Is 2^(y+z)*3^x*5^y*7^z < 90^y*14^z?
(1) y and z are positive integers; x = 1
(2) x and z are positive integers; y = 1We should know the rule n^y*n^z = n^(y+z)
So first of all we have to reformat the equation.
90^y*14^z = (3*3*5*2)^y * (7*2)^z =
3^2y * 5^y * 7^z * 2^(y+z)Next what I see is that both left and right are equal except the 3 number
2^(y+z) *
3^x * 5^y * 7^z < 2^(y+z) *
3^2y * 5^y * 7^z
which means that we can eliminate all number except 3
So now the question should be changed to
Is 3^x < 3^2y?Let's look at the question
(1) y and z are positive integers; x = 1if x = 1
y = positive integers (y = 1,2,3,4,...)
This mean that even y = 1 which is the lowest, 3^x will always less than 3^2y.
x=1, y=1; 3 < 3^2(1) YES
x=1, y=2; 3 < 3^2(2) YES
So (1) is sufficient to answer then (1) is
OK.(2) x and z are positive integers; y = 1Now we know that y = 1 and x could be 1,2,3,4,...
Let's input the number
x=1, y=1; 3 < 3^2(1) YES
x=2, y=1; 3^2 < 3^2(1) NO it is equal
x=3, y=3; 3^3 < 3^2(1) NO
So (2) is not sufficient to answer. (2) is
NOT OKSo i think that the answer should be
AMy learning
- when the question is about 2 comparing equation with a lot of xyz, we should reformat the question first before step in to calculate. This usually make everything easier (there are cases when reformat is not working when the answer is obviously full of xyz. So if we see the answer like that, just dont reformat, or else we have to reformat and reformat again just to match the answer choice
)
- when we see small equation, input number always be a good strategy