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# If a, b and x are integers such

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Joined: 04 Jan 2015
Posts: 3078
If a, b and x are integers such  [#permalink]

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Updated on: 31 May 2017, 05:26
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Difficulty:

65% (hard)

Question Stats:

58% (02:17) correct 42% (02:16) wrong based on 186 sessions

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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) $$a + b > 0$$

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.
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
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Originally posted by EgmatQuantExpert on 24 May 2017, 11:45.
Last edited by EgmatQuantExpert on 31 May 2017, 05:26, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
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If a, b and x are integers such  [#permalink]

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Updated on: 31 May 2017, 05:43

Originally posted by EgmatQuantExpert on 24 May 2017, 11:47.
Last edited by EgmatQuantExpert on 31 May 2017, 05:43, edited 1 time in total.
Intern
Joined: 12 Jan 2017
Posts: 39
Location: India
Re: If a, b and x are integers such  [#permalink]

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24 May 2017, 12:00
1
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 => a-b=0 or a-b=-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.

a-b=0

statement 2:

a+b >0 ,

if a=-1,then a+b=0. Therefore a=1.

a-b=0.

Both the statement satisfies ,so D.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3078
Re: If a, b and x are integers such  [#permalink]

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31 May 2017, 05:42

Official Solution

Steps 1 & 2: Understand Question and Draw Inferences

Given: 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 $$a = 1$$.

• $$a – b = 1 -1 = 0$$

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 $$a – b = 1 – 1 = 0$$.

Thanks,
Saquib
Quant Expert
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Joined: 18 Aug 2017
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Re: If a, b and x are integers such  [#permalink]

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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

2-a+b>0
or a+1 > 0
a can only be -1 or 1, so a =1
SUFF

Intern
Joined: 08 Feb 2015
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If a, b and x are integers such  [#permalink]

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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?

Sent from my iPhone using GMAT Club Forum
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Joined: 02 Sep 2009
Posts: 58434
Re: If a, b and x are integers such  [#permalink]

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27 Aug 2017, 02:42
antztheman wrote:
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?

Sent from my iPhone using GMAT Club Forum

b must be 1 but a can be 1 ass well as -1. For both values, 1 and -1, a^6 is still 1.

Possible values of $$a – b$$

• If $$a = 1$$ and $$b = 1, a – b = 0$$

• If $$a = -1$$ and $$b = 1, a- b = -2$$

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Re: If a, b and x are integers such  [#permalink]

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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,
Manager
Joined: 27 Oct 2017
Posts: 72
Re: If a, b and x are integers such  [#permalink]

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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?
Manager
Joined: 27 Oct 2017
Posts: 72
Re: If a, b and x are integers such  [#permalink]

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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   [#permalink] 18 Mar 2019, 11:14
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