If x 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Dec 20, 2019 6:42 pm

$$If\ x\ \ne\ 1,\ is\ y\ equal\ to\ x\ +\ 1?$$

(1) $\frac{y - 2}{x - 1} = 1$

(2) $y^2 = (x + 1)^2$

OA A

Source: Official Guide

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Source: Beat The GMAT — Data Sufficiency | Fri Dec 20, 2019 6:42 pm

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

by GMATGuruNY » Fri Dec 20, 2019 7:25 pm

BTGmoderatorDC wrote:$$If\ x\ \ne\ 1,\ is\ y\ equal\ to\ x\ +\ 1?$$

(1) $\frac{y - 2}{x - 1} = 1$

(2) $y^2 = (x + 1)^2$

Statement 1:
Multiplying both sides by x-1, we get:
y-2 = x-1
y = x+1
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
Let x=0, with the result that yÂ² = (0+1)Â² = 1
If x=0 and y=1, then y = x+1.
If x=0 and y=-1, then y â‰ x+1.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

The correct answer is A.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Dec 21, 2019 6:20 am

BTGmoderatorDC wrote:$$If\ x\ \ne\ 1,\ is\ y\ equal\ to\ x\ +\ 1?$$

(1) $\frac{y - 2}{x - 1} = 1$

(2) $y^2 = (x + 1)^2$

Target question: Is y equal to x+1?

Statement 1: (y - 2)/(x - 1)
Multiply both sides by (x - 1) to get: y - 2 = x - 1
Add 2 to both sides to get: y = x + 1
The answer to the target question is YES, y IS equal to x + 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: yÂ² = (x + 1)Â²
ASIDE: Some students will incorrectly conclude that, since yÂ² = (x + 1)Â², it must also be the case that y = x + 1
This, however, is not true.
Notice, for example, that 3Â² = (-3)Â², but we can't then conclude that 3 = -3

To better see what I mean, considere these two possible cases that satisfy statement 2:
Case a: If x = 1 and y = 2, we get: 2Â² = (1 + 1)Â², which works. In this case, the answer to the target question is YES, y IS equal to x + 1
Case b: If x = 1 and y = -2, we get: (-2)Â² = (1 + 1)Â², which also works. In this case, the answer to the target question is NO, y is NOT equal to x + 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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