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# If a and b are positive integers and a≠1, does a = b?

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Math Expert
Joined: 02 Sep 2009
Posts: 59725
If a and b are positive integers and a≠1, does a = b?  [#permalink]

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04 Apr 2019, 22:37
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Difficulty:

15% (low)

Question Stats:

71% (01:08) correct 29% (00:57) wrong based on 41 sessions

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If a and b are positive integers and a≠1, does a = b?

(1) a is a factor of b
(2) a is a multiple of b

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Re: If a and b are positive integers and a≠1, does a = b?  [#permalink]

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05 Apr 2019, 00:45
Bunuel wrote:
If a and b are positive integers and a≠1, does a = b?

(1) a is a factor of b
(2) a is a multiple of b

Given : a > 0 and b > 0

Question : Does a = b ?

Statement : a is a factor of b OR b/a = k (k = integer constant)

Let us check some values :

2/2 = 1 ( a = b = 2) YES

4/2 = 2 (a = 2, b = 4) NO

Not sufficient

Statement 2 :

a is a multiple of b OR a/b = q (q = integer constant)

Same values can be tested as in ST 1.

2/2 = 1 ( a = b = 2) YES

4/2 = 2 (a = 4, b = 2) NO

Not sufficient

Combining 1 and 2 we get,

a is a factor of b & a is a multiple of b

This is only possible when a = b

Sufficient (C)

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Re: If a and b are positive integers and a≠1, does a = b?  [#permalink]

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05 Apr 2019, 03:23
Bunuel wrote:
If a and b are positive integers and a≠1, does a = b?

(1) a is a factor of b
(2) a is a multiple of b

from given statement a≠1, that a,b cannot be prime
#1
a is a factor of b
b=6
so a= 2,3 or 6 not sufficient , a not equal b always; insufficient
#2
a is a multiple of b
a=6 , b = 2,3,6
again not sufficieint
from 1 & 2
common factor and multiple of a & b is 6
so a=b
IMO C
Re: If a and b are positive integers and a≠1, does a = b?   [#permalink] 05 Apr 2019, 03:23
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