. $25, $60, $70 -> 2 x 25 < 3 x 70 ❌

Samantha's investment portfolio consists of three stocks

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

a	b	c	Total
100%a	100%b	100%c	Overall
110%a	85%b	85%c	Increased overall

GMAT Problem Solving (PS) Questions

Samantha's investment portfolio consists of three stocks

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