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19 Mar 2020, 08:30
Kudos
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B
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:
89% (00:41) correct
11%
(01:02)
wrong
based on 64
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of b?
(1) 5b − a = 3b + 5a
(2) 4(b − a) = 12 − 4a
(1) 5b − a = 3b + 5a
(2) 4(b − a) = 12 − 4a
19 Mar 2020, 09:00
Kudos
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Bunuel
Asked: What is the value of b?
(1) 5b − a = 3b + 5a
2b = 6a
b = 3a
Since a is unknown
NOT SUFFICIENT
(2) 4(b − a) = 12 − 4a
4b = 12
b = 3
SUFFICIENT
IMO B
19 Mar 2020, 09:00
Kudos
Bookmarks
Bunuel
Target question: What is the value of b?
Statement 1: 5b − a = 3b + 5a
ASIDE: Don't fall into the trap of assuming an equation with two variables cannot be solved for one variable.
We will still need to verify this with each statement
Take: 5b − a = 3b + 5a
Subtract 3b from both sides: 2b − a = 5a
Subtract 5a from both sides: 2b − 6a = 0
At this point we can see that the equation 2b − 6a = 0 has infinitely many solutions.
Consider these two cases:
Case a: b = 3 and a = 1. In this case, the answer to the target question is b = 3
Case b: b = 6 and a = 2. In this case, the answer to the target question is b = 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 4(b − a) = 12 − 4a
Expand the left side to get: 4b − 4a = 12 − 4a
Add 4a to both sides to get: 4b = 12
Solve: b = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
