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17 Dec 2024, 12:11
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Given that the number of $0.25 coins is 8, and the number of $0.50 coins is 4. Value of $0.25 coins is $2 and that of $0.5 coins is also $2. Total value = 4 + x (value of $1 coins)
Statement 1:
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
x = 0.5(4+x)
x = 2 + 0.5X
0.5X = 2
x = 4
Total value of $1 coins is $4. Hence there are 4 $1 coins. Sufficient
Statement 2:
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
Means the $0.25 and $0.5 make up 75% of the total number of coins
if 12 coins is 75% then 25% is 4. Sufficient
Statement 1:
(1) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
x = 0.5(4+x)
x = 2 + 0.5X
0.5X = 2
x = 4
Total value of $1 coins is $4. Hence there are 4 $1 coins. Sufficient
Statement 2:
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
Means the $0.25 and $0.5 make up 75% of the total number of coins
if 12 coins is 75% then 25% is 4. Sufficient
17 Dec 2024, 12:17
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Number of $0.25 coins = 8
Value of $0.25 coins = 0.25 * 8 = $2
Number of $0.5 coins = 4
Value of $0.5 coins = 0.5 * 4 = $2
Problem statement : How many $1 coins ?
Statement 1 -
Value of $1 coins = 50% of total value of all coins
Let value of $1 coins be $'x'
Total value = x + 2 + 2 = x+4
Also given x is 50% of total
x = \(\frac{(x+4)}{2}\)
x = $4
Number of $1 coins = 4
Statement 1 is sufficient
Statement 2:
Let number of coins of $1 be 'y'
Total number of coins = 8 + 4 + y
Given y is 25% of total coins
y = 25% of (y+12)
Solving, y = 4
Number of $1 coins are 4
Statement 2 is sufficient
Statement 1 and Statement 2 are alone sufficient independently(OPTION D)
Value of $0.25 coins = 0.25 * 8 = $2
Number of $0.5 coins = 4
Value of $0.5 coins = 0.5 * 4 = $2
Problem statement : How many $1 coins ?
Statement 1 -
Value of $1 coins = 50% of total value of all coins
Let value of $1 coins be $'x'
Total value = x + 2 + 2 = x+4
Also given x is 50% of total
x = \(\frac{(x+4)}{2}\)
x = $4
Number of $1 coins = 4
Statement 1 is sufficient
Statement 2:
Let number of coins of $1 be 'y'
Total number of coins = 8 + 4 + y
Given y is 25% of total coins
y = 25% of (y+12)
Solving, y = 4
Number of $1 coins are 4
Statement 2 is sufficient
Statement 1 and Statement 2 are alone sufficient independently(OPTION D)
Bunuel
17 Dec 2024, 12:21
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Answer is D. Both statements are independently sufficient
We know that Warren has $0.25 x 8 + $0.50 x 4 = $4 currently. His total value must be $0.25 x 8 + $0.50 x 4 + $1 x A = $4 + $A. His total number of coins must be 8 + 4 + A.
1) $A = 0.50($4 + $A) --> $A = $2 + $0.50A --> $A = $4. Therefore, Statement 1 tells us Warren has 4 $1 coins. We can check this: $0.25 x 8 + $0.50 x 4 + $1 x 4 = $8, and $4 is 50% of $8, so this is sufficient.
2) A = 0.25(8 + 4 + A) --> A = 3 + 0.25A --> A = 4. We can check this: 8 + 4 + 4 = 16, and 4 is 25% of 16, so this is sufficient.
We know that Warren has $0.25 x 8 + $0.50 x 4 = $4 currently. His total value must be $0.25 x 8 + $0.50 x 4 + $1 x A = $4 + $A. His total number of coins must be 8 + 4 + A.
1) $A = 0.50($4 + $A) --> $A = $2 + $0.50A --> $A = $4. Therefore, Statement 1 tells us Warren has 4 $1 coins. We can check this: $0.25 x 8 + $0.50 x 4 + $1 x 4 = $8, and $4 is 50% of $8, so this is sufficient.
2) A = 0.25(8 + 4 + A) --> A = 3 + 0.25A --> A = 4. We can check this: 8 + 4 + 4 = 16, and 4 is 25% of 16, so this is sufficient.
