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12 Days of Christmas GMAT Competition - Day 7: An investor has two

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MG121

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24 Dec 2024, 23:47

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Bunuel

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An investor has two cryptocurrency wallets, Main and Backup. The Main wallet holds m% of its maximum capacity, while the Backup wallet holds b% of its maximum capacity. Both wallets have identical maximum capacities.

Due to new regulations, the investor must optimize storage by transferring tokens from the Backup wallet to the Main wallet until the Main wallet reaches its maximum capacity. After this transfer, the Backup wallet contains exactly half of its previous percentage.

If the Backup wallet initially held a higher percentage than the Main wallet, select for m the possible value of m, and select for b the possible value of b that would be jointly consistent with the given information. Make only two selections, one in each column.

Let 1 be the max wallet can hold which is identical for both main and backup
1-m/100=b/200 post the transfer from backup to main
Additionally we have b>m
so when we check for b=90 we get m=55

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25 Dec 2024, 00:03

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correct

MinhChau789

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25 Dec 2024, 00:45

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From the provided info, we have: b - (100 - m) = b/2
m = 100 - b/2

From the selections, the only solutions satisfying the above equation are m = 55, b = 90.

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Bunuel

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Actually I think there are two group of answer in this question

As backup wallet will contain exactly half of its previous percentage, then B must be divisible by 2 in integer because the answer does not have decimal places.
In the option, there are two possible combination including
(1) m = 45, b = 90
(2) m = 30, b = 60

Therefore I randomly select (2)'s as the answer

Seb2m02

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25 Dec 2024, 00:58

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b=200−2m

m=55 b=90 is the only solution

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25 Dec 2024, 01:03

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Hello ,
As per question
Currently there is m% and and B% now
after transfer your main is 100% and B is 50% of previous
that means
100-m=0.5*b
So equation is b+2m=200
when we solve equation putting B as 90 as B is higher we get m as 55.

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25 Dec 2024, 01:52

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Ans: m = 55 and b = 90

Due to new regulations, the investor must optimize storage by transferring tokens from the Backup wallet to the Main wallet until the Main wallet reaches its maximum capacity. After this transfer, the Backup wallet contains exactly half of its previous percentage.

If the Backup wallet initially held a higher percentage than the Main wallet, select for m the possible value of m, and select for b the possible value of b that would be jointly consistent with the given information. Make only two selections, one in each column.

given main has m% of its max capacity and Backup has b% of its max capacity and both wallet have identical max capacity = C

also when half % of b transferred to Main it reaches its full capacity

m*C/100 + b*C/2*100 = C
or m/100 + b/200 = 1
2m+b = 200

replace the values m = 55 and b =90 and these will satisfy the equation

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25 Dec 2024, 01:56

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Hi everyone

Straight forward.
*The crucial sentence here is: Both wallets have identical maximum capacities.
Thus, we can come up with the equation:

m+b/2=100%
the only 2 answer choices we can get 100% are:
m=55
b=90

55+45=100%

Our Answers: m=55, b=90

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25 Dec 2024, 02:28

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2m+b=200
M=55, b=90 fit from the ans choices

Ans m=55, b=90

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Let the maximum capacity of Main wallet be M and Backup wallet be B.
M = B
Current status = m% of B, b% of B

(b% of B) - x = (m% of B) + x = B = b/2%

b% > m%

HIT AND TRAIL

Suppose the maximum quantity B is 100.

b% > m%

We're subtracting from b% such that it remains it's half and half of it when added to m% makes it 100.

Looking at the options, we see that if we take b to be 90, it's half would be 45.
If we add this 45 to m which can be 55, then it becomes maximum which is 100.

Therefore,

m = 55, b = 90.

Bunuel

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LastHero

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25 Dec 2024, 03:46

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C is the common maximum capacity

The remaining freen space in Main wallet is C-Cm/100

Cb/100 - C + Cm/100 = Cb/200
2b - 200 + 2m = b
m=100 - b/2

Only values of b that are even work.

Cheking the values, the answers are:
m=55, b=90

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25 Dec 2024, 04:06

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Initial amount in backup = b %
Final amount in backup = $\frac{b}{2}$ %

Given m becomes full capacity after this exchange

$m + \frac{b}{2} = 100$

Among the options, b = 90 and m = 55 satisfies this condition.

Bunuel

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25 Dec 2024, 04:08

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let us assume the max capacity as 100 and out of 100 it is holding m% and b%.
after optimizing Main wallet reaches its max capacity
so we have to fill Main wallet completely
after observing the options we can say
if M=50 then half of b should fill it completely that is
M+B/2=100
checking one case
50+B/2=100 {for this B have to 100 but not in options}, so again checking with different value
,let M=55 and B=90
55+90/2=100
matching hence
M=55 and we can take B=90

Bunuel

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Bunuel

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Main = m%
Backup = b%
Total is the same = Assume that it is 100% for both the wallets as it is given in percentage

Half of whatever was in Backup wallet has been transferred to the Main wallet.
New Main = m% + (b/2)%
New Backup = (b/2)%

Now, the Main wallet has to add up to 100% as it reaches its maximum capacity after the transfer.
If m = 55% and b = 90%, then b/2 = 45%

Main Wallet = m% + (b/2)% = 55% + 45% = 100%
Old Wallet = (b/2)% = 45%

Hence, m = 55 and b = 90

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25 Dec 2024, 05:02

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Since the maximum capacity of both are equal, let the maximum capacity be 100
We know that b% > m%
Hence, 100 * b/100 > 100 * m/100 i.e. b > m

After transferring b/2 % of the maximum amount from the backup wallet to the main wallet we get -
b / 2 + m = 100 (as it reaches full capacity)

Substituting values from the options so find the correct answer, we get
when b = 90
b/2 + m = 45 + 55 = 100

Hence, m = 55 & b = 90

Bunuel

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25 Dec 2024, 06:08

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Given: Both wallets have identical maximum capacities. So, let the maximum capacity be C

	Main	Backup
Max capacity	C	C
Original tokens	m/100*C	b/100*C
New tokens	C	b/2% = b/200*C

Tokens transferred from the backup wallet to the main wallet can be calculated by taking the difference between new and original tokens of the main wallet
i.e., C-m/100*C = C(1-m/100)

This diff is equal to the difference between new and original tokens in the backup wallet
i.e., C(1-m/100) = b/100*C - b/200*C
On solving, we will get the below equation:
b = 200 - 2m

Now, we have to substitute values from the given options which will satisfy the equation:

The correct answer is m = 55 and b = 90.

Bunuel

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m	b
		30
		45
		50
		55
		60
		90

Given,
Maximum Capacity Holding Capacity
Main wallet --> C m %
Backup wallet --> C b %

Given, post transfer of tokens,

(b/2) % of C = (100-m) % of C
b/2 = 100-m
b + 2m = 200

Given, b > m (as per he question prompt)

Putting b= 90, m = 55 ....Consistent, since b>m
b= 60, m = 70....Inconsistent, since b<m
b = 55, m = 72.5 ....Inconsistent, since b<m

m = 55, b= 90 is the CORRECT answer

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25 Dec 2024, 06:23

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M= Max. Capacity of each vallet
M= M*m/100 + M*b/200
2m+b=200
Since b>m
Start checking with larger number
b=90
m= 55

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25 Dec 2024, 07:07

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Let the max. capacity that both the wallets have= C.
Let main wallet contents= M
and Backup wallet contents= B

So, M= m/100 x C tokens
and, B= b/100 x C tokens
Also, b>m.

After the transfer-

tokens left in Backup= 1/2 of (b/100 x C)
Therefor, no. tokens transfered from this account= 1/2 x (b/100 xC)= bC/200.

Also, capacity of tokens to be received by the main account= C- M=> C- (m/100 x C)=> C(1-m/100).

we know, both the values, tokens transferred and received are the same values, Therefor- bC/200= C(100-m)/100=> 2m+b= 200.

By hit and trial the only two opts. that satisfies the above equation is- m=55, b=90.

ans. opt. m=55, b=90.

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25 Dec 2024, 07:31

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We do know that m/100*C + b/100*C

b/100*C > m/100*C

new balance of the backup account is b/200*C and the new balance of the main account is C since it's filled up to capacity.

b/100*C + m/100*C = C + b/200*C
Simplifying we'd reach
b = 200 -2*m

and we'd start testing values:

Testing Values:
- m=45
- b=200−2(45)=200−90=110(not valid)
- m=55
- b=200−2(55)=200−110=90

Final Answer: