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

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Bunuel

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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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(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.

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Bunuel

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Bunuel

12 Days of Christmas 2024 - 2025 Competition with $30,000 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.

GMAT Club's Official Explanation:

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.

If the total value of the $1 coins is 50% of the total value of all the coins, the value of the $0.25 and $0.50 coins must account for the other 50%. The value of the $0.25 and $0.50 coins is $0.25 * 8 + $0.50 * 4 = $4. Since the value of the $1 coins is also $4, the number of $1 coins is $4 / $1 = 4. Sufficient.

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

The total number of $0.25 and $0.50 coins is 8 + 4 = 12. This represents 75% of the total number of coins. If 75% corresponds to 12 coins, then 25% corresponds to 12/3 = 4 coins. Thus, the number of $1 coins is 4. Sufficient.

Answer: D.

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Bunuel

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Here, total value of
0.25*8 = 2 $
0.5 *4 = 2 $
1*X = ?

1) 1*x = 2+2= 4$ -> 4 coins, so this works
2) 1*X = 8+4 = 12*3/4 = 9 coins, so this works

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The Ans. is D.

From statement 1, we understand the value of $1 is 50 % of the total which is sufficient to know the total number of $1 coins.

From statement 2, if we consider total $1 coins to be x, we can find out the number of $1 coins to be equal to x / 12 + x = 1/4. Which gives us x = 4.

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No. of $0.25 = 8; Total Value = $2
No. of $0.5 = 4; Total Value = $2

No. of $1 = ?

Statement 1.

Value of $1 / Total Value of all coins = 1/2

=> Value of $1 / ($4 + Value of $1) = 1/2
=> Value of $1 = $4
=> no. of $1 = 4 SUFFICIENT

Statement 2.

No. of $1 / Total No. of coins = 1/4

=> No. of $1 / (12 + No. of $1) = 1/4
=> No. of $1 = 4 SUFFICIENT

Answer D.

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Quote:

(1) Current total = 0.25*8 + 0.5*4 = $4
If the $1 coins is 50% of the total value, it would be 2x current value = $4
SUFFICIENT

(2) Total coins = 8+4=12
If $1 coins is 25% total number of coins, total $1 coins = 4 coins
This would be 25% from 16 coins
SUFFICIENT

Answer: D

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Let x be $1 coins

Coin denomination	Number of coins	Total value
0.25	8	2
0.5	4	2
1	x	x

Statement 1 - Total value / 2 = value of $1 coins

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

This statement is sufficient.

Statement 2 - Total number of coins * 1 / 4 = number of $1 coins

(8 + 4 + x) / 4 = x
12 + x = 4x
x = 4

This statement is sufficient.

As both statements are independently sufficient, answer is D.

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Let's first understand the question and try to simplify by forming an equation -

$0.25 * 8 + $0.50 * 4 + $1 * x

We need to find 'x'.

Statement 1 -

Total value of $1 coins = x (since, the value of 1 coin is 1$, hence value of x coins will be $x)
Total value of all coins = $0.25 * 8 + $0.50 * 4 + $1 * x = (2 + 2 + x)

so, x = 50% * (2 + 2 + x)
Since we have 1 equation and 1 variable, we can easily get the answer for x and we don't need to solve further.

Just for clarification,

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

SUFFICIENT.

Statement 2 -

Number of $1 coins = x
Number of total coins = 8 + 4 + x = (12 + x)

x = 25% (12 + x)
Same situation as in first. One equation, one variable, easily solvable.

Just of clarification,

x = (12 + x)/4
4x = 12 + x
3x = 12
x = 4.

SUFFICIENT.

Hence, D.

**Important point - GMAT will never have the two statements in contradiction with each other. Therefore, if you reach a certain answer which is not the same in both the statements, you might've gone wrong somewhere in your calculations.

Bunuel

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D
(1)
1*x = (8*0.25 + 4*0.5 + 1*x)/2 (The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.)
x = 4. sufficient

(2)
x = 25%(x + 8 + 4)
x = 4. sufficient

Each statement alone is sufficient.

Bunuel

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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?

Let the number of $1 coins Warren has be x.

(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
$1*x = 50%($1*x + $.5*4 + $.25*8) = .5($x + $2 + $2) = .5($x + $4)
x = .5(x+4) = .5x + 2
x = 4
The number of $1 coins Warren has is 4
SUFFICIENT

(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
x = 25% (x+8+4) = .25(x+12) = .25x + 3
x = 3/.75 = 1/.25 = 4
The number of $1 coins Warren has is 4
SUFFICIENT

IMO D

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From the information in the question, we know 2 things:
Assuming total number of 1$ coins is x (to find),
total value = (4+x)$
total coins = (12+x)

I. x = 0.5(4+x) => can be solved for x. Sufficient
II. x = 0.25(12+x) => can be solved for x. Sufficient.

D) - each statement is sufficient on its own

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Given:
- 8 quarters = $2
- 4 half-dollars = $2
- Total value = $4 + x, where x is the number of $1 coins.

Statement 1: Total value of $1 coins = 50% of total value.
x = 0.5 * (4 + x) → x = 4.
Sufficient.

Statement 2: $1 coins = 25% of total coins.
x = 0.25 * (12 + x) → x = 4.
Sufficient.

Answer: D.

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let there be 'x' coins of $1. To find x

Total value ($) = 4+x
Total number of coins = 12+x

St1) x=50% of (4+x) ---> Sufficient

St2) x= 25% of (12+x) ---> Sufficient

Hence ans is D

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To solve this, let x represent the number of $1 coins Warren has.

Given:
- Number of $0.25 coins = 8 → total value = 8 × 0.25 = 2 dollars.
- Number of $0.50 coins = 4 → total value = 4 × 0.50 = 2 dollars.
- Number of $1 coins = x, so their total value = x.

Statement (1): The total value of $1 coins is 50% of the total value of all coins.
- Total value of all coins = 2 + 2 + x = 4 + x.
- According to the statement, the value of $1 coins is 50% of the total value:
x = 0.5 × (4 + x).
- Simplify:
x = 2 + 0.5x.
0.5x = 2 → x = 4.
- The number of $1 coins is uniquely determined as 4. Statement (1) is sufficient.

Statement (2): $1 coins make up 25% of the total number of coins.
- Total number of coins = 8 + 4 + x = 12 + x.
- According to the statement, $1 coins make up 25% of the total number of coins:
x = 0.25 × (12 + x).
- Simplify:
x = 3 + 0.25x.
0.75x = 3 → x = 4.
- The number of $1 coins is uniquely determined as 4. Statement (2) is sufficient.

Final Answer:
Since each statement independently determines the value of x, the answer is:

D: Each statement is sufficient on its own.

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W has
0.25$ (8 Coins) = 2$
0.5$ (4 Coins) = 2$
1$(x Coins) = x$

We need to determine the 1$ Coins

Now Take the Statement A.
x$ = 1/2(2+2+x)
That gives me x = 4 coins
So, statement A is enough

Now Take the Statmene B
X = 1/4(8+4+x)
X = 4 Coins
So, statement B is enough

So Answer is D, as both statements alone are sufficient.

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Statement (1):
The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
Step 1: Total value of the coins:
Value of 0.25 Coin
8×0.25=2 dollars.
Value of 0.50-coins:
4×0.50=2 dollars.
Value of 1-coins:
x×1=x dollars.

total value of all the coins is: 4+x

From the statement, the value of 1-coins is 50% of the total value:
x=2+0.5x
From which Value Of "X" Can be determined i.e. Statement 1 is sufficient

Statement (2):
The $1-coins make up 25% of the total number of coins in the piggy bank.
Thus, the total number of coins is:
8+4+x=12+x
From the statement:
x=0.25*(12+x)
From which the value of "X" can be found out i.e. Statement 2 is sufficient.
Answer Option D

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17 Dec 2024, 09:56

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option e is the correct answer

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here we have 25c, 50c and 100c-
so total value will be 25*8+50*4+100x= t
200+200+100x=t
400+100x=t
option 1- 100x= (400+100x)/2= 200 + 50x - 50x=200- x=4
ans option 1 sufficient.
option 2
x= 1/4(8+4+x)= x=(12+x)/4= 4x= 12+x= 3x=12= x=4
ans option 2 sufficient
ANS- D

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According to statement 1, total value of $1 coins is 50% of total value of all coins. That means:

total value of $1 coins = total value of rest of coins

Since we can figure out total value of rest coins, we can figure out total no of $1 coins

According to statement 2, total no of $1 coins is 25% of total no of coins. This means total no of rest of the coins is 75% of total of all coins. So, we can find the total of all coins then find the value of 25% of that

Another shorter way to think: there are 8 coins of $0.25 and 4 coins of $0.50. If total no of $1 coins was 4, it would be 25% of full total.

Since each statement is sufficent AO=LONE to find the answer, the answer is D.

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Let Z be the number of $1 coins.
From Statement 1 : The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
Total value of coins = 0.25 * 8 + 0.50 * 4 + 1 * Z = 4 + Z
given , Z = (4+Z)/2 => Z = 4. Solved. Statement 1 is sufficient to answer the question.

From Statement 2: The $1 coins make up 25% of the total number of coins in the piggy bank.
Total coins = 8 + 4 + Z = 12 + Z
given, Z = (12+Z) * 25/100 => Z = 4. Solved. Statement 2 is sufficient to answer the question.

Either Statement is sufficient to answer the question.
So, Option D