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11 May 2022, 06:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:25) correct
24%
(01:22)
wrong
based on 38
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of x + y ?
(1) x + y + z = x + y – z + 1
(2) x – y + z = 0
(1) x + y + z = x + y – z + 1
(2) x – y + z = 0
11 May 2022, 06:57
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Bunuel
Target question: What is the value of x + y ?
Statement 1: x + y + z = x + y – z + 1
Subtract x and subtract y from both sides of the equation: z = –z + 1
Add z to both sides of the equation: 2z = 1
Solve: z = 0.5
Since statement 1 provides no information about x and y, it's NOT SUFFICIENT
Statement 2: x – y + z = 0
Statement 2 is clearly NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 indirectly tells us that z = 0.5
Statement 2 tells us that x – y + z = 0
Substitute z = 0.5 in the second equation to get: x – y + 0.5 = 0
Since we don't have enough information to the find the value of x+y, the combined statements are NOT SUFFICIENT
If you need more proof, let's examine values of x, y and z that satisfy BOTH statements:
Case a: x = 0.5, y = 1 and z = 0.5. In this case, the answer to the target question is x + y = 0.5 + 1 = 1.5
Case b: x = 1.5, y = 2 and z = 0.5. In this case, the answer to the target question is x + y = 1.5 + 2 = 3.5
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
11 May 2022, 12:22
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Step 1: Analyse Question Stem
We have to find out a unique value for the expression x + y.
Therefore, we should be able to manipulate expressions to obtain x + y OR we should be able to find the individual values of x and y, and then add them to obtain x + y.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: x + y + z = x + y – z + 1
Transferring all variable terms to the LHS, we have,
x + y + z – x – y + z = 1
Simplifying, z = ½.
Knowing the value of z is not sufficient to find out x, y or x + y.
The data in statement 1 is insufficient to find out a unique value of the given expression.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: x – y + z = 0
Knowing that the value of the expression equals Zero, is not sufficient to find out x, y or x + y.
The data in statement 2 is insufficient to find out a unique value of the given expression.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: z = ½
From statement 2: x – y + z = 0
Combining both, we can say that x – y = - \(\frac{1}{2}\)
Knowing the value of x – y is not sufficient to find x, y or x + y, since infinite combinations of x and y can satisfy this equation.
The combination of statements is insufficient to find out a unique value of the given expression.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.
The correct answer option is E.
We have to find out a unique value for the expression x + y.
Therefore, we should be able to manipulate expressions to obtain x + y OR we should be able to find the individual values of x and y, and then add them to obtain x + y.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: x + y + z = x + y – z + 1
Transferring all variable terms to the LHS, we have,
x + y + z – x – y + z = 1
Simplifying, z = ½.
Knowing the value of z is not sufficient to find out x, y or x + y.
The data in statement 1 is insufficient to find out a unique value of the given expression.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: x – y + z = 0
Knowing that the value of the expression equals Zero, is not sufficient to find out x, y or x + y.
The data in statement 2 is insufficient to find out a unique value of the given expression.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combining
From statement 1: z = ½
From statement 2: x – y + z = 0
Combining both, we can say that x – y = - \(\frac{1}{2}\)
Knowing the value of x – y is not sufficient to find x, y or x + y, since infinite combinations of x and y can satisfy this equation.
The combination of statements is insufficient to find out a unique value of the given expression.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.
The correct answer option is E.
