j_shreyans wrote:If v≠0, is |w|<|v|?
(1) w/v < 1
(2) w²/v² < 1
Since an absolute value must be NONNEGATIVE, we can safely rephrase the question stem by squaring both sides:
(|w|)² < (|v|)²
w² < v².
Question stem, rephrased:
Is w² < v²?
Statement 1: w/v < 1
If w=0 and v=1, then w² < v².
If w=-1 and v=1. then w² = v².
INSUFFICIENT.
Statement 2: w²/v² < 1
Since v≠0, we know that v²>0, implying that we can safely multiply each side by v²:
(w²/v²) * v² < 1 * v²
w² < v².
SUFFICIENT.
The correct answer is
B.
When an inequality is multiplied or divided by a NEGATIVE VALUE, the direction of the inequality must FLIP.
In statement 1: w/v<1
in this we can not divide by v both side right but why??
If v is NEGATIVE, then multiplying each side of w/v < 1 by v requires that the direction of the inequality FLIP from < to >
If v is POSITIVE, then multiplying each side of w/v < 1 by v does NOT change the direction of the inequality.
Since the sign of v is UNKNOWN, it might be best to avoid algebra here.
In statement 2- w^2/v^2<1
in this we can divide by v^2 both side right why??
The square of a value cannot be negative.
Since the question stem indicates that v≠0, v² must be POSITIVE.
Thus, we can safely multiply each side of w²/v² < 1 by v², knowing that the direction of the inequality will NOT change.
I used this approach in my solution above.
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