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A merchant has 435 litres, 493 litres and 551 litres of three differen

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Bunuel
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A merchant has 435 litres, 493 litres and 551 litres of three differen [#permalink] New post   04 Aug 2021, 05:45
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A merchant has 435 litres, 493 litres and 551 litres of three different kinds of milk. Find the least number of casks of equal size required to store all the milk without mixing.

(A) 61
(B) 51
(C) 49
(D) 47
(E) 45
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B
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rajatchopra1994
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Re: A merchant has 435 litres, 493 litres and 551 litres of three differen [#permalink] New post   04 Aug 2021, 06:58
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Explanation:
435- 3x5x29
493- 17x29
551- 19x29
HCF of 435, 493, 551 - 29

No. of casks = 435/29 + 493/29 + 551/29
= 15 + 17 + 19
= 51

IMO-B
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Re: A merchant has 435 litres, 493 litres and 551 litres of three differen [#permalink] New post   07 Aug 2021, 07:49
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Bunuel wrote:
A merchant has 435 litres, 493 litres and 551 litres of three different kinds of milk. Find the least number of casks of equal size required to store all the milk without mixing.

(A) 61
(B) 51
(C) 49
(D) 47
(E) 45


Note the differences are 58. Then we know the GCF has to be a factor of 58, and it has to be odd so we likely have a GCF of 29. 435 = 290 + 145 is a multiple of 29, so all the numbers are multiples of 29.

435/29 = (290 + 135)/29 = 15. Then we know the other ones result in 17 and 19 when we divide by 29. The sum would be 17*3 = 51.

Ans: B
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Re: A merchant has 435 litres, 493 litres and 551 litres of three differen [#permalink] New post   19 Jan 2024, 08:47
Bunuel wrote:
A merchant has 435 litres, 493 litres and 551 litres of three different kinds of milk. Find the least number of casks of equal size required to store all the milk without mixing.

(A) 61
(B) 51
(C) 49
(D) 47
(E) 45

Required no of casks of equal size is HCF(435, 493 & 551) = 29

So, No of casks required is \(\frac{435}{29} + \frac{493}{29} + \frac{551}{29} = 15 + 17 + 19 = 51\), Answer must be (B)
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Re: A merchant has 435 litres, 493 litres and 551 litres of three differen [#permalink]
19 Jan 2024, 08:47
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