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25 Nov 2024, 01:30
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B
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Difficulty:
65%
(hard)
Question Stats:
61% (02:41) correct
39%
(02:53)
wrong
based on 219
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Amy had $2400, which comprises of her school fee and her pocket money. The amount was in denominations of $50, $100 and $500 notes. She gave 5 notes at her school fee counter. What is the minimum possible amount that she got as her pocket money if the number of $500 notes is greater than the number of $100 notes which in turn was less than the number of $50 notes?
A. $250
B. $300
C. $350
D. $400
E. None of these
A. $250
B. $300
C. $350
D. $400
E. None of these
25 Nov 2024, 08:08
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We needed minimum possible pocket money.
Given, \(500 \times X > 100 \times Y\), and \(50\times Z > 100 \times y\)
\(X_n + Y_n + Z_n = 5\) paid for fees and we needed to maximize this value.
Possible arrangements,
\(4\times 500 + 1\times 100 + 6\times 50 = 2400 \to (1)\)
\(4\times 500 + 2\times 100 + 4\times 50 = 2400 \to (2)\)
Only two combinations are possible as mentioned in 1 and 2.
The Fees maximum amount in both cases \(= 4\times 500 + 1\times 100 = 2100\)
Pocket money \(= 2400 - 2100 = 300\)
ANS B
Given, \(500 \times X > 100 \times Y\), and \(50\times Z > 100 \times y\)
\(X_n + Y_n + Z_n = 5\) paid for fees and we needed to maximize this value.
Possible arrangements,
\(4\times 500 + 1\times 100 + 6\times 50 = 2400 \to (1)\)
\(4\times 500 + 2\times 100 + 4\times 50 = 2400 \to (2)\)
Only two combinations are possible as mentioned in 1 and 2.
The Fees maximum amount in both cases \(= 4\times 500 + 1\times 100 = 2100\)
Pocket money \(= 2400 - 2100 = 300\)
ANS B
25 Nov 2024, 09:10
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Am I wrong if I say that there is another possible combination which is :
4 x 500 + 3 x 100 + 2 x 50 = 2400.
Moreover, it is specified in the problem that the number of denominatios of 100 is more than the number of denominations of 50.
Thus, with this reasoning, the less amount whe could have taken out of her pocket is
2 x 50 + 3 x 100 = 400.
4 x 500 + 3 x 100 + 2 x 50 = 2400.
Moreover, it is specified in the problem that the number of denominatios of 100 is more than the number of denominations of 50.
Thus, with this reasoning, the less amount whe could have taken out of her pocket is
2 x 50 + 3 x 100 = 400.
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