Data Sufficiency

Question 1

If xyz ≠ 0, is x (y + z) ≥ 0?

(1) |y + z| = |y| + |z|
(2) |x + y| = |x| + |y|

Question 2

How many different prime factors does N have?

(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.

Answers will be posted in 24 hrs time in my blog.

Thanks,
Quant-Master

for the 1st question the answer should be C

Stmt1 |y + z| = |y| + |z|, this means that Y and Z have same sign. We dont know the sign of X here, so insufficient

Stmt2 |x + y| = |x| + |y|, this means that X and Y have the same sign. We dont know the sign of Z here, so insufficient

Combine both Y and Z are both positive or both negative, from stmt2, the sign of Y is same as the sign of X,hence x (y + z) will either
be negative * negative or positive * positive, implying that the x (y + z) is always greater than equal to 0.


for the 2nd question the answer should be D

Stmt 1 : 2N has 4 different prime factors. Since 2 is a prime factor, so N should have 3 different prime factors

Stmt 2 : N^2 has 4 different prime factors. There N should have 4 different prime factors.

pandeyvineet24 wrote:for the 1st question the answer should be C

Stmt1 |y + z| = |y| + |z|, this means that Y and Z have same sign. We dont know the sign of X here, so insufficient

Stmt2 |x + y| = |x| + |y|, this means that X and Y have the same sign. We dont know the sign of Z here, so insufficient

Combine both Y and Z are both positive or both negative, from stmt2, the sign of Y is same as the sign of X,hence x (y + z) will either
be negative * negative or positive * positive, implying that the x (y + z) is always greater than equal to 0.


for the 2nd question the answer should be D

Stmt 1 : 2N has 4 different prime factors. Since 2 is a prime factor, so N should have 3 different prime factors

Stmt 2 : N^2 has 4 different prime factors. There N should have 4 different prime factors.

First question: I Agree.
Second question:

Statement 1: 2N has 4 different prime factors.

Take N=210 -> prime factors are 2,3,5,7
Prime factors for 2N will still be 2,3,5,7 and hence 4
However if N =105 -> prime factors now are 3,5,7
2N=210 -> prime factors are 2,3,5,7

So, I think 1st statement is insufficient
Statement 2 is sufficient as you pointed out
So answer should be (B)

Question 1 - Would you be able to explain with values.

Question 2 - Answer should be 'B'

Statement 1 is insufficient.

N = 7*5*3 -> 2N will have four different prime factors
N = 7*5*3*2 -> 2N will have four different prime factors

pandeyvineet24 wrote:for the 1st question the answer should be C

Stmt1 |y + z| = |y| + |z|, this means that Y and Z have same sign. We dont know the sign of X here, so insufficient

Stmt2 |x + y| = |x| + |y|, this means that X and Y have the same sign. We dont know the sign of Z here, so insufficient

Combine both Y and Z are both positive or both negative, from stmt2, the sign of Y is same as the sign of X,hence x (y + z) will either
be negative * negative or positive * positive, implying that the x (y + z) is always greater than equal to 0.


for the 2nd question the answer should be D

Stmt 1 : 2N has 4 different prime factors. Since 2 is a prime factor, so N should have 3 different prime factors

Stmt 2 : N^2 has 4 different prime factors. There N should have 4 different prime factors.

hi Vikas,
try with Y = 3 Z =-3 and vice versa

also X =2 and Y =-2 and vice versa.

HTH

My mistake i agree for the 2nd question. The answer should be B.
2 can be a common factor for N and 2N.

Detailed explanation to both the questions has been posted in my blog.

OA is 1) C
2)B

Thanks,
Quant-Master