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If the greatest common divisor of p and s is 6, which of the following [#permalink]

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23 Sep 2016, 05:34

Top Contributor

Bunuel wrote:

If the greatest common divisor of p and s is 6, which of the following must be true?

I) s+p is divisible by 18 II) s+2p is divisible by 18 III) s·p is divisible by 18

A. I only B. II only C. III only D. I and II only E. II and III only

p and s must be multiple of 6.

I) when p=6,s=12,then s+p=18 is divisible by 18.But when p=6,s=24,p+s=30 is NOT divisible by 18 II) when p=6,s=6,then s+2p=18 is divisible by 18.But when p=6,s=12,p+s=20 is NOT divisible by 18 III) since lowest value of p and s is 6 ,lowest s*p=36,is divisible by 18.So all the multiple of p*s must be divisible by 18

Re: If the greatest common divisor of p and s is 6, which of the following [#permalink]

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24 Sep 2016, 19:17

I) s+p is divisible by 18 II) s+2p is divisible by 18 III) s·p is divisible by 18

A. I only B. II only C. III only D. I and II only E. II and III only

I first started w/ p=6 and s=12. From there I got that I and III were valid. Then I tried p=6 and s=18. From there I found that only statement 3 was valid. C.

Re: If the greatest common divisor of p and s is 6, which of the following [#permalink]

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01 May 2017, 14:17

I chose two sets of numbers to test each case: {1} s=6, p=12 and {2} s=12, p=18.

Case 1: s+p is divis by 18. True in {1}, not true in {2} Case 2: s+2p is divis by 18. True in {2}, not true in {1}. Right here we can eliminate A, B, D, and E. I tested C just in case though. Case 3: s*p is true in both {1} and {2}, because s and p will contribute the factors necessary to reach divisibility by 18.

If the greatest common divisor of p and s is 6, which of the following [#permalink]

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05 Jul 2017, 21:23

1

This post received KUDOS

Bunuel wrote:

If the greatest common divisor of p and s is 6, which of the following must be true?

I) s+p is divisible by 18 II) s+2p is divisible by 18 III) s·p is divisible by 18

A. I only B. II only C. III only D. I and II only E. II and III only

Because "greatest common divisor of p and s is 6", p= 6m and s=6n (m, n are positive integers)

s+p= 6(m+n). If (m+n) is a multiple of 3, e.g. (m+n)=3, then (s+p) is divisible by 18 If (m+n) is not a multiple of 3, e.g. (m+n)=5, then (s+p) is not divisible by 18 --> Inconsistent answers --> (I) is not a must Eliminate options (A), (D)

s+2p= 6(m+2n). Similar to the above reasoning, (m+2n) could be either a multiple of 3 or not a multiple of 3 --> Inconsistent answers --> (II) is not a must Eliminate options (B), (E)

Only (III) left, and there is no kind of "all the above choices are wrong" option, so option (C) is the winner.

For assessment on statement (III) s.p=6m x 6n= 36mn. 36 is already divisible by 18, so 36mn is too. --> (III) must be true.

Re: If the greatest common divisor of p and s is 6, which of the following [#permalink]

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16 Aug 2017, 08:11

1

This post was BOOKMARKED

Bunuel wrote:

If the greatest common divisor of p and s is 6, which of the following must be true?

I) s+p is divisible by 18 II) s+2p is divisible by 18 III) s·p is divisible by 18

A. I only B. II only C. III only D. I and II only E. II and III only

Since GCD (P,S) is 6 Let S=6a & P=6b where a,b are +ve integers Therefore S+P = 6a+6b =6(a+b) S+2P = 6a+12b=6(a+2b) & S*P = 6a*6b =36ab

In the light of above deductions I) (S+P)/18=6(a+b)/18= Integer if (a+b) is a multiple of 3 so NOT TRUE always II)(S+2P)/18=6(a+2b)/18= Integer if (a+2b) is a multiple of 3 so NOT TRUE always III)(S*P)/18=36(ab)/18= Integer ALWAYS TRUE irrespective of the value of a,b

If the greatest common divisor of p and s is 6, which of the following must be true?

I) s+p is divisible by 18 II) s+2p is divisible by 18 III) s·p is divisible by 18

A. I only B. II only C. III only D. I and II only E. II and III only

Bunuel, I need help here.

In such questions, Can I take a number which is multiple of 6. Like in here, (6 & 60 ) And then perform the operations on them as given?

We are given that the greatest common divisor of p and s is 6, so yes, p = 6 and s = 60 is one of the possible cases. Generally the greatest common divisor of p and s is 6, means that p = 6m and s = 6n, where m and n are co-prime integers (integers, which do not share any common factors but 1).

Notice though that the question asks which of the following MUST be true, not COULD be true. So, one possible set might not be enough. For example, p = 6 and s = 6 is possible, which will make II true, but II is true only for some of the values (so it could be true) but it won't be true for all cases (so it's not always true) while III is always true, it's true for any (all) possible cases (so III must be true).

Re: If the greatest common divisor of p and s is 6, which of the following [#permalink]

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17 Aug 2017, 08:14

GCD(p,s) = 6 p,s are 6, multiple of 6 so take 6,6 for eg: 1) p+s=12 not divisible by 18. 2) p+2s=18 now take p=6,s=12 , p+2s = 30 not divisible by 18 3) p*s , take 6, any multiple of 6 their multiplication will be divisible by 18.

therefore C is correct _________________

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