oneo wrote:hey guys... got this question in a prep test.... please help me out... Could not understand the explanation
If a5≤a, then which of the following must be true?
i. -1≤a≤0
ii. a=0
iii. 0≤a≤1
a. None of the above
b. i only
c. ii only
d. iii only
e. i and iii
Try to show that statements I, II and III DON'T have to true.
When a problem involves EXPONENTS, consider the following types of values:
positive integers greater than 1
0
±1
negative integers less than -1
positive and negative fractions
roots
Statement I: -1≤ a≤ 0
Try a value OUTSIDE this range.
If we plug a=1 into a� ≤ a, we get:
1� ≤ 1
1 ≤ 1.
This works.
Thus, it does NOT have to be true that -1≤a≤0.
Eliminate B and E, which say that statement I must be true.
Statement II: a=0
Since it's possible that a=1, it does NOT have to be true that a=0.
Eliminate C, which says that statement II must be true.
Statement III: 0≤a≤1
Try a value OUTSIDE this range.
If we plug a=-1 into a� ≤ a, we get:
(-1)� ≤ -1
-1 ≤ -1.
This works.
Thus, it does NOT have to be true that 0≤a≤1.
Eliminate D, which says that statement III must be true.
The correct answer is
A.
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