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09 Feb 2020, 07:51
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:41) correct
34%
(02:42)
wrong
based on 220
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Not Attempted Yet
A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
09 Feb 2020, 09:29
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rheam25
A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
We can't have too many ten cent coins, so Statement 1 can only be true for very specific numbers. We might have 16 one-dollar coins and 5 ten-cent coins, or we might have 15 one-dollar coins and 15 ten-cent coins. If we have any fewer one-dollar coins, we'll need to have more ten-cent coins than dollar coins, and that's not allowed. So Statement 1 is almost sufficient, since it leaves us only two possibilities.
Statement 2 is not sufficient since it can be true if we have any odd number of dollar coins. For example, if we have just one dollar coin, and eight dimes, changing five dimes into dollars will make 2/3 of the coins into dollar coins. Or if we have 1001 dollar coins and 508 dimes, again changing five dimes to dollars will make 2/3 of the coins into dollar coins. So Statement 2 is not sufficient.
Using both Statements, Statement 2 rules out one of the two possibilities we had when considering Statement 1, and we must have 15 of each type of coin, so the answer is C.
09 Feb 2020, 11:06
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rheam25
A bag contains only two types of coins: 10 cent coins or 1 dollar coins and number of 10 cent coins does not exceed the number of 1 dollar coins. How many 10 cent coins are there in the bag?
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
(1) The total amount of money in the bag is $16.50.
(2) If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins.
Let the number of 10 cent coins be \(t\) and the number of 1 dollar coins be \(d\) => \(t ≤ d\)
We need to determine the value of \(t\)
From statement 1:
Total amount = 1650 cents \(=> 10t + 100d = 1650\)
\(=> t + 10d = 165\)
There can be two possible solutions for this: \(t = 5, d = 16\) OR \(t = 15, d = 15\) - Insufficient
From statement 2:
If five 10-cent coins are removed and replaced with five 1-dollar coins then two-third of all the coins in the bag are 1 dollar coins
Number of 10 cent coins after 5 are removed = \((t - 5)\)
Number of 1 dollar coins after 5 are added = \((d + 5)\)
=> Total coins (remain unchanged) = \(t + d\)
\(=> \frac{(d+5)}{(t+d)} = \frac{2}{3}\)
\(=> 3d + 15 = 2t + 2d\)
\(=> d = 2t - 15\)
Multiple solutions exist: \(t = 20, d = 25\); \(t = 15, d = 15\); etc - Insufficient
Combining:
\(t + 10d = 165\)
\(2t - d = 15\)
Solving: \(d = t = 15\) - Sufficient
Answer C
