Data Sufficiency

ajith wrote:DS004

is |x+y| = 5?

1) |x| = 3
2) |y| = 2

Answer is E.

x+y = -5 or +5

1. x = -3 or 3 => insuff

2. y = -2 or 2 => insuff

together still insuff since |x+y| <= |x| + |y|

I am sorry, guys

I am on a break till 19th of this month ,

Be back after that.

If somebody can manage this this thread till then I will be grateful,

Miss u guys,

Ajith

Just a question

Since we have the absolulte value of x+y and both x and y and absolulte value, shouldnt both of them together be 5?

thats my reasoning.

Ajith asked me to post in this thread till he gets back.

Answers in 3 days time as usual.

DS005

If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3

(2) N is divisible by 7

rajs.kumar wrote:Ajith asked me to post in this thread till he gets back.

Answers in 3 days time as usual.

If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3

(2) N is divisible by 7

1) 4321 div by 3 remainder 1 -->
implies K=2 or 5 or 8 INSUFF
2) 4321 div by 7 remainder 2 -->
implies K=5 only SUFFF

limits660 wrote:Just a question

Since we have the absolulte value of x+y and both x and y and absolulte value, shouldnt both of them together be 5?

thats my reasoning.

I will give an attempt at proving it. Hope I am correct and I dont confuse you.

consider this

(a + b)^2 = a^2 + b^2 + 2ab

(|a| + |b|)^2 = |a|^2 + |b|^2 + 2.|a|.|b|

a <= |a|, and b <= |b| --- (1) (depending on a and b is less than or greater than 0)

a^2 = (|a|)^2, and b^2 = (|b|)^2 --- (2)

using (1) and (2) we can say

(a + b)^2 <= (|a| + |b|)^2

Take the square root on both sides (Note: |x| = x^2)

|a + b| <= |a| + |b|

DS 006

13. If a, b, and c are integers, is the number 3(a + b) - c divisible by 3?
(1) a + b is divisible by 3
(2) c is divisible by 3

DS 007

If &#9651; denotes an operation, what is the value of (a&#9651;b) &#9651;c ?

1. a &#9651; b = 5
2. 5 &#9651; c = 3

rajs.kumar wrote:

ajith wrote:DS004

is |x+y| = 5?

1) |x| = 3
2) |y| = 2

Answer is E.

x+y = -5 or +5

1. x = -3 or 3 => insuff

2. y = -2 or 2 => insuff

together still insuff since |x+y| <= |x| + |y|

my comments on 4.
answer is E.
But i am sorry to say that rajs kumar reasoning has flaw.
@jeff , x+y not necessarily equals to +/- 5.

@rajs , jeff.
case A: X=3 Y=2.........ok
case B: X=-3 Y=-2.....,..ok.

case C: X=-3 Y=2.
case D: X=3 Y=-2
FOR LATTER two cases we dnt know.

is X odd

X^3 odd

is this info suff to answer the question??

aim-wsc wrote: my comments on 4.
answer is E.
But i am sorry to say that rajs kumar reasoning has flaw.
@jeff , x+y not necessarily equals to +/- 5.

@aim
This is my approach. probably there is an error in the reasoning

1 and 2 alone are obviously insufficent.

(1) + (2) => |x| + |y| = 5 --- (3)

We know that |x + y| <= |x| + |y| --- (4)

Combining (3) and (4) we can arrive at |x + y| <= 5 => insufficient

rajs.kumar wrote:Ajith asked me to post in this thread till he gets back.

Answers in 3 days time as usual.

DS005

If K is a positive integer less than 10 and N = 4,321 + K, what is the value of K?

(1) N is divisible by 3

(2) N is divisible by 7

Answer is B.

same explanation as zipper

(1) => K could be 2, 5, 8
(2) => K can only be 5

rajs.kumar wrote:DS 006

13. If a, b, and c are integers, is the number 3(a + b) - c divisible by 3?
(1) a + b is divisible by 3
(2) c is divisible by 3

Answer is B.

(1) nothing known about C => insuff
(2) 3(a+b) and c are divisable => suff

DS 008

If x is not equal to 0, is |x| less than 1?

(1) x/|x| < x
(2) |x| > x