Problem Solving

Hi I have 4 problems from one of my GmatPrep Test can some1 please explain how to solve these?

I am attaching all four problems in 1 document

Next time, please post the questions in the thread itself. Makes it easier for all to answer.

Q1. At the very least n has to be 30 or multiples thereof. Prime factors of 30 are 2,3 and 5

Thus 3 different factors.

Q2. The problem states
1X +2Y +3Z = 1.5(X+Y+Z)
Simplify this to get your answer

For Q3 Consider positive numbers 1 and 2 and substitute. Only option E suffices. Think Commutative Property.

For Q4, 1Equation 2 Unknowns means neither statement will suffice. That immediately eliminates options A,B, D . You are left with either C or E.

Thanks NEO

Neo2000 wrote:Next time, please post the questions in the thread itself. Makes it easier for all to answer.

Q1. At the very least n has to be 30 or multiples thereof. Prime factors of 30 are 2,3 and 5

Thus 3 different factors.

Q2. The problem states
1X +2Y +3Z = 1.5(X+Y+Z)
Simplify this to get your answer

For Q3 Consider positive numbers 1 and 2 and substitute. Only option E suffices. Think Commutative Property.

For Q4, 1Equation 2 Unknowns means neither statement will suffice. That immediately eliminates options A,B, D . You are left with either C or E.

Hi can you plz explain your ans to problem #3? thanks a lot

preciousrain7 wrote:Hi can you plz explain your ans to problem #3? thanks a lot

For number 3, it states

f(a+b) = f(a) + f(b)

This means if you substitute 'a' for 'x', and then substitute 'b' for 'x', and then add the two together, then it equals substituting 'a+b' for 'x'.

You can see that see that some obviously don't work:
f(x) = x+1
f(a) = a+1
f(b) = b+1
f(a) + f(b) = a+1+b+1 = a+b+2

f(a+b) = a+b+1

Some are less obvious
f(x) = x^2
f(a) = a^2
f(b) = b^2
f(a) + f(b) = a^2 + b^2

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


And only answer E works
f(x) = -3x
f(a) = -3a
f(b) = -3b
f(a) + f(b) = -3a - 3b

f(a+b) = -3(a+b) = -3a - 3b