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'a' and 'b' are positive integers such that their LCM is 20

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'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 04 Jun 2011, 08:52
1
9
00:00
A
B
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D
E

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Question Stats:

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'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?

A. 0

B. 12

C. 13

D. 9

E. 11

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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 04 Jun 2011, 09:33
a = 4, b = 5 as they have to co-primes (HCF being 1 and LCM = 20)

So A+B = 9 is their max and min value

hence Difference = 0

Answer - A
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 04 Jun 2011, 09:52
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soaringAlone wrote:
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?

A. 0

B. 12

C. 13

D. 9

E. 11


LCM = 20 = 2*2*5
HCF = 1 => both the numbers are coprime.

max value of a+b = 20+1 = 21
min value = 4+5 = 9

difference = 21-9 = 12 Hence B
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 04 Jun 2011, 10:05
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Agree with Gurpreetsingh,

possible values of a and b can be 5,4; 4,5 (which are same for a+b) and 1,20; 20,1 (same result for a+b)
so 21-9 = 12. ans B.
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 11 Jun 2011, 15:29
B for me...

1 and 20
4 and 5

are the 2 possible combos

21 - 9 = 12
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 11 Jun 2011, 17:48
LCM is 20

GCF is 1 => numbers are coprime

possible values of the numbers are

a b
1 20

4 5

5 4

=>difference between max value of a+b and a-b = 21-9 = 12

Answer is B.
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 12 Feb 2016, 19:12
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soaringAlone wrote:
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?

A. 0

B. 12

C. 13

D. 9

E. 11


ok, we can use the formula: a*b= GCF*LCM
we have the last 2. we know that a*b=20.
now, let's see what are the possible values for a and b
a=1 - b=20
a=2 - b=10 -> can't be, since GCF=1.
a=4 - b=5

as we see, only 2 options work. the values might be switched, yet still, only 2 options work. when a+b=21, and when a+b=9.
difference is 21-9=12.
B.
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 05 Jul 2017, 08:46
soaringAlone wrote:
'a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the difference between the maximum and minimum possible values of 'a + b'?

A. 0

B. 12

C. 13

D. 9

E. 11


The two possible number sets are -

1. (4,5) So, a + b = 9
2. (20,1) So, a + b = 21

Thus the difference will be 21 - 9 = 12

Answer will be (B) 12
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Re: 'a' and 'b' are positive integers such that their LCM is 20  [#permalink]

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New post 10 Apr 2019, 03:17
I took 40 seconds to solve.

Given a and b are positive integers.

We know product of two integers = product of LCM and HCF of those two integers.
i.e axb=LCM(a,b)xHCF(a,b)

Back to the question.
We have axb= 20x1

Multiples of 20 are : (1,20) (2,10) (4,5)
Highest possible value of a+b is 1+20=21
Least possible value of a+b is 4+5=9

Difference is 21-9=12
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Re: 'a' and 'b' are positive integers such that their LCM is 20   [#permalink] 10 Apr 2019, 03:17
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