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# Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0

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Senior DS Moderator
Joined: 27 Oct 2017
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Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0  [#permalink]

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Updated on: 06 Sep 2018, 22:06
1
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:30) correct 38% (01:26) wrong based on 55 sessions

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Is $$3^x >\frac{x}{|x|}$$

(1) $$|x| = 3$$

(2) $$x < 0$$

_________________

Originally posted by gmatbusters on 06 Sep 2018, 21:50.
Last edited by Bunuel on 06 Sep 2018, 22:06, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Aug 2009
Posts: 7334
Re: Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0  [#permalink]

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06 Sep 2018, 22:40
Is $$3^x >\frac{x}{|x|}$$
two cases..
a) x is negative $$\frac{x}{|x|}=-1$$ and $$3^x>0$$ as $$3^{-a}=\frac{1}{3^a}$$...$$3^x >\frac{x}{|x|}$$
b) x is positive $$\frac{x}{|x|}=1$$ and $$3^x>1$$ ........$$3^x >\frac{x}{|x|}$$
c) x is 0, $$\frac{x}{|x|}=undefined$$ and $$3^x=1$$

so Only in case (c), we cannot say anything as it is undefined...
But would GMAT give you an undefined qty.. doubtful

(1) $$|x| = 3$$
$$x\neq{0}$$
case (a} or case (b), ans is YES
suff

(2) $$x < 0$$
$$x\neq{0}$$
case (a} , ans is YES
suff

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0  [#permalink]

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06 Sep 2018, 22:30
Hi,

Question: Is 3^x > x/|x| ?

This is a YES-NO DS question.

Before moving onto the question, always analyse the given question stem.

If “x” is a positive integer, then answer to the question would be YES. Because 3 raised to a power(Integer) always a greater value than 1(Right hand side).

Example: 3 ^10 > 10 /|10| = 3^10 > 1

If “x” is a negative value, then answer to the question would be YES. Because 3 raised to a power of negative value brings the value to the denominator(1/3^x) which is a positive number and right
hand side is a negative value(-1)

If “x” is a fraction, then it depends on the what fraction it is, So answer could be either YES or NO. Because 3 raised to a fractional power maybe equal to or greater than 1.

So, now let’s look at what statements have to offer.

Statement I is sufficient:

|x| = 3

x = +3 / -3

For both x = 3 and -3

3^x is greater than x/|x|

Answer to the question would be YES.

Sufficient.

Statement II is sufficient:

x < 0

As we did the analysis above, if “x” is a negative value then answer to the question would be YES. Because right hand side value of the question is a negative(-1) and left hand side would be positive number.

Sufficient.

Hope it helps.
_________________

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Joined: 02 Aug 2009
Posts: 7334
Re: Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0  [#permalink]

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06 Sep 2018, 22:44
Byjus wrote:
Hi,

Question: Is 3^x > x/|x| ?

This is a YES-NO DS question.

Before moving onto the question, always analyse the given question stem.

If “x” is a positive integer, then answer to the question would be YES. Because 3 raised to a power(Integer) always a greater value than 1(Right hand side).

Example: 3 ^10 > 10 /|10| = 3^10 > 1

If “x” is a negative value, then answer to the question would be YES. Because 3 raised to a power of negative value brings the value to the denominator(1/3^x) which is a positive number and right
hand side is a negative value(-1)

If “x” is a fraction, then it depends on the what fraction it is, So answer could be either YES or NO. Because 3 raised to a fractional power maybe equal to or greater than 1.

So, now let’s look at what statements have to offer.

Statement I is sufficient:

|x| = 3

x = +3 / -3

For both x = 3 and -3

3^x is greater than x/|x|

Answer to the question would be YES.

Sufficient.

Statement II is sufficient:

x < 0

As we did the analysis above, if “x” is a negative value then answer to the question would be YES. Because right hand side value of the question is a negative(-1) and left hand side would be positive number.

Sufficient.

Hope it helps.

You are wrong on the point of a fraction as mentioned by you in coloured portion above..
$$3^0 =1$$ as 0 moves up to even 0.0000000001, $$3^{0.00000000001}>1$$

so the point is NOT of a fraction but x as 0
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0  [#permalink]

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06 Sep 2018, 23:05
1
Hi Chetan2u,

Thanks for pointing out, that is what exactly I too wanted to say, maybe my language was little wordy and didnt express the intended thoughts.

My point is 3^1/n and if n gets bigger that is value of 1/n will be closer to 0, then 3^0 is equal to 1, where answer to the question would be NO.

Believe we are on the same page here.

chetan2u wrote:

Byjus wrote:

Hi,

Question: Is 3^x > x/|x| ?

This is a YES-NO DS question.

Before moving onto the question, always analyse the given question stem.

If “x” is a positive integer, then answer to the question would be YES. Because 3 raised to a power(Integer) always a greater value than 1(Right hand side).

Example: 3 ^10 > 10 /|10| = 3^10 > 1

If “x” is a negative value, then answer to the question would be YES. Because 3 raised to a power of negative value brings the value to the denominator(1/3^x) which is a positive number and right
hand side is a negative value(-1)

If “x” is a fraction, then it depends on the what fraction it is, So answer could be either YES or NO. Because 3 raised to a fractional power maybe equal to or greater than 1.

So, now let’s look at what statements have to offer.

Statement I is sufficient:

|x| = 3

x = +3 / -3

For both x = 3 and -3

3^x is greater than x/|x|

Answer to the question would be YES.

Sufficient.

Statement II is sufficient:

x < 0

As we did the analysis above, if “x” is a negative value then answer to the question would be YES. Because right hand side value of the question is a negative(-1) and left hand side would be positive number.

Sufficient.

Hope it helps.

You are wrong on the point of a fraction as mentioned by you in coloured portion above..
$$3^0 =1$$ as 0 moves up to even 0.0000000001, $$3^{0.00000000001}>1$$

so the point is NOT of a fraction but x as 0

_________________

GMAT Mentors

Is 3^x > x/|x| ? (1) |x| = 3 (2) x < 0   [#permalink] 06 Sep 2018, 23:05
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