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If the expression #(a,b)# is defined to be the sum of a and b divided

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If the expression #(a,b)# is defined to be the sum of a and b divided [#permalink] New post   23 Nov 2020, 04:35
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If the expression #(a,b)# is defined to be the sum of a and b divided by the greatest common factor of a and b, what is the value of #(6,x)#, for positive integer x ?

(1) The greatest common factor of 6 and x is 1/7 the sum of 6 and x

(2) x is a positive odd integer not equal to 1
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NabilSaleem
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Re: If the expression #(a,b)# is defined to be the sum of a and b divided [#permalink] New post   23 Nov 2020, 07:22
#(a,b)# = a+b / G.C.F (a,b)

Find value of #(6,x)# = ? X+ve Int

st1:The greatest common factor of 6 and x is 1/7 the sum of 6 and x

#(6,x)# = 6+x / 6+x/7 => 7

sufficient

st2: x is a positive odd integer not equal to 1 -> Insufficient

Answer A
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Re: If the expression #(a,b)# is defined to be the sum of a and b divided [#permalink] New post   23 Nov 2020, 10:43
the greatest common factors between 6 and x can be {1 or 2 or 3 or 6}
1. if gcf is 1, then x = 1 i.e 1=(6+1)/7
if gcf is 2, then x = 8 i.e 2=(6+8)/7
if gcf is 3, then x = 15 i.e 3=(6+15)/7
if gcf is 6, then x = 36 i.e 6 =(6+36)/7
NOT SUFFICIENT
2. x is a positive odd integer not equal to 1
NOT SUFFICIENT

ON COMBINING : we get x = 15
ANS : C
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If the expression #(a,b)# is defined to be the sum of a and b divided [#permalink] New post   24 Nov 2020, 20:56
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PgRaul wrote:
the greatest common factors between 6 and x can be {1 or 2 or 3 or 6}
1. if gcf is 1, then x = 1 i.e 1=(6+1)/7
if gcf is 2, then x = 8 i.e 2=(6+8)/7
if gcf is 3, then x = 15 i.e 3=(6+15)/7
if gcf is 6, then x = 36 i.e 6 =(6+36)/7
NOT SUFFICIENT
2. x is a positive odd integer not equal to 1
NOT SUFFICIENT

ON COMBINING : we get x = 15
ANS : C


For statement 1 we were given that the ratio of the sum over their GCF is 7, the numbers you picked for x are all not viable except for x = 1. In fact according to your method, we can only choose x = 1 so it should be sufficient.
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If the expression #(a,b)# is defined to be the sum of a and b divided [#permalink]
24 Nov 2020, 20:56
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Bunuel
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