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27 Jan 2020, 10:46
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Difficulty:
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Question Stats:
66% (02:10) correct
34%
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based on 38
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Lisa has 45 coins, which are worth a total of $3.50. If the coins are all nickels and dimes, what is the difference between the number of dimes and the number of nickels?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Source: Master GMAT
Updated on: 27 Jan 2020, 12:23
Originally posted by sujoykrdatta on 27 Jan 2020, 11:29.
Last edited by sujoykrdatta on 27 Jan 2020, 12:23, edited 1 time in total.
Last edited by sujoykrdatta on 27 Jan 2020, 12:23, edited 1 time in total.
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SajjadAhmad
Lisa has 45 coins, which are worth a total of $3.50. If the coins are all nickels and dimes, what is the difference between the number of dimes and the number of nickels?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Source: Master GMAT
We can easily solve by equations: d + n = 45 and 10d + 5n = 350
But let us try a different approach here.
Note: 1 nickel = 5 cents, 1 dime = 10 cents
There are 45 coins worth $3.50 = 350 cents
If all coins were dimes, the total value of the coins would have been 45 * 10 = 450 cents
Thus, we need to reduce the total value by 100 cents
If we convert a dime to a nickel, we would reduce the value of that coin by 5 cents
Thus, number of times such a change needs to be done so that the value falls be 100 cents = 100/5 = 20
Thus, there are 20 nickels and the remaining 25 are dimes
Thus, difference = 5
Answer A
27 Jan 2020, 11:42
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Let the number of dimes = n and the number of nickel = 45-n
Now, 10n +5(45-n) = 350( 1 dime = 10 cents, and 1 nickel = 5 cents)
10n + 225 -5n = 350
5n =125
n = 25
Number of dimes = 25 and Number of nickels = 45-25 = 20
Difference between dimes and nickels = 25-20 = 5(A)
Now, 10n +5(45-n) = 350( 1 dime = 10 cents, and 1 nickel = 5 cents)
10n + 225 -5n = 350
5n =125
n = 25
Number of dimes = 25 and Number of nickels = 45-25 = 20
Difference between dimes and nickels = 25-20 = 5(A)
