If (x + 1)y = 4, what is the value of x ? (1) xy = 2 (2) y 0

Question

If (x + 1)y = 4, what is the value of x ?

(1) xy = 2
(2) y > 0

CareerGeek · Answer

(x + 1)y = 4
—> xy + y = 4

(1) xy = 2
—> 2 + y = 4
—> y = 2
—> x*2 = 2
—> x = 1 —>  Sufficient

(2) y > 0
Infinite values of x are possible. —>  Insufficient

IMO Option A

Posted from my mobile device

siddharthkapoor · Answer

(1) We know that (x+1)y=4
=> xy+y=4
As per this statement, xy=2
=> 2+y=4
=> y=2
As, xy=2 and y=2, we get x=1.
Thus, sufficient.

(2) Clearly insufficient.

Therefore, the answer is option A.

MathRevolution · Answer

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. Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each condition on its own first. Actually, since only condition 1) has an equation and condition 2) does not, A is most likely the answer Condition 1) Since xy = 2 from condition 1), we have (x+1)y = xy + y = 2 + y = 4 or y = 2. Then we have x = 1. Since condition 1) yields a unique solution, it is sufficient. Condition 2) If y = 1, then we have x = 3. If y = 2, then we have x = 1. Since condition 2) does not yield a unique solution, it is not sufficient. Therefore, A is the answer. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

Kinshook · Answer

Asked: If (x + 1)y = 4, what is the value of x ?
xy + y = 4

(1) xy = 2
2 + y = 4
y = 2
x = y/2 = 2/2 =1
SUFFICIENT

(2) y > 0
x = 4/y -1 ; x will change with change in value of y
NOT SUFFICIENT

IMO A

If (x + 1)y = 4, what is the value of x ? (1) xy = 2 (2) y > 0

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions