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03 Jul 2019, 09:25
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:54) correct
36%
(01:43)
wrong
based on 306
sessions
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Not Attempted Yet
03 Jul 2019, 09:26
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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.
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.
Updated on: 17 May 2021, 08:29
Originally posted by BrentGMATPrepNow on 19 Mar 2020, 07:08.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:29, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 08:29, edited 1 time in total.
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GeorgeKo111
Is y < z ?
(1) y + z = 1
(2) y² < z²
(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
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