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11 May 2025, 03:23
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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)!
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Is x > y ?
(1) \(y^2\) < \(z^2\) < \(x^2\)
(2) z < x
(C): This problem deals with both squares and inequalities. Remember
that negative numbers become positive when squared and that
squaring a number less than 1 results in a value that is even closer to 0.
(1) INSUFFICIENT: Without any more information about z, this
statement only tells you that x2 is greater than y2. However, x could be
either greater than y or less than y, depending on whether x is positive
or negative.
Case 1: x = –100, y = 1. Since all squares are positive, x2 is much greater
than y2. However, x is less than y.
Case 2: x = 100, y = 1. In this case, x2 is greater than y2 and x is greater
than y.
(2) INSUFFICIENT: This statement does not provide any information
about y, so y could be greater than, less than, or equal to x.
(1) AND (2) SUFFICIENT: According to statement (2), x is greater than z.
According to statement (1), x2 is greater than z2. This implies that |x| is
greater than |z|.
There are only two situations in which x is greater than z and the
absolute value of x is greater than the absolute value of z.
One possibility is that x is positive and z is a lesser positive number. Another
possibility is that x is positive and z is a negative number with an
absolute value that is less than x.
There are no valid cases in which x is negative because in order to fit
statement (2), z would have to be even more negative than x, in which
case |z| would be greater than, not less than, |x|. Therefore, x is definitely
positive.
Statement (1) says that x2 > y2, which implies that |x| > |y|. Since x is
positive, |x| = x, so x > |y|. If x is greater than the absolute value of y, x
must also be greater than y itself, so the answer to the question is
definitely Yes.
The correct answer is (C).
(1) \(y^2\) < \(z^2\) < \(x^2\)
(2) z < x
(C): This problem deals with both squares and inequalities. Remember
that negative numbers become positive when squared and that
squaring a number less than 1 results in a value that is even closer to 0.
(1) INSUFFICIENT: Without any more information about z, this
statement only tells you that x2 is greater than y2. However, x could be
either greater than y or less than y, depending on whether x is positive
or negative.
Case 1: x = –100, y = 1. Since all squares are positive, x2 is much greater
than y2. However, x is less than y.
Case 2: x = 100, y = 1. In this case, x2 is greater than y2 and x is greater
than y.
(2) INSUFFICIENT: This statement does not provide any information
about y, so y could be greater than, less than, or equal to x.
(1) AND (2) SUFFICIENT: According to statement (2), x is greater than z.
According to statement (1), x2 is greater than z2. This implies that |x| is
greater than |z|.
There are only two situations in which x is greater than z and the
absolute value of x is greater than the absolute value of z.
One possibility is that x is positive and z is a lesser positive number. Another
possibility is that x is positive and z is a negative number with an
absolute value that is less than x.
There are no valid cases in which x is negative because in order to fit
statement (2), z would have to be even more negative than x, in which
case |z| would be greater than, not less than, |x|. Therefore, x is definitely
positive.
Statement (1) says that x2 > y2, which implies that |x| > |y|. Since x is
positive, |x| = x, so x > |y|. If x is greater than the absolute value of y, x
must also be greater than y itself, so the answer to the question is
definitely Yes.
The correct answer is (C).
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
11 May 2025, 03:27
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Sketchitesh
Check here: https://gmatclub.com/forum/is-x-y-1-y-2 ... 85419.html
P.S. Pure algebraic questions are no longer a part of the DS syllabus of the GMAT.
DS questions in GMAT Focus encompass various types of word problems, such as:
- Word Problems
- Work Problems
- Distance Problems
- Mixture Problems
- Percent and Interest Problems
- Overlapping Sets Problems
- Statistics Problems
- Combination and Probability Problems
While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."
Check GMAT Syllabus for Focus Edition
You can also visit the Data Sufficiency forum and filter questions by OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources to see the types of questions currently tested on the GMAT.
So, you can ignore this question.
Hope it helps.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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