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Re: A $10 bill (1,000 cents) was replaced with 50 coins having the same to [#permalink]
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gmatt1476 wrote:
A $10 bill (1,000 cents) was replaced with 50 coins having the same total value. The only coins used were 5-cent coins, 10-cent coins, 25-cent coins, and 50-cent coins. How many 5-cent coins were used?

(1) Exactly 10 of the coins were 25-cent coins and exactly 10 of the coins were 50-cent coins.
(2) The number of 10-cent coins was twice the number of 5-cent coins.



DS02871.01

Let number of coins of different denominations(in increasing order 5,10,25,50 cents) be a, b, c, d, e respectively.
Acc. to question: a + b + c + d = 50 (i)
5*a + 10*b + 25*c + 50*d = 1000 (ii)
Moving on to the statements:
1) This tells us that c = 10 and d = 10.
Putting these values in above equations we get 2 equations and two variables. So we can easily find the value of a.
Sufficient

2) b = 2*a. Even if we put this in equations we left with two equations and 3 variable. Multiple solutions are possible.
Not Sufficient

Hence answer is A.
A very good variation of this question that looks too similar to this one but is quite sneaky is (Merle's spare change jar has exactly 16 U.S. coins). Search for the phrase in the parenthesis. Not allowed to post link at this stage. Will update with link once allowed.
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Re: A $10 bill (1,000 cents) was replaced with 50 coins having the same to [#permalink]
gmatt1476 wrote:
A $10 bill (1,000 cents) was replaced with 50 coins having the same total value. The only coins used were 5-cent coins, 10-cent coins, 25-cent coins, and 50-cent coins. How many 5-cent coins were used?

(1) Exactly 10 of the coins were 25-cent coins and exactly 10 of the coins were 50-cent coins.
(2) The number of 10-cent coins was twice the number of 5-cent coins.



DS02871.01


(1) Exactly 10 of the coins were 25-cent coins and exactly 10 of the coins were 50-cent coins.

\(10 * 25 = 250\)
\(10 * 50 = 500\)

We have 30 coins still unaccounted for, equating to 250 cents.

These 250 cents will consist of only 5-cent coins and 10-cent coins. We don't really have to determine an amount because we know 250 cents will consists of 30 coins -- only one combination of the two will work. SUFFICIENT.

(2) If the number of 10-cent coins is twice the number of 5-cent coins, there could be several possibilities. INSUFFICIENT.
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Re: A $10 bill (1,000 cents) was replaced with 50 coins having the same to [#permalink]
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This is a medium difficulty level question. It can be made harder by involving more conditions. It is important to write the equations down.

Also, check out the question in the link below to understand the variation of the question in context:

https://gmatclub.com/forum/merle-s-spare-change-jar-has-exactly-16-u-s-coins-each-of-which-is-a-305945.html#:~:text=Hence%203%20and%206%20is%20one%20combination.&text=Jul%2011%2C%202020-,gmatt1476%20wrote%3A%20Merle's%20spare%20change%20jar%20has%20exactly%2016%20U.S.,or%20a%2050%2Dcent%20coin.
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Re: A $10 bill (1,000 cents) was replaced with 50 coins having the same to [#permalink]
(1) let 5c = w, 10c = x, 25c = y, and 50c = z

1000 = 5w + 10x + 25y + 50z

y = 10, and z = 10

1000 = 500 + 250 + 5w + 10x

250 = 5w + 10x

BUT w + x = 50-10-10 = 30

2 equations, 2 unknown -> SUFFICIENT

(2) x = 2w

40 = 2z + y + w

Clearly insufficient.

Answer is A
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Re: A $10 bill (1,000 cents) was replaced with 50 coins having the same to [#permalink]
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Re: A $10 bill (1,000 cents) was replaced with 50 coins having the same to [#permalink]
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