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Re: pretty hard one [#permalink]
28 Jul 2010, 01:22

1

This post received KUDOS

Expert's post

mehdiov wrote:

The positive integers r, s, and t are such that r is divisible by s and s is divisible by t. Is r even? (1) st is odd. (2) rt is even.

(1) st=odd, clearly not sufficient as no info about r, for example if r=6, s=1 and t=1 then answer is YES but if r=3, s=1 and t=1 then the answer is NO.

(2) rt=even. For product of 2 integers to be even either one or both must be even. Can r not to be even? The only chance would be if t is even and r is odd. Let's check if this scenario is possible: if t is even, so must be s, as s is divisible by t (if an integer is divisible by even it's even too). Now, if s is even so must be r by the very same reasoning. So scenario when r is not even is not possible --> r=even. Sufficient.

Re: pretty hard one [#permalink]
28 Jul 2010, 01:37

Bunuel wrote:

mehdiov wrote:

The positive integers r, s, and t are such that r is divisible by s and s is divisible by t. Is r even? (1) st is odd. (2) rt is even.

(1) st=odd, clearly not sufficient as no info about r, for example if r=6, s=1 and t=1 then answer is YES but if r=3, s=1 and t=1 then the answer is NO.

(2) rt=even. For product of 2 integers to be even either one or both must be even. Can r not to be even? The only chance would be if t is even and r is odd. Let's check if this scenario is possible: if t is even, so must be s, as s is divisible by t (if an integer is divisible by even it's even too). Now, if s is even so must be r by the very same reasoning. So scenario when r is not even is not possible --> r=even. Sufficient.

Answer: B.

many thanks looks easy after the explanation

Do you have an idea about the level of this question ?

Re: pretty hard one [#permalink]
28 Jul 2010, 01:44

Expert's post

mehdiov wrote:

Bunuel wrote:

mehdiov wrote:

The positive integers r, s, and t are such that r is divisible by s and s is divisible by t. Is r even? (1) st is odd. (2) rt is even.

(1) st=odd, clearly not sufficient as no info about r, for example if r=6, s=1 and t=1 then answer is YES but if r=3, s=1 and t=1 then the answer is NO.

(2) rt=even. For product of 2 integers to be even either one or both must be even. Can r not to be even? The only chance would be if t is even and r is odd. Let's check if this scenario is possible: if t is even, so must be s, as s is divisible by t (if an integer is divisible by even it's even too). Now, if s is even so must be r by the very same reasoning. So scenario when r is not even is not possible --> r=even. Sufficient.

Answer: B.

many thanks looks easy after the explanation

Do you have an idea about the level of this question ?

Not very hard (600+) but tricky, as it's C-trap question: the question which is obviously sufficient if we take statements together. When we see such questions we should become very suspicious. _________________

Re: pretty hard one [#permalink]
07 Aug 2010, 02:44

Not very hard (600+) but tricky, as it's C-trap question: the question which is obviously sufficient if we take statements together. When we see such questions we should become very suspicious.[/quote]

Re: pretty hard one [#permalink]
07 Aug 2010, 04:47

Bunuel wrote:

(1) st=odd, clearly not sufficient as no info about r, for example if r=6, s=1 and t=1 then answer is YES but if r=3, s=1 and t=1 then the answer is NO. Answer: B.

thanks...i was able to get to B but may be in 3 minutes..... i complicated the question thinking like 2 4 8 and not thinking infact one can be one number or 2 numbers can be same 8 2 2 and so on...

Re: pretty hard one [#permalink]
27 Apr 2014, 02:01

Bunuel wrote:

mehdiov wrote:

The positive integers r, s, and t are such that r is divisible by s and s is divisible by t. Is r even? (1) st is odd. (2) rt is even.

(1) st=odd, clearly not sufficient as no info about r, for example if r=6, s=1 and t=1 then answer is YES but if r=3, s=1 and t=1 then the answer is NO.

(2) rt=even. For product of 2 integers to be even either one or both must be even. Can r not to be even? The only chance would be if t is even and r is odd. Let's check if this scenario is possible: if t is even, so must be s, as s is divisible by t (if an integer is divisible by even it's even too). Now, if s is even so must be r by the very same reasoning. So scenario when r is not even is not possible --> r=even. Sufficient.

Answer: B.

HI Bunnel,

I have a doubt on this.

Generally we treat both the statements as seprate statements. then why are you mixing them.

If I will go with st2 i can r can be even or odd because rt = even ( r and t both can be even or one of them is even) now if we refer even to r and t then st1 will contradict.

is this the reason you are not considering both r and t as even?

Re: pretty hard one [#permalink]
28 Apr 2014, 01:27

Expert's post

PathFinder007 wrote:

Bunuel wrote:

mehdiov wrote:

The positive integers r, s, and t are such that r is divisible by s and s is divisible by t. Is r even? (1) st is odd. (2) rt is even.

(1) st=odd, clearly not sufficient as no info about r, for example if r=6, s=1 and t=1 then answer is YES but if r=3, s=1 and t=1 then the answer is NO.

(2) rt=even. For product of 2 integers to be even either one or both must be even. Can r not to be even? The only chance would be if t is even and r is odd. Let's check if this scenario is possible: if t is even, so must be s, as s is divisible by t (if an integer is divisible by even it's even too). Now, if s is even so must be r by the very same reasoning. So scenario when r is not even is not possible --> r=even. Sufficient.

Answer: B.

HI Bunnel,

I have a doubt on this.

Generally we treat both the statements as seprate statements. then why are you mixing them.

If I will go with st2 i can r can be even or odd because rt = even ( r and t both can be even or one of them is even) now if we refer even to r and t then st1 will contradict.

is this the reason you are not considering both r and t as even?

Please clarify

Thanks.

The statements do not contradict: st is odd and rt is even is possible when r is even and both s and t are odd. _________________

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