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Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2
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03 Jul 2019, 08:26
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SOLUTION
Choice (C) is correct.
The stem doesn't give us much information to work with, so we can go directly to the statements. They will be sufficient only if y must be less than z or cannot be less than z.
Statement (1): insufficient. This tells us the sum of y and z, but it says nothing about their relative values. It is possible that y and z are equal (if each is 0.5), or that either variable is greater (e.g., y = 1 and z = 0, or vice versa). Eliminate (A) and (D).
Statement (2): insufficient. Let's say that y2 = 9 and that z2 = 25. Then y = 3 or -3 and z = 5 or -5. If y = 3 and z = 5, then z is greater. However, if y = -3 and z = -5, then y is greater. The question cannot be answered definitively, so the statement is insufficient. Eliminate (B).
Statements (1) and (2): sufficient. Picking numbers may be difficult, since there are many possibilities for y and z. Instead, try to work with the equations. Since y + z = 1, it follows that y = 1 - z. Replace y with 1 - z in the equation y2 < z2 to get (1 - z)2 < z2. Using FOIL to expand the left side, you get z2 - 2z + 1 < z2. Subtracting z2 from both sides you have -2z + 1 < 0, or 1 < 2z. Dividing both sides by 2 you are left with < z. Since z must be greater than and y + z = 1, y must be less than . Therefore, y must be less than z. The statements combined are sufficient, so choice (C) is correct.
Is y < z ? (1) y + z = 1 (2) y^2 < z^2
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Updated on: 17 May 2021, 07:29
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GeorgeKo111 wrote:
Is y < z ?
(1) y + z = 1 (2) y² < z²
Target question:Is y < z ?
Statement 1: y + z = 1 Let's TEST some values. There are several values of y and z that satisfy statement 1. Here are two: Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z Case b: y = 1 and z = 0. In this case, the answer to the target question is NO, y is not less than z Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y² < z² There are several values of y and z that satisfy statement 2. Here are two: Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z Case b: y = 0 and z = -1. In this case, the answer to the target question is NO, y is not less than z Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that: y² < z² Subtract z² from both sides of the inequality to get: y² - z² < 0 Factor the left side to get: (y + z)(y - z) < 0 Since statement 1 tells us that y + z = 1, we can replace (y + z) with 1 to get: (1)(y - z) < 0 Simplify: y - z < 0 Add z to both sides to get: y < z The answer to the target question is YES, y is less than z Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2
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09 Oct 2020, 22:40
BrentGMATPrepNow wrote:
GeorgeKo111 wrote:
Is y < z ?
(1) y + z = 1 (2) y² < z²
Target question:Is y < z ?
Statement 1: y + z = 1 Let's TEST some values. There are several values of y and z that satisfy statement 1. Here are two: Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z Case b: y = 1 and z = 0. In this case, the answer to the target question is NO, y is not less than z Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y² < z² There are several values of y and z that satisfy statement 2. Here are two: Case a: y = 0 and z = 1. In this case, the answer to the target question is YES, y is less than z Case b: y = 0 and z = -1. In this case, the answer to the target question is NO, y is not less than z Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that: y² < z² Subtract z² from both sides of the inequality to get: y² - z² < 0 Factor the left side to get: (y + z)(y - z) < 0 Since statement 1 tells us that y + z = 1, we can replace (y + z) with 1 to get: (1)(y - z) < 0 Simplify: y - z < 0 Add z to both sides to get: y < z The answer to the target question is YES, y is less than z Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers, Brent
RELATED VIDEO FROM MY COURSE]
Hi Brent,
Can't we answer the question from statement 2 itself?
y^2-z^2<0 (y+z)(y-z)<0 -z<y<z So y in any case is less than z from second statement itself, isn't that so?
Concentration: General Management, International Business
GMAT 1:570 Q49 V20
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WE:Engineering (Education)
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2
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09 Oct 2020, 23:52
Quote:
Is y < z ?
Step 1: Understanding statement 1 alone (1) y + z = 1 When y = 0.4, z = 0.6; y < z When y = 0.6, x = 0.4; y > z Insufficient
Step 2: Understanding statement 2 alone (2) y^2 < z^2 Taking square root on both the sides \(\sqrt{y^2}\) < \(\sqrt{z^2}\) |y| < |z| When y = -1, z = 2; y < z When y = 1, z = -2; y > z Insufficient
Step 3: Combining statement 1 and 2 y^2 < z^2 y^2 - z^2 < 0 (y - z) ( y+z) < 0 As (y + z) = 1; (y - z) < 0 Hence, y < z Sufficient
C is correct _________________
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Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2
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11 Oct 2020, 05:11
Expert Reply
Alternate approach:
GeorgeKo111 wrote:
Is y < z ?
(1) y + z = 1
(2) y^2 < z^2
Statement 1: Clearly INSUFFICIENT.
Statement 2, rephrased: |y| < |z| Case 1: y=0 and z=1 In this case, the answer to the question stem is YES. Case 2: y=0 and z=-1 In this case, the answer to the question stem is NO. Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statements combined: Substituting z=1-y into |y| < |z|, we get: |y| < |1-y| Implication: The distance between y and 0 is less than the distance between y and 1. In other words, Y IS CLOSER TO 0 THAN TO 1, implying that y < 1/2.
Substituting y=1-z into |y| < |z|, we get: |1-z| < |z| Implication: The distance between z and 1 is less than the distance between z and 0. In other words, Z IS CLOSER TO 1 THAN TO 0, implying that z > 1/2.
Since y < 1/2 and z > 1/2, we get: y < 1/2 < z y < z Thus, the answer to the question stem is YES. SUFFICIENT.
Re: Is y < z ? (1) y + z = 1 (2) y^2 < z^2
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12 Oct 2020, 10:18
Expert Reply
We want to know if z-y is positive. Statement 1 tells us that z+y is positive, and Statement 2 tells us that z^2 - y^2 is positive. But z^2 - y^2 = (z + y)(z-y), and if z+y is positive, then z-y must also be positive for it to be true that the product (z-y)(z+y) is positive. So the two Statements together are sufficient.
Statement 1 is clearly insufficient alone, because it's symmetric in y and z (if you can find numbers that work for y and z where y < z, you can just flip the numbers and you'll automatically have a situation where z < y). Statement 2 is clearly insufficient alone also, since if y = 0, z can be -100 or +100. So the answer is C. _________________
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