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12 Days of Christmas GMAT Competition - Day 2: Warren has exactly

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crimson_king

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On analzying option B , we find that the total number of 1 dollar coins is 25% of the total number of overall coins. Since we already know that the total number of non 1 dollar coins is (8+4=12) which comprises of 75% of the total number of coins, we find that the total number of coins are 3/4*x=12, x=16

Hence the total number of 1 dollar coins is equal to 4 & we can find the total sum value of all the coins accordingly. Hence (B) is sufficient & we can eliminate options (A),(C),(E).

For checking if option (D) is valid, we need to validate the sufficiency for statement (A) alone hence
if total sum value of 1 dollar coins is 50%, by that logic the total sum value of non 1 dollar coins is 50% as well. This value is calculated as 0.25*8+0.5*4=4 dollars. 50% of 4 dollars is 8 dollars so the remaining number of one dollar coins turns out to be 4. Since we know all of the required information, answer (A) is also sufficient.

Since both (A) & (B) are sufficient by themselves, the answer to this question is option (D)

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This is a value Data sufficiency.

Before getting into the statements let evaluate the given information.

$0.25 - 8 coins = Total value of $0.25 is $2.
$0.50 - 4 coins = Total value of $0.50 is $2.

12 coins of $0.25 and $0.50 with the total value of $4. But we need to find number of $1. So, if we know any information about total value or number of coins, we can answer the question.

Let's discuss the statement.
St. (1) says $1 coins contribute 50% of total value, which means the remaining 50% of the value is $0.25 and $0.50 coins.

Total value of $1 coins = Total value of $0.25 and $0.50 = $ 4
We can find there are 4 coins of $1. This statement is SUFFICIENT.
A nd D are the possible answers.

St.(2) says 25% of total number of coins is $1 coins, means 75% is $0.25 and $0.50 coins, which is 12 coins. 75% * (Total coins) = 12. By solving this, we can find total coins is 16. Hence 4 is $1 coins.
This statement s also SUFFICIENT. Answer is D

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Representing the numbers for the different currencies as follows:

0.25= Q
0.50= C
1=D
Total value= M

0.25Q+0.50C+1D=M ---(1)

Statement 1:

(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.

setting up the equation

0.5M=D

M=2D

substitute in equ 1

Meanwhile Q=8, C=4

2+2+D=2D

4+D=2D
D=4

equ 1 is sufficient

We strike out options C and E

Statement 2: The $1 coins make up 25% of the total number of coins in the piggy bank.

this time we let the total quantity of coins to be N

8+4+D=N

12+D=N

D=0.25N

N=4D

12+D=4D

3D=12

D=4

Statement 2 is also sufficient

Both statement are sufficient. So Option D is correct.

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given- no. of $0.25 coins= 8, therefore total amount= $2, $0.5 coins= 4, total amount= $2, and let no. of $1 coins= x

According to (1), 0.5(2+2+ 1x(x))= x, therefore, 2+x/2= x, therefore x= 4. therefore, statement (1) is sufficient.

According to (2), 0.25(Total no. of coins)= no. of $1 coins (x), therefore, 0.25(12+x)=x, x=4. therefore, statement (2)is also sufficient.

Ans.- opt. (D) either alone is sufficient.

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Explanation

We need to find out how many $1 coins Warren has in his piggy bank. He already has 8 quarters ($0.25 each) and 4 half-dollars ($0.50 each).

Total Coins and Value:
- Number of $0.25 coins: 8
- Number of $0.50 coins: 4
- Number of $1 coins: Let’s call this x
- Total number of coins: 8 + 4 + x = 12 + x
- Total value: (8 × $0.25) + (4 × $0.50) + (x × $1) = $2 + $2 + $x = $4 + $x
Statement (1):
The total value of the $1 coins is 50% of the total value of all the coins.
- Equation:
  $x = 0.5 × ($4 + $x)
  $x = $2 + $0.5x
  $0.5x = $2
  x = 4
- Conclusion: Statement (1) alone tells us that Warren has 4 $1 coins.
Statement (2):
The $1 coins make up 25% of the total number of coins.
- Equation:
  x = 0.25 × (12 + x)
  x = 3 + 0.25x
  0.75x = 3
  x = 4
- Conclusion: Statement (2) alone also tells us that Warren has 4 $1 coins.

Final Answer:
D) EACH statement ALONE is sufficient to answer the question asked.

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Information Given:

The number of $0.25 coins is 8, so the total value of these coins is: 8×0.25=2 dollars8 \times 0.25 = 2 \text{ dollars}8×0.25=2 dollars
The number of $0.50 coins is 4, so the total value of these coins is: 4×0.50=2 dollars4 \times 0.50 = 2 \text{ dollars}4×0.50=2 dollars
Let the number of $1 coins be xxx. Therefore, the total value of $1 coins is: 1×x=x dollars1 \times x = x \text{ dollars}1×x=x dollars

Thus, the total value of all the coins is:
2+2+x=4+x dollars2 + 2 + x = 4 + x \text{ dollars}2+2+x=4+x dollars
The total number of coins is:
8+4+x=12+x coins8 + 4 + x = 12 + x \text{ coins}8+4+x=12+x coins
Statement (1):
The total value of the $1 coins is 50% of the total value of all the coins.
This translates to the equation:
x=0.5×(4+x)x = 0.5 \times (4 + x)x=0.5×(4+x)
Solving for xxx:
x=0.5×(4+x)x = 0.5 \times (4 + x)x=0.5×(4+x) x=2+0.5xx = 2 + 0.5xx=2+0.5x x−0.5x=2x - 0.5x = 2x−0.5x=2 0.5x=20.5x = 20.5x=2 x=4x = 4x=4
Thus, from Statement (1), we find that Warren has 4 $1 coins.
Statement (2):
The $1 coins make up 25% of the total number of coins.
This translates to the equation:
x=0.25×(12+x)x = 0.25 \times (12 + x)x=0.25×(12+x)
Solving for xxx:
x=0.25×(12+x)x = 0.25 \times (12 + x)x=0.25×(12+x) x=3+0.25xx = 3 + 0.25xx=3+0.25x x−0.25x=3x - 0.25x = 3x−0.25x=3 0.75x=30.75x = 30.75x=3 x=4x = 4x=4
Thus, from Statement (2), we also find that Warren has 4 $1 coins.
Conclusion:
Both statements (1) and (2) independently lead to the conclusion that Warren has 4 $1 coins. Therefore, the answer is D: Each statement alone is sufficient to answer the question.

Bunuel

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

Warren has exactly three types of coins in his piggy bank: $0.25, $0.50, and $1. If the number of $0.25 coins is 8, and the number of $0.50 coins is 4, how many $1 coins does he have?

(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.

(2) The $1 coins make up 25% of the total number of coins in the piggy bank.

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anshgupta433

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Given
0.25(8) + 0.50(4) + 1 (x)
2 + 2 + x = 4 + x

1) x = 1/2 (4 + x)
x = 4

Therefore 1 is Sufficient

2) 1/4 (12 + x) = x
solving 12 + x = 4x
x = 4
Sufficient

Answer D

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$0.25 : 8 = $2
$0.5 : 4 = $2
$1. : x = $x

Taking statement 1 : x = (x+4)/2 , solving this we can get x.
Taking statement 2 : x = (12+x)/4, solving this we can get x.

Hence answer is D.

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$0.25 (8)
$0.5 (4)
$1 (X)

$4 + $X = $Y

1. $1 * X = 0.5 ($4 + $1 * X)
X = 4

Sufficient

2. X = 0.25 * (12 + X)
X = 4

Suficient

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Ans is D (Each is sufficient)

let x be number of 1$ coin,
Statement 1
The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins
1.x(price multiplied by number of coins)=.5*((.25*8)+(.5*4)+x)
which gives x=4. Suffcient.
2.The $1 coins make up 25% of the total number of coins in the piggy bank.
x=.25*(8+4+x)
Sufficient

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Let the number of 1 dollar coins be x

Statement 1-

x = 0.5(2+2+x)

From this statement, we can find x. Therefore, sufficient

Statement 2-

x = 0.25(8+4+x)

From this statement, we can find x

Therefore, Option D

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Let x be the number of $1 coins.
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all coins
Total value of all coins = 8.0,25 + 4.0,5 + 1.x = 4+x
From the statement: x = [1][/2]. (4+x) --> x = 2 + 0,5.x --> 0,5x = 2 --> x = 4

(2) The $1 coins make up 25% of the total coins in the piggy bank.
--> x = [1][/4].(8 + 4 + x)
--> x = 2 + 1 + 0,25.x
--> 0,75.x = 3
--> [3][/4].x = 3
--> x = 4

Both statements alone are sufficient to determine that Warren has 4 $1 coins. --> ANSWER D

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Option D is correct, I attach the explanation.

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Bunuel

	$0.25	$0.50	$1
No. of coin	8	4	x
Total Value ($)	2	2	x

Question: What is x?

Statement 1: The total value of the $1 coins is 50% of the total value of all the coins.

$x = \frac{2 + 2 + x}{2}$
$x = \frac{4 + x}{2}$
x = 4

Sufficient.

Statement 2: The $1 coins make up 25% of the total number of coins in the piggy bank.

Total number of coins = 8 + 4 + x = 12 + x

The $1 coins make up 25%;
$\frac{x}{12 + x} = \frac{1}{4}$
x = 4

Sufficient.

Answer: D

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Option d - either statements

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1 ->

Total Value of all coins = 2+2+x = 4+x
Value of $1 coins = x
=> x = 0.5(4+x)
=> x =4

2->

Total Number of all coins = 8+4+x = 12+x
No. of $1 coins = x
=> x = 0.25(12+x)
=> x=4

D ) Each statement is sufficient on its own

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We are tasked with determining how many $1 coins Warren has in his piggy bank, given the following information:

The number of $0.25 coins is 8.
The number of $0.50 coins is 4.
The number of $1 coins is unknown and represented as x.
Step 1: Analyze the information
Value of $0.25 coins:
8×0.25=2 dollars.

Value of $0.50 coins:
4×0.50=2 dollars.

Value of $1 coins:
x×1=x dollars.

Thus, the total value of all coins is
2+2+x=4+x dollars.
The total number of coins is
8+4+x=12+x.

Step 2: Evaluate the statements
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
This means:
x=0.5×(4+x)

Simplify:

x=2+0.5x
x−0.5x=2⇒0.5x=2⇒x=4
Thus, statement (1) alone is sufficient to determine
x=4.

(2) The $1 coins make up 25% of the total number of coins in the piggy bank.

This means:
x/(12+x) =0.25
Simplify:
x=0.25×(12+x)
x=3+0.25x
x−0.25x=3⇒0.75x=3⇒x=4
Thus, statement (2) alone is sufficient to determine x=4.

Step 3: Combine the statements
Since both statements are individually sufficient, combining them is unnecessary.

Final Answer: D. Each statement alone is sufficient.

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To know the number of one dollar coins, we just need to know the total value of the coins or the percentage of the value of $1 coins and luckily the statements give us exactly that so both statements are sufficient hence D

Bunuel

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Value of the $0.25 coins = $0.25 * 8 = $2
Value of $0.50 coins = $0.50 * 4 = $2

Statement 1
Total value of the $1 coins is 50% of the total value
The other 50 % = $0.25 and $0.50 = $4
Value of the $1 coins = $4
Number of $1 coins = $4 / $1 = 4

Statement 1 is sufficient

Statement 2
Total number of $0.25 coins = 8
Total number of $0.50 coins = 4
$0.25 coins and $0.50 coins = 12

12 coins are 75% of the total number of coins
25% corresponds to 12/3 = 4 coins

Statement 2 is sufficient
Answer D

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