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

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4 00:00

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

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The official solution has been posted. Looking forward to a healthy discussion.. _________________

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  B
Joined: 12 Jan 2017
Posts: 39
Location: India
Re: If a, b and x are integers such  [#permalink]

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

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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
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts  _________________
Intern  B
Joined: 18 Aug 2017
Posts: 30
GMAT 1: 670 Q49 V33 Re: If a, b and x are integers such  [#permalink]

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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

In sum, answer is D.
Intern  B
Joined: 08 Feb 2015
Posts: 22
If a, b and x are integers such  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: If a, b and x are integers such  [#permalink]

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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 $$b = 1, a- b = -2$$

_________________
Intern  B
Joined: 23 Feb 2017
Posts: 36
Re: If a, b and x are integers such  [#permalink]

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

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I thought the absolute value operator will always give a positive value. Can someone please clarify?
Manager  B
Joined: 27 Oct 2017
Posts: 72
Re: If a, b and x are integers such  [#permalink]

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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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