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

1 2 3 4 5

Shubham.Sharma

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17 Dec 2024, 10:04

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In these types of questions, sometimes its better to convert the currency from dollar to cents. Let's assume the number of $1 (100 cent) coins are n.

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

This means that 100n=0.5(25*8 + 50*4 + 100n). A single variable is there in the equation. No further calculation is required. Sufficient.

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

This means that n=0.25(8+4+n). A single variable is there in the equation. No further calculation is required. Sufficient.

The correct answer is D.

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17 Dec 2024, 10:06

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2$, 2$, 1$xn

S1) n$ is 0.5*(4+n)$ Suff to get n

S2) n$ is 0.25(8+4+n)
=> 4n=12+n, n=4 Suff

D)

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Let's solve this systematically:

1) First, let's calculate the known coins:
8 × $0.25 coins = $2
4 × $0.50 coins = $2
Known number of coins: 8 + 4 = 12 coins

Let x be the number of $1 coins

Statement 1:
Total value of $1 coins = 50% of total coin value
1x = 0.5(1x + $4)
1x = 0.5x + $2
0.5x = $2
x = 4 $1 coins

SUFFICIENT

Statement 2:
$1 coins = 25% of total coins
x / (12 + x) = 0.25
x = 0.25(12 + x)
x = 3 + 0.25x
0.75x = 3
x = 4 $1 coins

SUFFICIENT

Both statements independently lead to the same solution of 4 $1 coins => Each statement alone is sufficient (D)

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$0.25 -> 8 coins => $2
$0.50 -> 4 coins => $2
$1.00 -> x coins => $x

(I)
x = (50/100)(2+2+x)
solve for x
Sufficient

(II)
x = (25/100)(8+2+x)
solve for x
Sufficient

(I) and (II) are alone sufficient.

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.

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

Nikhil17bhatt

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17 Dec 2024, 10:14

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IMO D

Given Information:
Warren has three types of coins: $0.25, $0.50, and $1.
Number of $0.25 coins = 8
Number of $0.50 coins = 4
Statement (1):
The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.

Let's denote:

The number of $1 coins as
x
x.
Calculate the total value of the coins:
Value of $0.25 coins:
8
×
0.25
=
2
8×0.25=2 dollars
Value of $0.50 coins:
4
×
0.50
=
2
4×0.50=2 dollars
Value of $1 coins:
x
×
1
=
x
x×1=x dollars
Total value of all coins:
2
+
2
+
x
=
4
+
x
2+2+x=4+x

According to statement (1), the value of $1 coins is 50% of the total value:
x
=
0.5
×
(
4
+
x
)
x=0.5×(4+x)

Solving for
x
x:
x
=
2
+
0.5
x
x=2+0.5x
x
−
0.5
x
=
2
x−0.5x=2
0.5
x
=
2
0.5x=2
x
=
4
x=4

So, Warren has 4 $1 coins.

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

Let's denote:

The number of $1 coins as
x
x.
Calculate the total number of coins:
Number of $0.25 coins: 8
Number of $0.50 coins: 4
Number of $1 coins:
x
x
Total number of coins:
8
+
4
+
x
=
12
+
x
8+4+x=12+x

According to statement (2), the $1 coins make up 25% of the total number of coins:
x
=
0.25
×
(
12
+
x
)
x=0.25×(12+x)

Solving for
x
x:
x
=
3
+
0.25
x
x=3+0.25x
x
−
0.25
x
=
3
x−0.25x=3
0.75
x
=
3
0.75x=3
x
=
4
x=4

So, Warren has 4 $1 coins.

Conclusion:
Both statements (1) and (2) independently lead us to the conclusion that Warren has 4 $1 coins in his piggy bank.

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Let number of $1 coins = a

(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
1a = (8 x 0.25 + 4 x 0.5 + a) x 50%
we can solve for a

(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
a = (8 + 4 + a)/4
We can solve for a

Answer: D

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17 Dec 2024, 10:19

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Let n $1 coins.

1. 1*n = 0.5(2+2+n)....n=4...SUFFICIENT
2. n=0.25*(n+8+4).....n=4...SUFFICIENT

Both Sufficient alone

Answer D

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Quote:

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.

from the question stem, we know the value total value from 0.25 and 0.5 $ coins= 0.25*8 + 0.5*4= 4$

Using sentence 1) we can find the total 1$ coins as if 50% is 4$ then number of 1$ coins = 4

Using sentence 2) if the total coins of 0.25 and 0.5 $ is 12 and that is 75% of the total coins, then total coins becomes 16, hence number of 1$ coins = 4

Hence answer is (D)

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The answer is D, either alone is sufficient

Given:
1/4 = 0.25 are 8 coins = 8*1/4 = $2
1/2 = 0.50 are 4 coins = 4*1/2 = $2
$1 coins = how many?

Statement 1: 50% of total value where x is the total value of $1 --> x= 1/2(4+x) = $4 and thus 4 coins are there. Sufficient alone
Statement 2: 25% of total number of coins. Again x is the number of $1 coin = x=1/4(12+x) = 4 coins which is sufficient.

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Total 1$ coins = x
Total coins = x + 4 + 8 = x + 12
Total value = 4 + x

(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
x = (4 + x)/2 => x = 4.
1 alone is sufficient.

(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
x = (12 + x)/4 => x = 4.
2 alone is sufficient.

Answer: D

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Bunuel

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

Let 'x' be the number of $1 coins.
(1) Value of $1 coins = 50% of total value:
Value of $0.25 coins: 8 * $0.25 = $2
Value of $0.50 coins: 4 * $0.50 = $2
Total value: $x + $2 + $2 = $x + $4
Statement (1) gives x = 0.5(x + 4). Solving for x gives x = 4. SUFFICIENT.
(2) $1 coins = 25% of total number of coins:Total number of coins: 8 + 4 + x = 12 + x
Statement (2) gives: x = 0.25(12 + x). Solving for x gives x = 4. SUFFICIENT.

IMO D

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Bunuel

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

Let the number of 1$ coins be z.
Total value = 0.25x8 + 0.5x4 + z
Total value = 2+2+z = 4+z.
Total number of coins = 12+z.

St1:-
Total value of z makes up 50% of the total value of all coins.

Z/(4+z) = 1/2
2z= 4+z
Z=4. Therefore, sufficient.

St2:-
Z makes up 25% of the total number of coins.
z/(12+z)= 1/4
4z= 12+z
3z=12
Z=4. Therefore, sufficient.

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Bunuel

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

Let x be the number of $1 coins

(1) Total value of all the coins = Total value of $0.25 coins + Total value of $0.5 coins + $1x
Total value of $0.25 coins: $0.25*8=2
Total value of $0.5 coins: $0.5*4 = 2

$1x/ (2+2+$1x) = 50%
x = (4+x)*0.5
x = 2+0.5x
0.5x = 2
x = 4 (sufficient)

(2) Let Y be the total number of coins
It means the sum of $0.25 coins and $0.5 coins = 75% of total number of coins
12 = 0.75y
y = 16
Therefore the number of $1 coin is 16-12 = 4

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Let x be the number of coins of $1

(I) x=50/100(2+2+x)

Solve for x
Sufficient.

(II) x=25/100(8+4+x)

Solve for x
Sufficient.

Both (I) and (II) alone are sufficient.

Bunuel

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

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$0.25 * 8 = $2, $0.5 * 4 = $2 and let the total coins of $1 be Z.

1) Z = ($4 + Z)/2, Z is easily found(Sufficient)
2) Z = (12 + Z)/4, Z is easily found(Sufficient)

Option D

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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?

(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
1/2(2+2+1x)=1x
x=4 - single equation hence sufficient

(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
1/4(8+4+x)=x
x=4 Sufficient

Ans D

Ans D

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17 Dec 2024, 10:49

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The value of $.25 coins is 2 and the value of $.5 is also 2
Now separately, trying for both the options, we can get an answer
Therefore, the answer is option D

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Bunuel

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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We are given .25 x 8 = 2, .5 x 4 = 2. Total being $4. Using the first statement we understand the total of $1 coins is 50% of the total value. Hence, we can conclude the total value to be $8 and value of $1 to be 4.

Statement 1 is sufficient.

Similarly, let us assume total number of coins to be 8+4+x. This comes out to be 12+x. In the statement we are given that $1 coins make up 25% of the total number of coins which is x = .25 (12+x). On solving the equation, we get x = 4 which is the number of $1 coins.

Statement 2 is sufficient as well.

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Bunuel

This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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So given
1/4 -> 8,
1/2 -> 4,
1 ->??

Let that be x.

From stmt 1 : x=1/2(x+2+2) => x=4.

From stmt2: x= 1/4(12+x)=> x=4.

Hence IMO D

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Statement (1) states that the value of the $1 coins is 50% of the total value of all the coins.
x=0.5×(4+x) x=4.
Statement (2) states that the $1 coins make up 25% of the total number of coins.
x=0.25×(12+x) x=4.

Thus, both statements alone are sufficient, answer is D.