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12 Sep 2021, 07:45
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Difficulty:
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55%
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If \(a < b\), is \((x − a)^2 > (x − b)^2\)?
1) x > \(\frac{a + b}{2}\)
2) \(x − a > x − b\)
1) x > \(\frac{a + b}{2}\)
2) \(x − a > x − b\)
12 Sep 2021, 07:57
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sjuniv32
If \(a < b\), is \((x − a)^2 > (x − b)^2\)?
1) x > \(\frac{a + b}{2}\)
2) \(x − a > x − b\)
1) x > \(\frac{a + b}{2}\)
2) \(x − a > x − b\)
Given: a < b
Is (x-a)^2 > (x-b)^2?
(x-a)^2 - (x-b)^2 > 0
(x - a + x - b)(x - a - x + b) > 0
(2x - b - a)(b - a)>0
From above, we already know that b > a
So, we need to know if:
2x>a + b
\(x> \frac{a+b}{2}\)?
1) Directly gives us the answer - Sufficient!
2) x - a > x - b
a < b, we already know this - Insufficient!
IMO, (A)!
12 Sep 2021, 09:11
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sjuniv32
If \(a < b\), is \((x − a)^2 > (x − b)^2\)?
1) x > \(\frac{a + b}{2}\)
2) \(x − a > x − b\)
1) x > \(\frac{a + b}{2}\)
2) \(x − a > x − b\)
\((x-a)^2>(x-b)^2………..x^2-2ax+a^2>x^2+b^2-2bx……….a^2-b^2+2bx-2ax………….(a-b)(a+b)+2x(b-a)>0………..(a-b)(a+b-2x)>0\)
Now we know that a-b<0, so IS a+b-2x<0?
So the question is: Is 2x>a+b
1) x > \(\frac{a + b}{2}\)
\(2x>a+b\).
Sufficient
2) \(x − a > x − b…………….a<b\)
We already know this.
Insufficient
A
