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18 Nov 2022, 10:47
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A
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Difficulty:
35%
(medium)
Question Stats:
57% (00:45) correct
43%
(00:55)
wrong
based on 44
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What is the highest common factor of positive integers u and v?
(1) u and v are consecutive integers
(2) v is a prime number
(1) u and v are consecutive integers
(2) v is a prime number
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
18 Nov 2022, 12:19
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Bunuel
Question Stem Analysis:
We are told that u and v are positive integers, and we need to determine the GCF of u and v.
Statement One Alone:
\(\Rightarrow\) u and v are consecutive integers
Recall that two consecutive integers never share factors, which means the greatest common factor of u and v is 1. Statement one alone is sufficient.
Eliminate answer choices B, C, and E.
Statement Two Alone:
\(\Rightarrow\) v is a prime number
Without any information about u, we cannot determine the greatest common factor of u and v. For instance, if u = v + 1, then u and v are consecutive integers and as we explained earlier, the GCF of u and v is 1. On the other hand, if u = 2v, then the GCF of u and v is v, which is greater than 1. Statement two alone is not sufficient.
Answer: A
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