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Exponents..Numbers

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Source: — Data Sufficiency |
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by vk_vinayak » Thu Aug 30, 2012 2:22 am
nroy347 wrote:If a^2b^2c^3 = 4500 . Is b+c = 7 ?
(1) a, b and c are positive integers
(2) a > b

after i solved . i got C, however the answer shown was E.Can anyone explain this...
Even I got C. Not sure what am I missing.
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by neelgandham » Thu Aug 30, 2012 3:50 am
Interesting!

If a^2 * b^2 * c^3 = 4500. Is b+c = 7?
(1) a, b and c are positive integers
a^2 * b^2 * c^3 = 4500

Case 1: a^2 * b^2 * c^3 = 2^2 * 3^2 * 5^3
a = 2, b = 3 and c = 5.
Is b+c=7 ? No! b+c = 3+5 = 8.

Case 2: a^2 * b^2 * c^3 = 3^2 * 2^2 * 5^3
a = 3, b = 2 and c = 5.
Is b+c=7 ? Yes! b+c = 2+5 = 7.

I am sure that you might have considered the above cases BUT(and a big one) did you consider the case where the value of a or b is 1?

Case 3: a^2 * b^2 * c^3 = 6^2 * 1^2 * 5^3
a = 6, b = 1 and c = 5.
Is b+c=7 ? No! b+c = 1+5 = 6.

Case 3: a^2 * b^2 * c^3 = 1^2 * 6^2 * 5^3
a = 1, b = 6 and c = 5.
Is b+c=7 ? No! b+c = 6+5 = 11.

Since we don't have a definite answer, statement I is insufficient to answer the question.
(2) a > b
So? Irrelevant.
Since we don't have a definite answer, statement II is insufficient to answer the question.
](1) a, b and c are positive integers PLUS (2) a > b
The value of a is greater than b in two cases, case 2 and case 3:

Case 2: a^2 * b^2 * c^3 = 3^2 * 2^2 * 5^3
a = 3, b = 2 and c = 5.(a>b)
Is b+c=7 ? Yes! b+c = 2+5 = 7.

Case 3: a^2 * b^2 * c^3 = 6^2 * 1^2 * 5^3
a = 6, b = 1 and c = 5.(a>b)
Is b+c=7 ? No! b+c = 1+5 = 6.

Since we don't have a definite answer, [Statement I + Statement II]-combined isn't sufficient to answer the question.
Answer E
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by vk_vinayak » Thu Aug 30, 2012 3:57 am
Oh dear! Tricky question indeed.
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by nroy347 » Thu Aug 30, 2012 6:34 am
Thnx!! Important to consider 1 as factor..:)
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by adthedaddy » Thu Aug 30, 2012 8:39 am
Nice explanation Anil. Thanks for giving a wholistic view to the problem :-)
"Your time is limited, so don't waste it living someone else's life. Don't be trapped by dogma - which is living with the results of other people's thinking. Don't let the noise of others' opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary" - Steve Jobs
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by neelgandham » Fri Aug 31, 2012 11:27 pm
Thanks all!

Most of the times we ignore to consider integers 1,0 and -1, if the variable used in the question is an integer. We also tend to assume that a variable is an integer and keep looking for possible integer solutions.

In order to avoid such mistakes you SHOULD
a) Practice a lot.
b) Read the question carefully.
c) Never assume.
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