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13 Jan 2021, 15:02
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
38% (01:35) correct
62%
(01:52)
wrong
based on 156
sessions
History
Date
Time
Result
Not Attempted Yet
The equation 4x + 3 = a(x + b), where a and b are constants, has no solutions. Which of the following must be true?
I. \(a=4\)
II. \(b=3\)
III. \(b≠\frac{3}{4}\)
A) I only
B) I and II
C) I and III
D) I, II, and III
E) None of the above
I. \(a=4\)
II. \(b=3\)
III. \(b≠\frac{3}{4}\)
A) I only
B) I and II
C) I and III
D) I, II, and III
E) None of the above
Source: original question
14 Jan 2021, 10:14
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Hello, everyone. So far, the question is proving to be harder than I had anticipated for the community, but the sample size is small. The keywords that stand out to me here are no solutions. For this to be true, we need to show that the two sides of the equation CANNOT be equal. How do we do that? Start by distributing that a:
\(4x+3=ax+ab\)
Notice the mirroring on each side of the equation: 4x would need to be equivalent to ax, and 3 would need to be equivalent to ab.
\(4x=ax\)
\(4=a\)
We know that a must equal 4. Hence, we can strike answer (E). Now, applying the same logic as before, we can work on the remainder of the right-hand side:
\(3=ab\)
Since we know the value of a, we can substitute:
\(3=(4)b\)
\(\frac{3}{4}=b\)
But now you have to be careful and remember the question. The problem tells us that the equation has no solutions, not an infinite number of them, so it must be true that although a = 4, b CANNOT be equal to 3/4. Hence, statements I and III must be true, and the answer is (C).
If you were wondering why b could equal 3, you could test that value independently of a, and you could easily create a workable equation (for instance, when a = 1).
I hope you had fun with this one. Good luck with your studies.
- Andrew
\(4x+3=ax+ab\)
Notice the mirroring on each side of the equation: 4x would need to be equivalent to ax, and 3 would need to be equivalent to ab.
\(4x=ax\)
\(4=a\)
We know that a must equal 4. Hence, we can strike answer (E). Now, applying the same logic as before, we can work on the remainder of the right-hand side:
\(3=ab\)
Since we know the value of a, we can substitute:
\(3=(4)b\)
\(\frac{3}{4}=b\)
But now you have to be careful and remember the question. The problem tells us that the equation has no solutions, not an infinite number of them, so it must be true that although a = 4, b CANNOT be equal to 3/4. Hence, statements I and III must be true, and the answer is (C).
If you were wondering why b could equal 3, you could test that value independently of a, and you could easily create a workable equation (for instance, when a = 1).
I hope you had fun with this one. Good luck with your studies.
- Andrew
22 Jan 2025, 04:44
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Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
