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(1) For both Y=0.3, Z=0.7 and Y=0.7, Z=0.3 we have Y+Z=1. Insufficient

(1) For both Y=0.3, Z=0.7 or Y=0.3, Z=-0.7 we have Y^2 < Z^2. Insufficient

(1)+(2) From Statement (1) Z=1-Y, and put in Statement (2): Y^2 < (1-Y)^2 Y^2 < 1-2Y+Y^2 2Y< 1 Y<1/2 Therefore, -Y>-1/2 and 1-Y>1-1/2 and Z=1-Y>1/2. Hence, Y<Z. Sufficient

The correct answer is C. _________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Statement 1 : y+z = 1 , This can be possible in different cases : Case 1 : 0<y<1 and 0<z<1 Case 2 : y>=1 and as Z = 1 - y so z<=0 Case 3 : Z>=1 and as y = 1-z so y<=0 As we can't conclude whether y>z or y<z, statement 1 is not sufficient

Statement 2 : y^2 < z^2 , again which is possible in many cases case 1 : z>y>0 case 2 : z>0>y and z>|y| case 3 : y>0>z and y<|z| case 4 : 0>y>z As we can't conclude whether y>z or y<z, statement 2 is also not sufficient

By combining two statements and observing all the cases from both statements we can eliminate case 4 and case 3 from statement 2 as they violate the condition y + z = 1 from statement 1. So from the remaining cases which satisfy both statements we can clearly observe z>y . Hence we can say yes y<z.

(1) y + z = 1. The sum of two numbers is 1. Obviously from this info we cannot say which one is bigger. Not sufficient.

(2) y^2 < z^2 --> take the square root from both sides (we can safely do that since we know that both sides are non-negative): |y| < |z| --> z is farther from 0 than y is. Not sufficient.

(1)+(2) From (2): (y - z)(y + z) < 0. This implies that y - z and y + z have opposite signs. Since we know from (1) that y + z is positive, then y - z must be negative: y - z < 0 --> y < z. Sufficient.

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