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Director
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If (a-1)(b-2) =0, which of the following must be true ? [#permalink]
 12 Aug 2004, 20:23
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If (a-1)(b-2) =0, which of the following must be true ?
I. a=1 and b=2
II. if a is not = 1, then b=2
III. if a=1, then b is not=2
A. I only
B. II only
C. III only
D. I and II
E. II and III
Explain your answer.
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GMAT Club Legend
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If (a-1)(b-2) =0, which of the following must be true ?
I. a=1 and b=2
II. if a is not = 1, then b=2
III. if a=1, then b is not=2
(II) is the answer.
For (a-1)(b-2) = 0, a =1 OR b=2
(I) is out because of the and
(III) is out because it says if a=1, then b must not be 2, which is wrong. b can still be 0.
(II) satisfiy the logic. If a is not 1, then the only way the equation can go to 0 is for b to be equals to 2.
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Director
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D.
I is got directly from the equation so no problem.
II If a = say 3 then we have (3-1)(b-2)=0 or 2b=4 or b=2. This is true for any value of A.
III is not ok...b can be 2 or any other value.
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Senior Manager
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venksune wrote: D.
I is got directly from the equation so no problem.
II If a = say 3 then we have (3-1)(b-2)=0 or 2b=4 or b=2. This is true for any value of A.
III is not ok...b can be 2 or any other value.
Venksune, please notice the question asks what MUST BE true. I can be true. The ans here is B
_________________
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Director
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Sorry guys...read it as a=1 or b=2..silly mistakes again.
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Director
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I still don't understand.
Can someone explain in detail ? Thank you.
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Joined: 31 Dec 1969
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Choice 1
If a = 1 AND b is any number (1, 2, 100), the equation in the question will still be satisfied. So, Choice 1 is wrong.
Choice 3
It says if a is 1 then b is not 2. If a is 1, b can certainly be 2 and this can be checked by plugging in. So, Choice 3 is wrong.
Choice 2.
It says if a is not 1 then b is 2. This is correct. If a is not 1, and b is not 2, then the equation in the question cannot be satisfied. So if a is not 1, then b HAS to be 2 (which is what Choice 2 says) and if b is not 2 then a HAS to be 1. So Choice 2 is correct and the answer is B.
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close
