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07 Oct 2018, 08:26
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Difficulty:
55%
(hard)
Question Stats:
60% (01:42) correct
40%
(00:15)
wrong
based on 5
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Not Attempted Yet
Hi All,
I found this question on one of the MGMAT CATs and am very confused about their explanation.
The question is as follows:
What is the distance between x and y on the number line?
(1) |x| – |y| = 5
(2) |x| + |y| = 11
Here is their explanation:
1) This tells us that the difference between the absolute value of x and the absolute value of y is 5. Let’s pick some numbers to prove that this is insufficient. Say, for example, x = 6 and y = 1. Then |x| – |y| = 5 and the distance between x and y is 6 – 1 = 5. However, let’s pick x = 6 and y = -1. Then |x| – |y| = 5 and the distance between x and y is 6 – (-1) = 7. Since we picked two sets of numbers that fit the criteria and got different answers, the statement is insufficient.
If we pick x = 6 and y = -1, then isn't |x| = 6 and |y| = 1?? Absolute value implies taking the difference from that number and 0, hence it'll always be positive. If we pick x = 6 and y = -1, why are we doing the following operation: 6 - (-1) and not 6 - 1??
Obviously, I am aware that if we draw these two points on the number line, we do indeed get a difference of 7 if y = -1 and x = 6. But could someone explain this algebraically or theoretically why if we pick y = -1 we input the minus sign inside the modulus?
Thanks!
I found this question on one of the MGMAT CATs and am very confused about their explanation.
The question is as follows:
What is the distance between x and y on the number line?
(1) |x| – |y| = 5
(2) |x| + |y| = 11
Here is their explanation:
1) This tells us that the difference between the absolute value of x and the absolute value of y is 5. Let’s pick some numbers to prove that this is insufficient. Say, for example, x = 6 and y = 1. Then |x| – |y| = 5 and the distance between x and y is 6 – 1 = 5. However, let’s pick x = 6 and y = -1. Then |x| – |y| = 5 and the distance between x and y is 6 – (-1) = 7. Since we picked two sets of numbers that fit the criteria and got different answers, the statement is insufficient.
If we pick x = 6 and y = -1, then isn't |x| = 6 and |y| = 1?? Absolute value implies taking the difference from that number and 0, hence it'll always be positive. If we pick x = 6 and y = -1, why are we doing the following operation: 6 - (-1) and not 6 - 1??
Obviously, I am aware that if we draw these two points on the number line, we do indeed get a difference of 7 if y = -1 and x = 6. But could someone explain this algebraically or theoretically why if we pick y = -1 we input the minus sign inside the modulus?
Thanks!
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
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07 Oct 2018, 08:45
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PierTotti17
Discussed here: what-is-the-distance-between-x-and-y-on-the-number-line-129638.html Please continue discussion there.
TOPIC IS LOCKED AND ARCHIVED.
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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