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Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A

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Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A [#permalink]

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New post 18 Oct 2017, 02:52
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E

Difficulty:

  55% (hard)

Question Stats:

59% (01:04) correct 41% (01:30) wrong based on 44 sessions

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Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to Anne and the ratio became 1 : 4. What is the minimum
possible number of coins that Jack gave Anne?

A. 1
B. 3
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

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email: nkmungila@gmail.com
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Re: Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A [#permalink]

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nkmungila wrote:
Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to Anne and the ratio became 1 : 4. What is the minimum
possible number of coins that Jack gave Anne?

A. 1
B. 3
C. 6
D. 7
E. 8


Jack (j), Anne (a), given coins (x)

\(\frac{j}{a} = \frac{3}{4}\)

\(j=3k\), \(a=4k\)

\(\frac{3k – x}{4k + x} = \frac{1}{4}\)

\(8k = 5x\)

\(x = \frac{8k}{5}\)

In order for x to be a positive integer min value of k should be 5. Hence x = 8

Answer E

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Re: Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A [#permalink]

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New post 22 Oct 2017, 16:52
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nkmungila wrote:
Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to Anne and the ratio became 1 : 4. What is the minimum
possible number of coins that Jack gave Anne?

A. 1
B. 3
C. 6
D. 7
E. 8


We can express the ratio of the number of Jack’s coins to the number of Anne’s coins as 3x : 4x. Let’s let n = the number of coins that Jack gave to Anne. Thus, Jack now has (3x - n) coins and Anne has (4x + n) coins, and this new ratio is 1 : 4, as shown in this equation:

(3x - n)/(4x + n) = 1/4

4(3x - n) = 4x + n

12x - 4n = 4x + n

8x = 5n

x = 5n/8

Since x is an integer and 8 does not divide 5, n must divide 8, and thus the minimum value for n is 8.

Answer: E
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Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A [#permalink]

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New post 22 Oct 2017, 23:05
Jack and Anne had coins in the ratio 3 : 4 => we can express the number of Jack's coin and that of Anne as 3x, 4x respectively. Let y be the the number of coins that Jack gave to Anne.
=> the number of Jack's coins becomes (3x - y); the number of Jack's coins becomes (4x + y).

"The ratio became 1 : 4" => (3x-y)/(4x+y) = 1/4 => y =8x/5

Since x,y are integers => the minimum value for y is 8 (as x = 5)

Hence the answer is E.

Kudos [?]: 18 [0], given: 9

Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A   [#permalink] 22 Oct 2017, 23:05
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Jack and Anne had coins in the ratio 3 : 4. Jack gave a few coins to A

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