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Problem Solving — algebra and arithmetic
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Newbie | Next Rank: 10 Posts
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by dee1711s » Fri Mar 29, 2019 12:50 am
If a is a factor of b and b is a factor of a, then a=b or a=−b.


I did not understand this. Could you please explain?
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Source: — Quantitative Reasoning |

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by [email protected] » Sun Mar 31, 2019 9:45 am
Hi dee1711s,

To start, the GMAT is NOT going to test you on the concept of "negative factors", as an example - if you are asked for the factors of 6, then those factors are 1, 2, 3 and 6.

If you're told that A is a factor of B, then that means that A is a positive integer that divides evenly into B.
IF.... B = 6, then A could be 1, 2, 3 or 6

Then, if you're told that B is also a factor of A, then the reverse must also be true (re: B is a positive integer that divides evenly into A).
In this same situation, if B is already equal to 6, then A must equal 6, 12, 18, 24.... etc.

The only situation in which A is a factor of B AND B is a factor of A is when the two values are EQUAL to one another (re: A = B).

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