Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Dec 1511:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.- Dec 14
11:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
11 May 2022, 06:00
Kudos
Bookmarks
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
Kudos
Bookmarks
Bunuel
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
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
Kudos
Bookmarks
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.
