OA is D.
This is testing your knowledge of exponents ... and how well you know your exponent rules.
Remember the rule for exponents:
An exponent expression with a base of 0 will always yield 0, regardless of the exponent
And exponent expression with a base of 1 will always yield 1, regardless of the exponent.
So if you are told that x^6 = x^7 = x^15, so x must be 0 or 1.
If you are told x^6 = x^8 = x^10, x could be 0, 1, or -1 (note even exponents here)
Lets take a look at the Q-stem:
x^n = x^n+2
What is this telling us.
This is telling ust that x could be 0, 1, or -1.
0^n will always = 0^n+2
1^n will always = 1^n+2
(-1)^n will always = (-1)^n+2 (Note: if n is even, then n+2 is also even. If n is odd, then n+2 is also odd.)
So from the Q-stem we know that the possible values of x are 0, 1, -1.
(1) x = x^2 - 2
=> 0 = x^2 + x - 2
=> 0 = (x+1)(x-2)
So x = -1 or x = 2.
We know from Q-stem that x could be 0, 1, or -1.
x = 2 is not in this list. Only -1 is. so (1) is SUFF.
(2) 2x < x^5
We use the possible values for x from q-stem (0, 1, -1) and plug them into this inequality, to see which will make this inequality true.
Lets try -1:
2(-1) < (-1)^5
-2 < -1
this is true so x could be -1
Lets try 0:
2(0) < (0)^5
0 < 0
this is NOT true, so x cannot be 0
Lets try 1:
2(1) < 1^5
2 < 1
this is NOT true, so x cannot be 1.
Only poss value of x is -1. So (2) is SUFF.
Hence answer D.
I think if you remember the exponent rules ... then it sets you off on the right foundation in answering this question.
I was really interested in finding out alternative ways in solving this question. Did anyone use a different approach in solving this ?
Thanks.
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