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chetan2u
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If x and y are positive integers such that x+y=750, what is the differ 16 Dec 2020, 00:46
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65% (01:41) correct 35% (01:46) wrong based on 375 sessions

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If x and y are positive integers such that x+y=750, what is the difference between the maximum and minimum possible value of HCF(x,y)?

(A) 750
(B) 375
(C) 374
(D) 373
(E) 148
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C
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If x and y are positive integers such that x+y=750, what is the differ 16 Dec 2020, 06:25
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If x and y are positive integers such that x+y=750, what is the difference between the maximum and minimum possible value of HCF(x,y)?
(A) 750
(B) 375
(C) 374
(D) 373
(E) 148
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If x = 749 and y = 1, then the HCF is 1. This is the minimum possible value.

To get the maximum value of the HCF, we divide 750 by 2 which is x = 375 and y = 375 and the HCF will be 375.


The difference is therefore 375 - 1 = 374


Option C

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ayerhs
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If x and y are positive integers such that x+y=750, what is the differ 20 Dec 2020, 19:43
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To get the maximum value of the HCF, we divide 750 by 2 which is x = 375 and y = 375 and the HCF will be 375. Can you explain this??

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If x and y are positive integers such that x+y=750, what is the differ 20 Dec 2020, 22:11
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ayerhs
To get the maximum value of the HCF, we divide 750 by 2 which is x = 375 and y = 375 and the HCF will be 375. Can you explain this?
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The sum of the 2 numbers has to be 750. When the number is equally divided, then the HCF is maximum.

Take for eg the number 10. If x + y is = 10, then we can have 1 + 9, 2 + 8, 3 + 7, 4+6 and 5 + 5

HCF (1,9) = 1, (2,8) = 2, (3,7) = 1, (4,6) = 2 and (5,5) = 5

So when we need to 2 find 2 numbers whose sum is given, then the HCF is maximum when they are equal (this is true for even numbers)


Hope this helps

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If x and y are positive integers such that x+y=750, what is the differ 31 Jul 2025, 10:06
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Hi CrackverbalGMAT

How are you taking lowest HCF as x = 749 and y = 1 ?

As far as i know HCF of two number is calculated by taking the lowest power of common prime, and if you take y = 1 then 1 is not a prime.

So why is the answer C and not D, because the lowest prime we can take is 2 either for x or y.

Please help me understand this.
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If x and y are positive integers such that x+y=750, what is the differ 31 Jul 2025, 10:09
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ayerhs
To get the maximum value of the HCF, we divide 750 by 2 which is x = 375 and y = 375 and the HCF will be 375. Can you explain this??

CrackVerbalGMAT
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Hi ayerhs

the HCF is 375 but only for the first part.
there are two parts to the question, 1] we have to find the maximum HCF which is 375 as you mentioned. 2] we also have to find the minimum HCF possible
And then take the difference of those two
Max HCF - Min HCF
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