Is 10 – 6x < 0 ? : Data Sufficiency (DS)

ldw28

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Re: Is 10 – 6x < 0 ? [#permalink]

04 Jun 2014, 08:08

Is 10 – 6x < 0 ?

10 – 6x < 0 -> simplifies -> x>5/3

(1) 5x^2 > 3x ^3

0 > 3x ^3 - 5x^2
0 > x^2(3x - 5)
x > 0 and x > 5/3, only x > 5/3 matters since if x < 5/3, the expression becomes negative and hence <0
Sufficient

(2) 4 > 3/x
4x > 3
x > 3/4
Not Sufficient

S

Sidhrt

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Re: Is 10 – 6x < 0 ? [#permalink]

04 Jun 2014, 21:56

Bunuel wrote:

Is 10 – 6x < 0 ?

Is \(10 - 6x < 0\)? --> is \(x>\frac{5}{3}\)?

(1) 5x^2 > 3x ^3 --> reduce by x^2: \(5>3x\) --> \(x<\frac{5}{3}\) (\(x\neq{0}\)). Hence the answer to the question is NO. Sufficient.

(2) 4 > 3/x --> x>3/4 or x<0. Not sufficient.

Answer: B.

P.S. Please tag the questions properly. This an Inequalities question not Algebra.

hi bunuel, i think some typing error. You have marked " B" as the right answer. pl change

S

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Re: Is 10–6x<0 ? [#permalink]

04 Jun 2014, 21:58

1

Kudos

nidhi12 wrote:

what if x=1/3 ???
A is failing

HI, A is not failing.

5(1/3)^2> 3(1/3)^3 => 5(1/3)^2> (1/3)^2 ..=> 5>1

WoundedTiger

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Re: Is 10–6x<0 ? [#permalink]

04 Jun 2014, 22:22

1

Kudos

nidhi12 wrote:

what if x=1/3 ???
A is failing

Hi,

For St 1, we have 5x^2- 3x^3 >0 or

x^2* (5-3x) >0

Now we know that product of 2 nos is greater than zero if both are of same sign. Also we know that\(x^2\geq{0}\).

Since it is given that expression is greater than zero that means x^2 >0 and therefore 5-3x > 0 or x<5/3.This is sufficient

We are told to find whether x>5/3 and we can answer the question based on above that x<5/3.

Consider x=1/3 so we have 1/9 (5-1)>0 or 4/9>0. So it is satisfying

St 2
4>3/x... This can be re-written as\(\frac{4x-3}{x}\) > 0

Agains either x>0 and x>3/4 or x> 3/4

or x<0 and x<3/4..There can be 2 possible answers to our question.

Ans is A

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Re: Is 10 – 6x < 0 ? [#permalink]

04 Jun 2014, 22:23

Sidhrt wrote:

Bunuel wrote:

Is 10 – 6x < 0 ?

Is \(10 - 6x < 0\)? --> is \(x>\frac{5}{3}\)?

(1) 5x^2 > 3x ^3 --> reduce by x^2: \(5>3x\) --> \(x<\frac{5}{3}\) (\(x\neq{0}\)). Hence the answer to the question is NO. Sufficient.

(2) 4 > 3/x --> x>3/4 or x<0. Not sufficient.

Answer: B.

P.S. Please tag the questions properly. This an Inequalities question not Algebra.

hi bunuel, i think some typing error. You have marked " B" as the right answer. pl change

Ans is A....It will be corrected.

Thank you

DesiGmat

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Re: Is 10 – 6x < 0 ? [#permalink]

04 Jun 2014, 22:38

Hi Nidhi12,

I took the following approach...

10-6x<0?

10<6x -> 5<3x -> 3x>5

To satisfy the above inequility we have to check whether x>1 or not?

COnsider Statement 1

5x^2 > 3x^3

a number's square can be greater than number's cube only when the number is negative.

Hence x must be negative. -> x<0

We can answer the question as NO. Hence Satisfied.

Statement 2

4> 3/x

Take x equal to 1. It satisfies statement 2 and answer to the question is NO.
Take x to be -2. It satisfies statement 2 and answer to the question is Yes.

We are getting two different answers. Hence statement 2 is insufficient.

Hence A is the correct option.

Hope I made myself clear.

L

Bunuel

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Jun 2014, 00:52

Expert Reply

Sidhrt wrote:

Bunuel wrote:

Is 10 – 6x < 0 ?

Is \(10 - 6x < 0\)? --> is \(x>\frac{5}{3}\)?

(1) 5x^2 > 3x ^3 --> reduce by x^2: \(5>3x\) --> \(x<\frac{5}{3}\) (\(x\neq{0}\)). Hence the answer to the question is NO. Sufficient.

(2) 4 > 3/x --> x>3/4 or x<0. Not sufficient.

Answer: B.

P.S. Please tag the questions properly. This an Inequalities question not Algebra.

hi bunuel, i think some typing error. You have marked " B" as the right answer. pl change

Thank you. Edited.

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Jun 2014, 01:29

@Sidhrt :

5> 1 if x=1/3 OK? So it means Answer to question becomes YES
but if x is not fraction but an integer then Answer to question becomes No
that is why I said 'A' is failing.
In this question , it is must to mention that x is an integer. Missing here

L

Bunuel

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Jun 2014, 01:54

Expert Reply

nidhi12 wrote:

@Sidhrt :

5> 1 if x=1/3 OK? So it means Answer to question becomes YES
but if x is not fraction but an integer then Answer to question becomes No
that is why I said 'A' is failing.
In this question , it is must to mention that x is an integer. Missing here

I don't understand what you mean.

\(5x^2 > 3x ^3\) means that \(x<\frac{5}{3}\) (\(x\neq{0}\)). So, the answer to the question whether \(x>\frac{5}{3}\) is NO.

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Sidhrt

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Jun 2014, 02:28

Bunuel wrote:

nidhi12 wrote:

@Sidhrt :

5> 1 if x=1/3 OK? So it means Answer to question becomes YES
but if x is not fraction but an integer then Answer to question becomes No
that is why I said 'A' is failing.
In this question , it is must to mention that x is an integer. Missing here

I don't understand what you mean.

\(5x^2 > 3x ^3\) means that \(x<\frac{5}{3}\) (\(x\neq{0}\)). So, the answer to the question whether \(x>\frac{5}{3}\) is NO.

Neither I can conclude what she is trying to say.

S

Sidhrt

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Jun 2014, 02:37

@Sidhrt :

5> 1 if x=1/3 OK? So it means Answer to question becomes YES
but if x is not fraction but an integer then Answer to question becomes No
that is why I said 'A' is failing.
In this question , it is must to mention that x is an integer. Missing here[/quote]

Is 10 – 6x < 0 ?

(1) 5x^2 > 3x ^3

(2) 4 > 3/x

Rephrase Question stem: x>5/3?

As bunuel explained clearly.

Stat #1: 5x^2 > 3x ^3 => x^2( 5-3x) >0 => 5-3x>0 => 5/3>x ( as x^2 can never be negative ) .. suff

Stat#2 not suff

I do not understand why you need author to specify x an integer

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Re: Is 10 – 6x < 0 ? [#permalink]

10 Jun 2014, 21:13

My doubt is cleared. Thanks.

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Sep 2020, 08:43

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Re: Is 10 – 6x < 0 ? [#permalink]

05 Sep 2020, 08:43

GMAT Data Sufficiency (DS) Questions

Is 10 – 6x < 0 ?