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# How many of the three different positive integers a, b, and c are div

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4071
GPA: 3.39
How many of the three different positive integers a, b, and c are div  [#permalink]

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25 Jan 2018, 10:09
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Difficulty:

55% (hard)

Question Stats:

62% (01:58) correct 38% (01:43) wrong based on 38 sessions

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How many of the three different positive integers a, b, and c are divisible by 7?

(1) The product of a, b, and c is divisible by 3, but only c is divisible by 21.
(2) Each of the three positive integers is divisible by 3, but only c is divisible by 21.
Retired Moderator
Joined: 22 Aug 2013
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Location: India
Re: How many of the three different positive integers a, b, and c are div  [#permalink]

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25 Jan 2018, 10:52
How many of the three different positive integers a, b, and c are divisible by 7?

(1) The product of a, b, and c is divisible by 3, but only c is divisible by 21.
(2) Each of the three positive integers is divisible by 3, but only c is divisible by 21.

A number which is divisible by 21 - must be divisible by 7 as well as by 3 (21 = 7*3). A number which is divisible by 3, might or might not be divisible by 21. Similarly, a number which is divisible by 7, might or might not be divisible by 21.

(1) c is divisible by 21, so 'c' contains both 3 and 7 as factors. So 'c' has already given a 3 in the product. Now its given that ONLY 'c' is divisible by 21. that means 'a' and 'b' are not divisible by 21, but they can be divisible by any one of '3' or '7'. So its possible that both a and b are divisible by 7, but not by 3. Thus we cant say how many of the three numbers are divisible by 7. Not Sufficient.

(2) 'a' and 'b' both are divisible by 3, but they are not divisible by 21 (given that only 'c' is). This means that neither 'a' nor 'b' has '7' as a factor. So only one number out of these three - 'c', is divisible by 7. Sufficient.

Re: How many of the three different positive integers a, b, and c are div   [#permalink] 25 Jan 2018, 10:52
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