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If a, b and x are integers such
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Updated on: 31 May 2017, 05:26
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Q. If a, b and x are integers such that \(a^6=b^3=\frac{x}{x}\), what is the value of a  b (1) \(a^3b^7 > 0\) (2) \(a + b > 0\) Answer Choices A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed. Thanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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If a, b and x are integers such
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Updated on: 31 May 2017, 05:43



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Re: If a, b and x are integers such
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24 May 2017, 12:00
IMO D \(a^6 = b^3 = \frac{x}{x}\)
\(\frac{x}{x}\) = 1 or 1 depending on the sign of x,but since this fraction is equal to \(a^6\),it has to be equal to 1.
Therefore x=some postive,b =1 and a =+1 or 1 => ab=0 or ab=2 depending on the value of a.
statement 1:
\(a^3b^7\)>0,
since b=1, \(a^3\)>0, not possible for this statment.
therefore a>0 => a=1.
ab=0
statement 2:
a+b >0 ,
if a=1,then a+b=0. Therefore a=1.
ab=0.
Both the statement satisfies ,so D.



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Re: If a, b and x are integers such
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31 May 2017, 05:42
Official Solution Steps 1 & 2: Understand Question and Draw InferencesGiven: Integers a,b,x • \(a^6=b^3=\frac{x}{x}\)
To Find: Value of a  b ? \(\frac{x}{x}\) can take two possible values: • If \(x > o, x = x, \frac{x}{x}=\frac{x}{x}=1\)
• If \(x < o, x = x, \frac{x}{x}=−\frac{x}{x}=−1\) • \(a^6=\frac{x}{x}\)
• As \(a^6\) is always positive,\(a^6 = 1\), i.e. \(a = 1\) or \(1\)
• So, we can reject the value of \(\frac{x}{x}=−1\)
• \(b^3=\frac{x}{x}=1\)
• b = 1 Possible values of \(a – b\) • If \(a = 1\) and \(b = 1, a – b = 0\)
• If \(a = 1\) and \(b = 1, a b = 2\) So, we need to find the unique value of a to find the value of \(a – b\). Step 3: Analyze Statement 1 independently(1) \(a^3*b^7 > 0\) • Rewriting \(a^3b^7\) as \(ab(a^2b^6)\)
• Therefore, \(ab(a^2b^6)>0\)
• We know that \(a^2b^6\) is always \(> 0\) (even power of any number is always positive)
• So, for \(ab(a^2b^6)> 0\)
• \(ab > 0\) • This tells us that a and b have same signs.
• Since \(b > 0\), therefore a will also be greater than 0, so the value of \(a = 1\).
Sufficient to answer Step 4: Analyze Statement 2 independently(2) \(a + b > 0\) • If \(a = 1\) and \(b = 1\), \(a + b = 2 > 0\)
• If \(a = 1\) and \(b = 1\), \(a + b = 0\), is not greater than zero
• Hence, we have a unique answer, where \(a =1\) and \(b = 1\) • Thus \(a – b = 1 – 1 = 0\). Sufficient to answer. Answer: DThanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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Joined: 18 Aug 2017
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Re: If a, b and x are integers such
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24 Aug 2017, 21:43
Since \(a^6\) >=0 \(\frac{x}{x}\) will be positive, and x >=0 so x must be positive => x = x (also x can't be 0) and the fraction can be reduced to 1.
\(b^3\)=1 => b = 1 \(a^6\) = 1 => a =1, or 1
After analyzing, we can see the true question here is whether a is 1 or 1.
1 \(a^3\) \(b^7\) >0 or \(a^3\) x 1 >0 so a>0 => a=1 SUFF
2a+b>0 or a+1 > 0 a can only be 1 or 1, so a =1 SUFF
In sum, answer is D.



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If a, b and x are integers such
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26 Aug 2017, 11:24
From the question, without looking at the statements, we can infer that the a=b=1 due to x/x. It cannot be 0 as 0/0 is undefined. It can't be 1 too due to b^3. Is this question legit?
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Re: If a, b and x are integers such
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27 Aug 2017, 02:42



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Joined: 23 Feb 2017
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Re: If a, b and x are integers such
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27 Aug 2017, 15:57
I thought a^6 = x/x => as a6 is positive x has to be positive: => a = 1? x>0 => be is +1 and x<0 means b= 1
Is my reasoning wrong?
Can someone help me.. Thanks,



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Joined: 27 Oct 2017
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Re: If a, b and x are integers such
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18 Mar 2019, 11:13
I thought the absolute value operator will always give a positive value. Can someone please clarify?



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Re: If a, b and x are integers such
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18 Mar 2019, 11:14
I thought the absolute value operator will always give a positive value. Can someone please clarify?




Re: If a, b and x are integers such
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18 Mar 2019, 11:14






