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Pritishd
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If the sum of two positive integers is 592 and their HCF is 37 18 May 2020, 09:26
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C
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95% (hard)

Question Stats:

43% (01:58) correct 57% (02:00) wrong based on 141 sessions

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If the sum of two positive integers is 592 and their HCF (GCD or greatest common divisor) is 37, then how many such pairs exist?

A. 8
B. 7
C. 4
D. 16
E. 15
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C
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If the sum of two positive integers is 592 and their HCF is 37 18 May 2020, 09:40
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If the sum of two positive integers is 592 and their HCF (GCD or greatest common divisor) is 37, then how many such pairs exist?

A. 8
B. 7
C. 4
D. 16
E. 15
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We are told that the greatest common factor of two integers is 37. So, these integers are \(37x\) and \(37y\), for some positive integers \(x\) and \(y\). Notice that \(x\) and \(y\) must not share any common factor but 1, because if they do then GCF of \(37x\) and \(37y\) will be more that 37.

Next, we know that \(37x+37y=592\) --> \(x+y=16\) --> since \(x\) and \(y\) don't share any common factor but 1 then (x, y) can be only (1, 15), (3, 13), (5, 11) and (7, 9) (all other pairs (2, 14), (4, 12), (6, 10), (8, 8) do share common factor greater than 1). So, there are only four pairs of such numbers possible: 37*1=37 and 37*15=555; 37*3=111 and 37*13=481; 37*5=185 and 37*11=407 AND 37*7=259 and 37*9=333.

Answer: C.
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If the sum of two positive integers is 592 and their HCF is 37 18 May 2020, 09:34
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If the sum of two positive integers is 592 and their HCF (GCD or greatest common divisor) is 37, then how many such pairs exist?
let, two numbers are 37x and 37y ( x and y are co-prime)
so,37x+37y=592
or,x+y=16
possible cases = (1,15) (3,13) (5,11) (7,9)
so, 4 such pairs exist .

correct answer C


Similar problem :
https://gmatclub.com/forum/the-sum-of-t ... 34111.html
discussed here.
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If the sum of two positive integers is 592 and their HCF is 37 18 May 2020, 09:45
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Bunuel
Pritishd
If the sum of two positive integers is 592 and their HCF (GCD or greatest common divisor) is 37, then how many such pairs exist?

A. 8
B. 7
C. 4
D. 16
E. 15

We are told that the greatest common factor of two integers is 37. So, these integers are \(37x\) and \(37y\), for some positive integers \(x\) and \(y\). Notice that \(x\) and \(y\) must not share any common factor but 1, because if they do then GCF of \(37x\) and \(37y\) will be more that 37.

Next, we know that \(37x+37y=592\) --> \(x+y=16\) --> since \(x\) and \(y\) don't share any common factor but 1 then (x, y) can be only (1, 15), (3, 13), (5, 11) and (7, 9) (all other pairs (2, 14), (4, 12), (6, 10), (8, 8) do share common factor greater than 1). So, there are only four pairs of such numbers possible: 37*1=37 and 37*15=555; 37*3=111 and 37*13=481; 37*5=185 and 37*11=407 AND 37*7=259 and 37*9=333.

Answer: C.
Show more

Thanks Bunuel!

I have a very basic question that should the question not ask for unique pairs instead of just pairs? I am talking about (1, 15) and (15, 1). I understand that they are both the same and yield the same result, but from a value stand point we are assigning two different values to \(x\) and \(y\)
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If the sum of two positive integers is 592 and their HCF is 37 18 May 2020, 09:53
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Bunuel
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If the sum of two positive integers is 592 and their HCF (GCD or greatest common divisor) is 37, then how many such pairs exist?

A. 8
B. 7
C. 4
D. 16
E. 15

We are told that the greatest common factor of two integers is 37. So, these integers are \(37x\) and \(37y\), for some positive integers \(x\) and \(y\). Notice that \(x\) and \(y\) must not share any common factor but 1, because if they do then GCF of \(37x\) and \(37y\) will be more that 37.

Next, we know that \(37x+37y=592\) --> \(x+y=16\) --> since \(x\) and \(y\) don't share any common factor but 1 then (x, y) can be only (1, 15), (3, 13), (5, 11) and (7, 9) (all other pairs (2, 14), (4, 12), (6, 10), (8, 8) do share common factor greater than 1). So, there are only four pairs of such numbers possible: 37*1=37 and 37*15=555; 37*3=111 and 37*13=481; 37*5=185 and 37*11=407 AND 37*7=259 and 37*9=333.

Answer: C.

Thanks Bunuel!

I have a very basic question that should the question not ask for unique pairs instead of just pairs? I am talking about (1, 15) and (15, 1). I understand that they are both the same and yield the same result, but from a value stand point we are assigning two different values to \(x\) and \(y\)
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The question asks: how many such pairs exist? 37 and 555 is the same pair of numbers as 555 and 37.
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If the sum of two positive integers is 592 and their HCF is 37 28 Apr 2025, 07:18
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