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11 Nov 2018, 19:11
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A
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Difficulty:
95%
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Question Stats:
45% (03:17) correct
55%
(03:17)
wrong
based on 309
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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?
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
14 Nov 2018, 04:56
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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
General Discussion
12 Nov 2018, 03:03
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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
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
