Q1)If a^2*b^2*c^3 = 4500.Is b+c =7
1)a b c are positive integers
2)a>b
Is the answer B??
Thanks
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soni_pallavi
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eaakbari
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IMO C
a^2*b^2*c^3 = 4500
a^2*b^2*c^3 = 3^2 * 2^2 * 5^3
c = 5, a can be 2 or 3, b can be 2 or 3 & c >0
(I) Only states that a,b,c,>0 . Clearly Insuff
(II)a>b that could mean 3>2 or -2>-3 .Its not precise. Insuff
(I) & (II)
Together there is only one option of a=3 and b = 2.
which makes b +c = 7. Hence Suff
Therefore answer is C
a^2*b^2*c^3 = 4500
a^2*b^2*c^3 = 3^2 * 2^2 * 5^3
c = 5, a can be 2 or 3, b can be 2 or 3 & c >0
(I) Only states that a,b,c,>0 . Clearly Insuff
(II)a>b that could mean 3>2 or -2>-3 .Its not precise. Insuff
(I) & (II)
Together there is only one option of a=3 and b = 2.
which makes b +c = 7. Hence Suff
Therefore answer is C
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soni_pallavi
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Anindya Madhudor
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I think you also need to consider the case that 4500=6^2*1^2*5^3. In this case, b+c=6. Hence, both statements together are not sufficient.
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Brent@GMATPrepNow
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Target question: Does b+c = 7?soni_pallavi wrote:If a^2*b^2*c^3 = 4500. Is b+c =7
1)a b c are positive integers
2)a>b
Given: a^2*b^2*c^3 = 4500
Find the prime factorization of 4500
4500 = (2^2)(3^2)(5^3)
Statement 1: a, b, and c are positive integers
There are different sets of numbers that meet this condition. Here are two:
Case a: a = 3, b = 2 and c = 5, in which case b+c equals 7
Case b: a = 6, b = 1 and c = 5, in which case b+c does not equal 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a>b
There are different sets of numbers that meet this condition. Here are two:
Case a: a = 3, b = 2 and c = 5, in which case b+c equals 7
Case b: a = 6, b = 1 and c = 5, in which case b+c does not equal 7
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Notice that I used the same sets of numbers to show that each individual statement (alone) is not sufficient. This means that we can automatically see that the two statements combined are not sufficient, since we still have two conflicting cases to consider:
Case a: a = 3, b = 2 and c = 5, in which case b+c equals 7
Case b: a = 6, b = 1 and c = 5, in which case b+c does not equal 7
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer = E
Cheers,
Brent
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soni_pallavi
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