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09 Mar 2020, 05:44
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
82% (00:49) correct
18%
(01:08)
wrong
based on 135
sessions
History
Date
Time
Result
Not Attempted Yet
If x and y are integers, what is the value of \(x^2 + 2xy + y^2\) ?
(1) \(x + y = 7\)
(2) \(2x = \frac{28 - 4y}{2}\)
(1) \(x + y = 7\)
(2) \(2x = \frac{28 - 4y}{2}\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
09 Mar 2020, 06:40
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To find the value of x^2+y^2+2xy
I.e (x+y)^2
1. X+y=7, puttin the value of x+y in above simplified expression. We get (x+y)^2=7^2=49, sufficient
2. 2x= (28 - 4y)/2
Simplifying we get x+y=7.
Putting the value in the expression we get the value as 49.
So,both are sufficient to arrive at a value. Hence, d is the correct choice.
Posted from my mobile device
I.e (x+y)^2
1. X+y=7, puttin the value of x+y in above simplified expression. We get (x+y)^2=7^2=49, sufficient
2. 2x= (28 - 4y)/2
Simplifying we get x+y=7.
Putting the value in the expression we get the value as 49.
So,both are sufficient to arrive at a value. Hence, d is the correct choice.
Posted from my mobile device
22 Jun 2020, 12:05
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Bunuel
Useful property: \(x^2 + 2xy + y^2 = (x+y)^2\)
Target question: What is the value of \(x^2 + 2xy + y^2\) ?
Statement 1: \(x + y = 7\)
Square both sides to get: \((x + y)^2 = 7^2\)
Expand and simplify to get: \(x^2 + 2xy + y^2 = 49\)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(2x = \frac{28 - 4y}{2}\)
Multiply both sides of the equation by \(2\) to get: \(4x = 28 - 4y\)
Add \(4y\) to both sides to get: \(4x + 4y= 28\)
Divide both sides by \(4\) to get: \(x + y= 7\)
At this point, we can see that statement 2 provides the EXACT SAME information that statement 1 provided.
Since statement 1 is SUFFICIENT, we can conclude that statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
