12 Days of Christmas GMAT Competition 2025 - Day 10: An investor : Two-part Analysis (TPA)

batman10bigman

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26 Dec 2025, 10:07

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Bunuel

Certificate is $2400
Optimistic change is 5%
so 5%.2400 = 120 per year
so over 2yrs gain = 120.2 = 240

Need remaining gain from bond = 600 - 240 = 360
Bond earns simple interest = 0.03 x 2 = 0.06 of principal
so 0.06P = 360
P = 6000

Pessimistic change is 10%
So 10%.2400 = 240 loss per year, so over 2yrs = 480
Bond must cover loss and still net $600: 600 + 480 = 1080
0.06P = 1080
P = 18000

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26 Dec 2025, 10:33

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An investor purchases a no interest certificate that he can not sell for 2 years. He buys certificate with a total purchase price of $2,400.
At the same time, he invests an additional sum in a treasury bond that earns 3% simple interest per year.

The investor's goal is a combined net gain of $600 from the two investments after 2 years.

Optimistic projection: Each year the market value of certificates increases by a fixed amount equal to 5% of the original $2400 purchase price = $120; Total increase = $240
Remaining net gain = $600 - $240 = $360
The amount to be invested in treasury bonds = $360/3%*2 = $6000

Pessimistic projection: Each year the market value of certificates decreases by a fixed amount equal to 10% of the original $2400 purchase price = $240; Total decrease = $480
Remaining net gain = $600 - (-$480) = $1080
The amount to be invested in treasure bonds = $1080/3%*2 = $18000

Bond investment, optimistic	$6000
Bond investment, pessimistic	$18000

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26 Dec 2025, 10:52

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principal= 2400
time- 2 yrs

for bond
p= x$
rate = 3%
interest earned= 3x/50

total interest earned= 600

optimistic calculation
each year interest= 2400*.05= 120
so two year total =240

240+ (3x/50)= 600
x= 6000

pessimistic calculation
loses each year= 0.1*2400= 240
so total=480

(3x/50) - 480 = 600
x= 18000

Bunuel

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26 Dec 2025, 11:36

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Bunuel

Optimistic Scenario

Value of $2400 bond considering market adjustment = $2400 * 1.05 * 1.05 = $2646

Amount earned = $246

Therefore the interest the person needs to earn from his treasury bond = $600 - $246 = $354

354 = P * 3 * 2/ 100

P = 354 * 100 / 6 = 5900

Closest = $6000

Pessimestic Scenario

Value of $2400 after 2 years = 2400 * 0.9 * 0.9 = $1944

Therefore to compensate the loss, the person should target an interest of = 600 + (2400-1944) = 1056

1056 = P * 3 * 2/ 100

P = 1056/6 * 100 = 17600

Closest = 18000

Bond investment, optimistic = $6000
Bond investment, pessimistic = $18000

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26 Dec 2025, 11:51

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OPTIMISTIC:
profit from certificate =(0.05*2400)*2=240
so 600-240= 360 has to be earned from bond.
p*2*0.03=360
p=6000

PESSIMISTIC
loss=(2400*0.1)*2=480
interest reqd= 600+480=1080
p*2*0.03=1080
p=18,000

Ans 6000 & 18000

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26 Dec 2025, 12:18

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You have all the data to determine how much profit/loss comes from the certificates, so you need to find how much he must invest in bonds to reach his goal of 600

Optimistic:
5% * 2400 * 2 years = 240
bonds must add 600-240=360
3% * 2 years * x = 360 -> x = 6,000

Pessimistic:
-10% * 2400 * 2 years = -480
bonds must add 600+480=1080
3% * 2 years * x = 1080 -> x = 18,000

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26 Dec 2025, 12:23

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Optimistic scenario:

5% of 2400 = 120$

Balance: 600-120 =480$

$480 = P * 2\text{ years} * 3$%

$480 = P * \frac{6}{100}$

P = 8000$

Pessimistic scenario:

-10% of 2400 = -240$

Balance: 600-(-240) =840$

$840 = P * 2\text{ year} * 3$%

$840 = P * \frac{6}{100}$

P = 14000$

ans: 8000, 14000 or B, D

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26 Dec 2025, 12:57

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Bunuel

First, we note that "increases by a fixed amount" indicates simple interest here. There are two questions here, and the boil down to the following:
1. If he gains 5% per year for 2 years on a $2,400 certificate, how much does he need to invest separately in a bond for the same time period at 3% per year to earn the difference between $600 and the certificate gains?
2. If he loses 10% per year for 2 years on a $2,400 certificate, how much does he need to invest separately in a bond for the same time period at 3% per year to earn not just $600, but also the loss from the certificate?

To answer the first question, we first calculate the gain on the certificate.

$2400*\frac{5}{100}*2=240$

That means we need $600-240=360$ from the separate bond. Let x equal the amount he needs to invest.

$x*2*\frac{3}{100}=360$

$x=6000$

Thus our column 1 answer is 6,000.

Now we need to find out what needs to be invested if the certificate loses 10% a year. It's a similar process, except that we add instead of subtract after interest is calculated.

$2400*\frac{10}{100}*2=240$

$240+600=1080$

Let y be how much needs to be invested in the bond.

$y*2*\frac{3}{100}=1080$

$y=18,000$

Thus our column 2 answer is 18,000.

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26 Dec 2025, 13:17

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investor buys no interest certificate for 3 yrs. at purchase price (PP) of $2400 for which two projections are given:
1. optimistic-->each year the market value increases by a fixed amount which is 5% of PP.
so total increase in two years=$240
2. pessimistic--> each year the market value decreases by a fixed amount which is 10% of PP.
so total decrease in two years=$480
now its also given that he also invests $ 'X'(let) in an another investment, treasury bond that pays him simple interest at the rate of 3% p.a. for two years.
also investor's goal is a net gain of $600 from these two investments in these two years.
need to find the value of X that is consistent with above constraints??
1. for treasury bond, optimistic
we know that a gain of $240 is already made from certificate, so we need to find X for which an interest of $360 is gained from the treasury bond
so X=360*100/6=$6000
2. for treasury bond, pessimistic
we know that a loss of $480 has already occurred from certificate, so we need to find the value of X for which an interest of $600+$480= $1080 is gained from the treasury bond
so X=1080*100/6=$18000

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26 Dec 2025, 13:31

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Bunuel