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.
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QuantMaster
Question of the Day  4th August, 2009
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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.
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.

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First question: I Agree.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.
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)
MS

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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
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.
 cubicle_bound_misfit
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hi Vikas,
try with Y = 3 Z =3 and vice versa
also X =2 and Y =2 and vice versa.
HTH
try with Y = 3 Z =3 and vice versa
also X =2 and Y =2 and vice versa.
HTH
Cubicle Bound Misfit

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

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Detailed explanation to both the questions has been posted in my blog.
OA is 1) C
2)B
Thanks,
QuantMaster
OA is 1) C
2)B
Thanks,
QuantMaster
https://gmatquants.blogspot.com  My Blog Updated almost daily with new quant fundas. Find collection of quants question in my blog