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Question of the Week- 22 (Jack and Jill have certain number of ....)

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Question of the Week- 22 (Jack and Jill have certain number of ....)  [#permalink]

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New post 11 Nov 2018, 19:11
12
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (03:21) correct 61% (03:23) wrong based on 87 sessions

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e-GMAT Question of the Week #22

Jack and Jill have certain number of apples with them. The total number of apples with both of them is less than 80. If Jill gives a certain number of apples to Jack, then Jack will have four times the number of apples Jill has. If Jack gives the same number of apples to Jill, then Jack will have thrice the number of apples that Jill has. What can be the number of apples that Jack initially has?

    A. 31
    B. 36
    C. 45
    D. 62
    E. 63

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Question of the Week- 22 (Jack and Jill have certain number of ....)  [#permalink]

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New post 12 Nov 2018, 03:03
1
1
Let the number of apples with Jack and Jill be a & b respectively.
Let k be the number of apples transferred.

a+k = 4(b-k)
=> a + k = 4b - 4k
=> a - 4b = -5k ------ 1

and a-k = 3(b+k)
=> a - 3b = 4k ------ 2

Solving 1 & 2 ,
we get k = b/9 ------- 3

From 1 & 3 , we get

a = 31b/9

Now , a+b < 80
or , 31b/9 + b < 80
or b < 18

b can take only 1 value i.e 9 otherwise "k" will not be an integer.

k = 1 ; b = 9

Using this value in equation 1 , a = 31

Option A
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Re: Question of the Week- 22 (Jack and Jill have certain number of ....)  [#permalink]

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New post 14 Nov 2018, 04:56

Solution


Given:
    • Total number of apples with both of them = 80
    • If Jill gives certain number of apples to Jack, then the number of apples with Jack = 4 * the number of apples with Jill
    • If Jack gives the same number of apples to Jill, then the number of apples with Jack = 3 * the number of apples with Jill

To find:
    • The number of apples that jack has initially

Approach and Working:
    • Let us assume that the number of apples with Jack and Jill initially are P and Q
      o Implies, P + Q < 80

Now, when Jill gives x apples to Jack
    • The number of apples with Jack will be = P + x, and
    • The number of apples with Jill = Q – x

As per given information, P + x = 4(Q - x)
    • Which implies that 4Q – P = 5x …………. (1)

And, when Jack gives x apples to Jill
    • The number of apples with Jack will be = P - x, and
    • The number of apples with Jill = Q + x

And we are given that P - x = 3(Q + x)
    • Which implies that P - 3Q = 4x …………. (2)

Solving equations (1) and (2), we get,
    • Q = 9x and P = 31x

Thus, P must be a multiple of 31, since x is an integer
    • And, we know that P + Q < 80
    • Implies, 31x + 9x < 80
    • Thus, x < 2

Therefore, the only possible value of P = 31 * 1 = 31

Hence the correct answer is Option A.

Answer: A

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Re: Question of the Week- 22 (Jack and Jill have certain number of ....)  [#permalink]

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New post 22 Nov 2018, 18:27
Let K be the apples with Jack. Total apples 80-x. Hence apples with Jill (80-x-K)

Jill gives A apples to Jack. The new arrangement
Jack = K+A
Jill = (80-x-K)-A
Given that, (K+A) = 4(80-x-K)- A ------------Eq 1

Similarly, the other arrangement
Jack = K-A
Jill = (80-x-K)+A
Given that, (K-A) = 3(80-x-K)+ A--------------Eq2

Solving the 2 equations, we get
A = k/31
Plugging values, we get that K = 31(gives A =1) satisfies the equations Eq 1 & 2
Hence A
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Re: Question of the Week- 22 (Jack and Jill have certain number of ....)  [#permalink]

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New post 29 Nov 2019, 23:15
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Re: Question of the Week- 22 (Jack and Jill have certain number of ....)   [#permalink] 29 Nov 2019, 23:15
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