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What is the value of a^(2)*b^(3)? [#permalink]
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11 Nov 2010, 10:02
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What is the value of \(a^{(2)}*b^{(3)}\)? (1) \(a^{(3)}*b^{(2)}=36^{(1)}\) (2) \(a*b^{(1)}=6^{(1)}\)
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Last edited by Bunuel on 30 Jan 2015, 06:04, edited 3 times in total.
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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Statement 1 alone is clearly insufficient since we have an additional ab^1 present. Statement 2 alone is also not adequate to calculate a^2*b^3
Multiplying both statements above (a^3*b^2) *(a*b^1) = a^2*b^3
which is 6/36 = 1/6,
Answer: C



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22 Apr 2011, 08:55
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dc123 wrote: anyone??
What is the value of (a^2)(b^3)
1) (a^3)(b^2) = (36^1)
2) ab^1 = 6^1 1) or 2) alone ins Consider 1)+2) from 2) we have \(6a=b\) plug it in 1) and solve for "a". Than plug it into 2). Now with known "a" and "b" you can find the value of \((a^(2))(b^(3))\) Remember that you don't need to solve it, you need to know that the equation could be solved. (C)



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Re: What is the value of a^(2)*b^(3)? [#permalink]
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22 Apr 2011, 10:14
dc123 wrote: What is the value of a^2b^3
1) a^3b^2 = 36^1
2) ab^1 = 6^1
the Ans says C but doesnt only B work? What is \(a^{2}b^{3}=\frac{1}{a^2b^3}=\frac{1}{(ab)^2b}\) 1) a^3b^2 = 36^1 \(a^{3}b^{2} = 36^{1}\) \(\frac{1}{a^3b^2} = \frac{1}{36}\) \(\frac{1}{a^3b^2} = \frac{1}{36}\) \(\frac{1}{(ab)^2a} = \frac{1}{36}\) \(\frac{1}{(ab)^2} = \frac{a}{36}\) \(\frac{1}{(ab)^2b}=\frac{a}{36b}\) 1\(a^3b^2=36\) Possible values of a and b; \(a=1; b=6\) \(a=2; b=\sqrt{\frac{36}{8}}\) \(a=0.1; b=\sqrt{\frac{36}{0.001}}\) Not Sufficient. 2) ab^1 = 6^1 \(ab^{1} = 6^{1}\) \(\frac{a}{b} = \frac{1}{6}\) 2a=1; b=6 a=2; b=12 a=3; b=18 a=3.2; b=19.2 Not Sufficient. Combining both and using 1 and 2: \(\frac{1}{(ab)^2b}=\frac{a}{36b}=\frac{1}{36*6}=\frac{1}{216}\) Sufficient. Ans: "C"
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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03 May 2011, 01:01
a. gives values (1,6) and (1,6) b gives values (1,6) and (1,6) a+b gives (1,6) hence C
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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03 May 2011, 17:48
dc123 wrote: What is the value of a^2b^3
1) a^3b^2 = 36^1
2) ab^1 = 6^1
the Ans says C but doesnt only B work? Putting the question in the right form can help you quickly arrive at the answer. What is \(\frac{1}{a^2b^3}?\) 1. \(\frac{1}{a^3b^2} = \frac{1}{36}\) Since a and b are real numbers so they can occur in many combinations to give 1/36. This statement alone is not sufficient. 2. \(\frac{a}{b} = \frac{1}{6}\) Again, a and b are real numbers and they can take many different values to give 1/6 (e.g. a = 1, b = 6 or a = 2, b = 12 etc). This statement alone is not sufficient. You can easily get the value of \(\frac{1}{a^2b^3}\) by combining the two statements. \(\frac{1}{a^2b^3} = \frac{1}{a^3b^2} * \frac{a}{b} = \frac{1}{36} * \frac{1}{6}\) Hence they are sufficient together. Answer (C)
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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22 Feb 2012, 02:39
I am a bit confused on (1)
Here is the way I thought: (a^3)(b^2)=(36^1) (1/a^3)(1/b^2)=1/36 (a^3)(b^2)=36 (a^3)(b^2)=(3^2)(2^2) (a^3)(b^2)=(1^3)(6^2) a= 1 ; b = 6
How using fractions would make this reasoning wrong?



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Re: What is the value of a^(2)*b^(3)? [#permalink]
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22 Feb 2012, 02:49



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Re: What is the value of a^(2)*b^(3)? [#permalink]
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16 Aug 2012, 00:32
Answer is C .
From 1: 1/a^3 *1/b^2= 1/36 Not sufficient From 2 : 1/ab =1/6 means a, b can be :2,3 ; 3,2 ;6,1;1,6 . not sufficient
Combining both statements only a=1 and b=6 fulfills the statement 1 so answer is C
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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13 Sep 2012, 07:53
Bunuel wrote: What is the value of a^2*b^3?
Note that we are not told that \(a\) and \(b\) are integers.
\(a^{2}*b^{3}=\frac{1}{a^2b^3}=?\) So, basically we need to find the value of \(a^2b^3\).
(1) \(a^{3}*b^{2}=36^{1}\) > \(a^3b^2=36\). Not sufficient. (2) \(ab^{1}=6\) > \(\frac{b}{a}=\frac{1}{6}\). Not sufficient.
(1)+(2) Multiply (1) by (2): \(a^3b^2*\frac{b}{a}=a^2b^3=36*\frac{1}{6}\). Sufficient.
Answer: C. Hi all, I would like to add to the explanation given by Bunuel. (1)as explained by bunuel \(a^3b^2=36\)  Insufficient > Why? Because we can be sure that a=1 but we b can be either +6 or 6 (2) b = 6aInsufficient because this is just a ratio & nothing is mentioned about their values. Hope it helps.
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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13 Sep 2012, 07:59
fameatop wrote: Bunuel wrote: What is the value of a^2*b^3?
Note that we are not told that \(a\) and \(b\) are integers.
\(a^{2}*b^{3}=\frac{1}{a^2b^3}=?\) So, basically we need to find the value of \(a^2b^3\).
(1) \(a^{3}*b^{2}=36^{1}\) > \(a^3b^2=36\). Not sufficient. (2) \(ab^{1}=6\) > \(\frac{b}{a}=\frac{1}{6}\). Not sufficient.
(1)+(2) Multiply (1) by (2): \(a^3b^2*\frac{b}{a}=a^2b^3=36*\frac{1}{6}\). Sufficient.
Answer: C. Hi all, I would like to add to the explanation given by Bunuel. (1)as explained by bunuel \(a^3b^2=36\)  Insufficient > Why? Because we can be sure that a=1 but we b can be either +6 or 6 (2) b = 6aInsufficient because this is just a ratio & nothing is mentioned about their values. Hope it helps. Let me correct you: we cannot be sure that \(a=1\) from (1). Since we are not told that \(a\) and \(b\) are integers, then \(a\) could, for example be 2 and \(b\) could be \(\frac{3}{\sqrt{2}}\) or \(\frac{3}{\sqrt{2}}\). Hope it's clear. P.S. This post might also help: whatisthevalueofa2b104673.html#p1047996
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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13 Jul 2013, 16:11
Bunuel,
Even if we were told a&b are postive integers does knowing a^3*b^2=constant ever gaurentee knowing the value of a^2*a^3??
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Re: What is the value of a^(2)*b^(3)? [#permalink]
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13 Jul 2013, 23:41



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Re: What is the value of a^(2)*b^(3)? [#permalink]
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29 Jan 2015, 18:12
Hi Bunuel  can you explain why ab^(1)=6^(1) yields b/a = 6?



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Re: What is the value of a^(2)*b^(3)? [#permalink]
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29 Jan 2015, 20:47
It would make it much clearer if you edited the original question to indicate for statement two "a * b^(1)". I got confused and thought the whole term ab was taken to the negative first power.



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