If a, b, c are integers, what is the value of a?
(1) (a-7)(b-7)(c-7) = 0
(2) bc = 1
My choice is A since a = 7 but the correct answer is C.
Please explain the concept why this is wrong?
Thank you
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- MBA Applicant 2007/8
- StaceyKoprince
- ManhattanGMAT Staff
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Based on statement 1, a could equal 7, but it could also equal anything else - it doesn't absolutely have to be 7.
This statement:
(a-7)(b-7)(c-7) = 0
indicates that one of the three variables, a, b, or c, is 7. You only need one of the terms to equal zero for the entire product to equal zero.
Statement 2 tells us that bc = 1, which means neither one can be 7, because you would then have to multiply 7 by 1/7 to get 1 - and the question told us that all three variables are integers. So if neither b nor c can be 7, then a MUST be 7, in order to give us the term from statement 1 that equals zero.
This statement:
(a-7)(b-7)(c-7) = 0
indicates that one of the three variables, a, b, or c, is 7. You only need one of the terms to equal zero for the entire product to equal zero.
Statement 2 tells us that bc = 1, which means neither one can be 7, because you would then have to multiply 7 by 1/7 to get 1 - and the question told us that all three variables are integers. So if neither b nor c can be 7, then a MUST be 7, in order to give us the term from statement 1 that equals zero.
Stacey Koprince
Instructor
Director, Content & Curriculum
ManhattanPrep
Instructor
Director, Content & Curriculum
ManhattanPrep
2 posts Page 1 of 1