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555-605 (Medium)|   Algebra|         
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gmatt1476
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 21 Sep 2019, 17:31
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If \(x ≠ 1\), is y equal to \(x + 1\)?


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

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


DS67602.01
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A
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BrentGMATPrepNow
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 21 Dec 2019, 07:38
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gmatt1476
If \(x ≠ 1\), is y equal to \(x + 1\)?


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

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


DS67602.01
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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: y² = (x + 1)²
ASIDE: Some students will incorrectly conclude that, since y² = (x + 1)², it must also be the case that y = x + 1
This, however, is not true.
Notice, for example, that 3² = (-3)², 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: 2² = (1 + 1)², 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)² = (1 + 1)², 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
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 22 Sep 2019, 10:42
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If x≠1, is y equal to x+1?

STATEMENT (1)--\(\frac{Y-2}{X-1}\) = 1
Y-2 = X-1
Y = X-1+2 = X+1--YES
SUFFICIENT

STATEMENT (2)--\(Y^2\) = \((X+1)^2\)
\(Y^2\) - \((X+1)^2\) = 0
(Y-{X+1})(Y+{X+1})=0
y can be {x+1}---then YES
y can be -{x+1}---then NO
INSUFFICIENT

A is the correct answer
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 21 Dec 2019, 08:21
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If \(x ≠ 1\), is y equal to \(x + 1\)?


(1) \(\frac{y - 2}{x - 1} = 1\) --> suff: y-2 = x-1 => y = x+1

(2) \(y^2 = (x + 1)^2\) --> insuff: y = x+1 or y = -(x+1)

Answer: A
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 21 Dec 2019, 20:38
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If \(x ≠ 1\), is y equal to \(x + 1\)?


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

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


DS67602.01
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 1)

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

Since condition 1) is equivalent to the question.
Condition 1) is sufficient.

Condition 2)
If \(x = 0, y = 1\), then \(y = x + 1 \)and the answer is 'yes'.
If \(x = -2, y = 1\), then \(y = x + 3\) and the answer is 'not.

Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, A is the answer.
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 09 Aug 2020, 09:23
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in statement two why can't we sq rt both the sides as y^2=(x+1)^2 can also be written as

y*y=(x+1)*(X+1)
which will give
y = x+1.
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 21 Oct 2024, 01:22
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If x≠1, is y equal to x+1?

(1) (y−2)/(x−1)=1
(2) y^2=(x+1)^2

1: y-2 = x-1 thus y = x+1

2:
now y = +-(x+1)
as (-x)^2 = (x)^2

thus only A
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If x ≠ 1, is y equal to x + 1? (1) (y-2)/(x-1)=1 (2) y^2=(x+1)^2 06 Jan 2026, 08:42
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