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17 Dec 2024, 20:10
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Given:
\($0.25\) coins = 8 → Value = \(8 \times 0.25 = 2\)
\($0.50\) coins = 4 → Value = \(4 \times 0.50 = 2\)
\($1\) coins = \(x\) → Value = \(x \times 1 = x\)
Total value = \(4 + x\)
Total number of coins = \(12 + x\)
(1) Total value of \($1\) coins is 50% of total value:
\(x = 0.5 \times (4 + x)\)
\(x = 2 + 0.5x\)
\(0.5x = 2 \implies x = 4\)
Sufficient.
(2) \($1\) coins are 25% of total coins:
\(x = 0.25 \times (12 + x)\)
\(x = 3 + 0.25x\)
\(0.75x = 3 \implies x = 4\)
Sufficient.
Answer: D]
\($0.25\) coins = 8 → Value = \(8 \times 0.25 = 2\)
\($0.50\) coins = 4 → Value = \(4 \times 0.50 = 2\)
\($1\) coins = \(x\) → Value = \(x \times 1 = x\)
Total value = \(4 + x\)
Total number of coins = \(12 + x\)
(1) Total value of \($1\) coins is 50% of total value:
\(x = 0.5 \times (4 + x)\)
\(x = 2 + 0.5x\)
\(0.5x = 2 \implies x = 4\)
Sufficient.
(2) \($1\) coins are 25% of total coins:
\(x = 0.25 \times (12 + x)\)
\(x = 3 + 0.25x\)
\(0.75x = 3 \implies x = 4\)
Sufficient.
Answer: D]
17 Dec 2024, 20:26
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Given: 0.25a+0.50b+1c=?
Also, a=8 & b=4
Find: C= ?
I) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
c=0.50*Total value
0.25*8+0.5*4+1c=Total value
2+2+0.5*T=T
Total value =8
c=4 .............SUFFICIENT
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
Number of 0.25 coins + Number of 0.5 coins + Number of 1 coins = Total number of coins
8+4+0.25*T=T
Total number of coins= 16
Number of 1 coins = 16-12=4 ............SUFFICIENT
Either (1) or (2) is sufficient to answer the question.
Answer: D
Also, a=8 & b=4
Find: C= ?
I) The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
c=0.50*Total value
0.25*8+0.5*4+1c=Total value
2+2+0.5*T=T
Total value =8
c=4 .............SUFFICIENT
(2) The $1 coins make up 25% of the total number of coins in the piggy bank.
Number of 0.25 coins + Number of 0.5 coins + Number of 1 coins = Total number of coins
8+4+0.25*T=T
Total number of coins= 16
Number of 1 coins = 16-12=4 ............SUFFICIENT
Either (1) or (2) is sufficient to answer the question.
Answer: D
17 Dec 2024, 20:46
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It is a value type of DS question.
Let the number of $1 coins be x.
Let’s look at statement 1;
The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
If this is the case then;
X=50/100*[(.25*8)+(.5*4)+(1*x)]
X=50/100*[(2)+(2)+( x)]
X=50/100*(4+x)
2x=4+x
X=4
So S1 is sufficient.
(Eliminate B, C and E)
Let’s look at statement 2;
The $1 coins make up 25% of the total number of coins in the piggy bank.
If this is the case then;
X=25/100*[(8)+(4)+( x)]
X=25/100*(12+x)
4x=12+x
X=4
So S2 is also sufficient.
(Eliminate A)
Correct answer is D.
Let the number of $1 coins be x.
Let’s look at statement 1;
The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
If this is the case then;
X=50/100*[(.25*8)+(.5*4)+(1*x)]
X=50/100*[(2)+(2)+( x)]
X=50/100*(4+x)
2x=4+x
X=4
So S1 is sufficient.
(Eliminate B, C and E)
Let’s look at statement 2;
The $1 coins make up 25% of the total number of coins in the piggy bank.
If this is the case then;
X=25/100*[(8)+(4)+( x)]
X=25/100*(12+x)
4x=12+x
X=4
So S2 is also sufficient.
(Eliminate A)
Correct answer is D.
17 Dec 2024, 21:20
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Converting into cents for ease of calculation, $0.25 = 25 cents, $0.50 = 50 cents, and $1 = 100 cents
Let number of coins of $1(100 cents) be x
Total number of coins = 8 + 4 + x
Total value of coins = 25(8) + 50(4) + 100(x)
St 1: The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
100(x) = \(\frac{1}{2}\) (25(8) + 50(4) + 100(x))
Solving, we get x = 4
St 2: The $1 coins make up 25% of the total number of coins in the piggy bank.
x = \(\frac{1}{4}\) = 8 + 4 + x
Solving, we get x = 4
Hence, option (D) each statement alone is sufficient.
Let number of coins of $1(100 cents) be x
Total number of coins = 8 + 4 + x
Total value of coins = 25(8) + 50(4) + 100(x)
St 1: The total value of the $1 coins in the piggy bank is 50% of the total value of all the coins.
100(x) = \(\frac{1}{2}\) (25(8) + 50(4) + 100(x))
Solving, we get x = 4
St 2: The $1 coins make up 25% of the total number of coins in the piggy bank.
x = \(\frac{1}{4}\) = 8 + 4 + x
Solving, we get x = 4
Hence, option (D) each statement alone is sufficient.
