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17 Jun 2019, 17:30
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Difficulty:
95%
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Question Stats:
45% (03:07) correct
55%
(03:38)
wrong
based on 56
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There are two packets – x and y. ‘x’ contains only 25 cents coins and ‘y’ contains only 50 cents coins. Total amount in both the packets put together is 80 Dollars. For every 4 coins transferred from x to y, 3 coins are transferred from y to x. It is also known that only 25 cents coins are transferred from x and only 50 cents coins are transferred from y. After ‘n’ such transfers, the total number of coins in both the packets becomes equal. Which of following can be a value of n?
A. 8
B. 12
C. 16
D. 20
E. 24
A. 8
B. 12
C. 16
D. 20
E. 24
17 Jun 2019, 20:19
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nick1816
let there be a 25 cent coin and b 50 cent coin
since the total amount in both packets are given
0.25a + 0.50b = 80
a + 2b = 320.......(1)
now
box (X).................box(Y)
a coins................b coins (For every 4 coins transferred from x to y, 3 coins are transferred from y to x and after n such transfer)
a-4n...................b+4n ( transfer from x to y)
a-4n+3n..............b+4n-3n (transfer from y to x)
a-4n+3n=b+4n-3n (given)
a-n=b+n
a-b = 2n.............(2)
solving equation (1) and (2)
we get a = \(\frac{320+4n}{3}\)
a = integer (number of coins)
so 320 + 4n must be multiple of 3
only option c satisfy
n = 16
eswarchethu135
GMAT 2: 640 Q49 V27
Posts: 276
17 Jun 2019, 21:25
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Let the number of coins in two packets - x and y be a and b.
Now 0.25a + 0.5b = $80 ______________(1)
Each time 4 coins are being taken from packet x and 3 coins are being taken from packet y. This operation is performed for n times.
a-4n --> b+4n
a-4n+3n --> b+4n-3n
After n operations, this count became equal in both packets.
a - n = b + n
a - b = 2n __________(2)
multiplying eq (2) by 0.5
0.5a - 0.5b = n
adding this with eq (1)
0.5a - 0.5b = n
0.25a + 0.5b = 80
---------------------------
0.75a = 80 + n
-----------------------
Now a has to be a positive integer as the number of coins cannot be any other value apart from a positive integer.
From options, only option C for n = 16, a value will be a positive integer. Only for n = 16, a = 128 and b = 96. These values satisfy the eq (1) andd hence n = 16.
OPTION: C
Now 0.25a + 0.5b = $80 ______________(1)
Each time 4 coins are being taken from packet x and 3 coins are being taken from packet y. This operation is performed for n times.
a-4n --> b+4n
a-4n+3n --> b+4n-3n
After n operations, this count became equal in both packets.
a - n = b + n
a - b = 2n __________(2)
multiplying eq (2) by 0.5
0.5a - 0.5b = n
adding this with eq (1)
0.5a - 0.5b = n
0.25a + 0.5b = 80
---------------------------
0.75a = 80 + n
-----------------------
Now a has to be a positive integer as the number of coins cannot be any other value apart from a positive integer.
From options, only option C for n = 16, a value will be a positive integer. Only for n = 16, a = 128 and b = 96. These values satisfy the eq (1) andd hence n = 16.
OPTION: C
