Few DS ...Plz discuss

[electrico]

1. If n and k are positive integers, is SQRT(n+k) > 2 SQRT(n)
(1) k > 3n
(2) n + k > 3n

2. Is the integer n a multiple of 15?
(1) n is a multiple of 20.
(2) n + 6 is a multiple of 3.

3. In a certain coding scheme, each word is encoded by replacing each letter in the word with another letter. The same code is used for all words, so that the same letter replaces a given letter each time the given letter occurs. What code will result when the word TAME is encoded by this scheme?
(1) When the word MAT is encoded, the result is DLX.
(2) When the word TEA is encoded, the result is XRL.

4. If d denotes a decimal, is d ≥ 0.5 ?
(1) When d is rounded to the nearest tenth, the result is 0.5.
(2) When d is rounded to the nearest integer, the result is 1.


My Answers are:

1. - E
2. - C
3. - C
4. - A

But I saw some differents answers for these question.

[electrico]

Is it really tough or its just that nobody cares here!!!

[vittalgmat]

@ electrico,
To get better discussion, pls dont post multiple quesitions in a single post.

I will try to answer.. as much as I can.. hang on.

[tohellandback]

answers for 1 and 2 with explanation:

question 1:
case 1:we know (and now you know:) for any two numbers n and k both >2
nk>n+k
sqrt(nk)>sq(n+k)
now k>3n so it is atleast 4
2sqrt(n)>sq(n=k) suficient
case 2: take sqrt on both sides
sqrt(n+k)>sq(3n)
now, in this case we are not sure if sqrt(n+k) >2sqrt(n)
so A

question 2

case A: take 60 and 40
case 2: take 12 and 15

answer E- both insufficient

let me work on the other two..and plz post different under different thread.

[tohellandback]

questions 3,
answers C,A

Explanation for 3
combine both and you get values for all the letters inTAME

explanation 4:
1) the number must be >=o.5 and <.6
so sufficient
2) number could be anything from 0.0 to 0.999999..

[electrico]

@tohellandback
question 1:
case 1:we know (and now you know:) for any two numbers n and k both >2
nk>n+k
sqrt(nk)>sq(n+k)
now k>3n so it is atleast 4
2sqrt(n)>sq(n=k) suficient
case 2: take sqrt on both sides
sqrt(n+k)>sq(3n)
now, in this case we are not sure if sqrt(n+k) >2sqrt(n)
so A

question 2

case A: take 60 and 40
case 2: take 12 and 15

answer E- both insufficient
---------------
For Q1. k > 3n => k+n > 4n => sqrt(k+n) > 2 sqrt(n)
But this will hold true only if we will consider the +ve square root. what if one is +ve and the other is -ve. (although agreed to your explanation. Thanks.)

For Q2.
case A: take 60 and 40
case 2: take 12 and 15 , and also 60.

combining both will give answer C. correct me if I am wrong?

[electrico]

Q3 and Q4 I also got it correct...but saw some other answers so thought of confirming. Thanks for that.

[tohellandback]

@tohellandback
question 1:
case 1:we know (and now you know:) for any two numbers n and k both >2
nk>n+k
sqrt(nk)>sq(n+k)
now k>3n so it is atleast 4
2sqrt(n)>sq(n=k) suficient
case 2: take sqrt on both sides
sqrt(n+k)>sq(3n)
now, in this case we are not sure if sqrt(n+k) >2sqrt(n)
so A

question 2

case A: take 60 and 40
case 2: take 12 and 15

answer E- both insufficient
---------------
For Q1. k > 3n => k+n > 4n => sqrt(k+n) > 2 sqrt(n)
But this will hold true only if we will consider the +ve square root. what if one is +ve and the other is -ve. (although agreed to your explanation. Thanks.)

For Q2.
case A: take 60 and 40
case 2: take 12 and 15 , and also 60.

combining both will give answer C. correct me if I am wrong?

Electricio: I think yuo are right..
silly mistake sorry

[electrico]

Means both my explanation are correct?

Can somebody suggets other explanation which lead to diff. answwrs?

Thanks tohellandback.

[gmat_dest]

1. A
2. C
3. C
4. B

1 and 2 are already done.

3 is correct.

4th one.

a) number can be from 0.45 to 0.54 --- not sufficient
b) number can be from 0.50 to 1.49 ---- sufficient