is y-x > 1/(x-y)

1) |x-y|>1
Let y=10, x=5
10 - 5> 1/(5-10)
5>-1/5 .. YES

let x=10, y=5
-5>1/5 .. NO

INSUFF

2) y>x
y-x>0
x-y <0
1/x-y will also be less than 0
Hence y-x is always greater than 1/x-y
SUFF

pick B

Hope this helps!!

M1 = 6, M2 = 96, M3 = 996,... Mk = 10^k -4

qn is is 10^k -4 divisible by an even number q??

1) q<45
10^k-4 is an even number.
hence q=2 will divide Mk
q=8 will not divide. Because M1 = 6 which is not divisible by 8.
INSUFF

2) Atleast 2 terms in the sequence are div by q.
q=2 will divide atleast 2 terms and also divides all terms.
q=12 will divide 96 and 996.. but it willnot divide M1 = 6
hence INSUFF

Combining:
We still have q=2 that satisfies both the conditions and also dividea all terms.
q =12 which also satisfies both the conditions but does not divide all terms.

Hence INSUFF

pick E.

Whats OA?

Answer: E

(1) BIFURCATES:

> Take q =2 , then it answers in the affirmative (all terms of the given sequence are even);

> Take q = 6, then M6 = 10^6 - 6 is a term of the sequence that is not divisible by q (=6), therefore q=6 answers in the negative.

(10^6 is not divisible by 3 and 6 is, therefore their subtraction is not)


(2) BIFURCATES:

> Take q =2 , please note that M1 and M2 are even (enough to validate this q), and all terms are even, therefore answers in the affirmative.

>Take q = 6, please note that M1 and M2 are disivible by 6 (enough to validate this q), and at least M6 is not divisible by 6, therefore this q=6 answers in the negative.


(1+2) BIFURCATES (with q =2 and q = 6), therefore the answer is E for sure!


Hope this is all clear!

Good studies,
Fábio.

fskilnik wrote:
> Take q = 6, then M6 = 10^6 - 6 is a term of the sequence that is not divisible by q (=6), therefore q=6 answers in the negative.

(10^6 is not divisible by 3 and 6 is, therefore their subtraction is not)

I made a mistake: M6 = 10^6 - 4 , therefore from the fact that this is divisible by 6, my arguments are wrong!

Arguments used by kvcpk are PERFECT and they are the best (lowest) counter-examples, therefore the answer is "E" by the BIFURCATIONS he used.

Congrats, kvcpk.

kvcpk wrote:M1 = 6, M2 = 96, M3 = 996,... Mk = 10^k -4

qn is is 10^k -4 divisible by an even number q??

1) q<45
10^k-4 is an even number.
hence q=2 will divide Mk
q=8 will not divide. Because M1 = 6 which is not divisible by 8.
INSUFF

2) Atleast 2 terms in the sequence are div by q.
q=2 will divide atleast 2 terms and also divides all terms.
q=12 will divide 96 and 996.. but it willnot divide M1 = 6
hence INSUFF

Combining:
We still have q=2 that satisfies both the conditions and also dividea all terms.
q =12 which also satisfies both the conditions but does not divide all terms.

Hence INSUFF

pick E.

Whats OA?

I agree the answer is E. I'd just like to point out a way to find the two qs for (2): all the numbers are even so q=2 is a possibility. for the seocnd one, note that 10^k is divisible by 4 (any integer power of 10, except for 10 itself, will be divisible by 4), so (10^k-4) will also be a multiple of 4: multiple of 4 - multiple of 4 = multiple of 4.
Thus, all of the terms except for M1 will be divisible by 4.
Since q could equal 2 or 4, with an answer if "yes" for the first and "no" for the second, and stat. (1) does not rule these two examples out, the answer is E.

fskilnik wrote: I made a mistake: M6 = 10^6 - 4 , therefore from the fact that this is divisible by 6, my arguments are wrong!

Arguments used by kvcpk are PERFECT and they are the best (lowest) counter-examples, therefore the answer is "E" by the BIFURCATIONS he used.

Congrats, kvcpk.

Thanks for the encouragement!!

Geva Stern wrote: Since q could equal 2 or 4, with an answer if "yes" for the first and "no" for the second, and stat. (1) does not rule these two examples out, the answer is E.

You are right, Geva, both kvcpk and myself missed the (easier) 4 that would come quicker than the 12 to do its "job" as a counter-example. Well observed, congrats.

Geva Stern wrote: Since q could equal 2 or 4, with an answer if "yes" for the first and "no" for the second, and stat. (1) does not rule these two examples out, the answer is E.

You are right, Geva, both kvcpk and myself missed the (easier) 4 that would come quicker than the 12 to do its "job" as a counter-example. Well observed, congrats.