On the number line, are the points x and y on the same side

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

On the number line, are the points x and y on the same side

by VJesus12 » Thu Dec 21, 2017 12:10 pm

On the number line, are the points x and y on the same side of zero?

(1) x and y are equidistant from zero
(2) The sum of the distances from x to 1 and from y to 1 is less then 1.

The OA is B.

I don't know why statement (1) is not sufficient. I think the answer should be D. Experts, may you give me an explanation here?

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Source: Beat The GMAT — Data Sufficiency | Thu Dec 21, 2017 12:10 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Jan 15, 2018 10:43 pm

VJesus12 wrote:On the number line, are the points x and y on the same side of zero?

(1) x and y are equidistant from zero
(2) The sum of the distances from x to 1 and from y to 1 is less then 1.

The OA is B.

I don't know why statement (1) is not sufficient. I think the answer should be D. Experts, may you give me an explanation here?

(1) x and y are equidistant from zero.

Statement (1) is not sufficient because if the points x and y are the same points and lie on one side, the answer is Yes; however if their magnitude is same, but they lie on the opposite side on the number line, the answer is No.

Case 1: Negative side <-----------(x and y)-------------0-------> positive side; The answer is Yes.
Case 2: Negative side <-----------------0----(x and y)----------> positive side; The answer is Yes.
Case 3: Negative side <---------x--------0--------y---------> positive side; The answer is No.

Insufficient.

(2) The sum of the distances from x to 1 and from y to 1 is less than 1.

Since the sum of the distances from x to 1 and from y to 1 is less than 1, neither x nor y can be on the negative side of the number line since if it were so, the distance would be greater than 1.

Say x lied on the negative side. The distance of x from 1 = 1 - (-x) = 1 +| x| > 1. So it's not possible.

Thus the only possibility is that x and y both lie on the positive (same) side. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Tue Jan 16, 2018 5:12 am

VJesus12 wrote:On the number line, are the points x and y on the same side of zero?

(1) x and y are equidistant from zero
(2) The sum of the distances from x to 1 and from y to 1 is less then 1.

Statement 1: x and y are equidistant from zero
Case 1: x=1 and y=1, with the result that x and y are both one place from 0
In this case, the answer to the question stem is YES.
Case 1: x=-1 and y=1, with the result that x and y are both one place from 0
In this case, the answer to the question stem is NO.
INSUFFICIENT.

Statement 2: The sum of the distances from x to 1 and from y to 1 is less then 1
A distance cannot be negative.
Thus, a distance is always a NONNEGATIVE VALUE.
Since the SUM of the two distances must be less than 1, each distance ON ITS OWN must also be less than 1.
Thus, x and y must each be LESS THAN ONE PLACE from 1 on the number line:
0<-----1----->2
Since x and y must each lie with the blue range above, they must be to the same side of 0.
SUFFICIENT.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jan 18, 2018 1:45 pm

VJesus12 wrote:On the number line, are the points x and y on the same side of zero?

(1) x and y are equidistant from zero
(2) The sum of the distances from x to 1 and from y to 1 is less then 1.

Statement One Alone:

x and y are equidistant from zero

Since x and y are equidistant from zero, x and y could be the same number, such as 2 and 2, and be on the same side of the number line, or they could be opposites, such as 2 and -2, and be on opposite sides of the number

line. Thus, statement one alone is not sufficient to answer the question.

Statement Two Alone:

The sum of the distances from x to 1 and from y to 1 is less than 1.

In order for the sum of the distances from x to 1 and from y to 1 to be less than 1, is if x and y are both on the positive side of the number line. Thus, statement two alone is sufficient to answer the question.

Answer: B

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