Is 10–6x

Question

Is 10 – 6x < 0?

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

(2) 4 > 3/x

Kudos for a correct  solution .

rajthakkar · Answer

(1) Sufficient. 5x2>3x3. we can remove x2 as it is positive.

so 5 > 3x or 10 - 6x > 0

(2) Insufficient : we do not know whether X is positive or negative.

So I will go with A

What is the answer?

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Solution: (A)

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

Because x^2 is always positive, we can divide both sides by x2 without needing to worry about changing the inequality. In doing so, we find that:

5 > 3x

Because our goal is to determine whether 10 < 6x, we can multiply the fact above by 2:

2(5) > 2(3x)

To find that 10 > 6x. Therefore, we can prove that the answer is no; 10 is GREATER THAN 6x, and the question asks whether it’s less than 6x.

Statement (2): 4 > 3/x

We can manipulate that statement to find that:

4 – 3/x > 0

(4x – 3)/x > 0

Since both factors should either be positive or both should be negative to make the division positive, x should either be less than 0 or greater than ¾. If x is less than 0, 10 – 6x is positive but if x is greater than ¾, (10 – 6x) could be negative. Hence statement (2) alone is not sufficient to answer the question.

Enderwiggin17 · Answer

Nice problem to test basic concepts: we can get rid of x^2 in (1) and we can not cross-multiply x in (2) since we do not know whether it is positive or negative. I go with A.

MathRevolution · Answer

Now we will solve this DS question using the Variable Approach

You can visit https://www.mathrevolution.com to learn and master this Approach along with other tips to quickly solve DS questions.

The first step of the Variable Approach: Modify the original condition and the question to suit the type of information given in the conditions. This is a priority and the most important step. The first step alone gives us a 30% chance of answering the question correctly.

=> We have to find whether 10 - 6x is less than 0?

=> We have to apply CMT 1 as we are looking for a yes or no answer.

=> Is 10 - 6x < 0 => 10 < 6x

=> \(\frac{5 }{ 3}\) < x or x > \(\frac{5 }{ 3}\)

=> Let's look at Condition (1) : It tells us that \(5x^2\) > \(3x^3\)

=> \(5x^2\) - \(3x^3\) > 0

=> \(x^2\)(5 - 3x) > 0

=> 5 - 3x > 0 Therfore, \(\frac{5 }{ 3}\) > x

Is x > 5 / 3 - NO

Since the answer is yes, the condition is sufficient by CMT 1 which means that the answer must be in terms of a unique yes or no.

=> Let's look at Condition (2): It tells us that 4 > 3x

=> \(\frac{4 }{ 3}\) > x

=> \( \frac{4 }{ 3}\) greater than x doesn't mean \( \frac{5 }{ 3}\) will be less than 'x'. It is possible that \( \frac{5 }{ 3}\) can be greater than 'x' too.

So we will not get a unique value. So, the condition is not sufficient by CMT 1 which means that the answer must be in terms of a unique yes or no.

Condition (1) ALONE is sufficient.

So, A is the correct answer.

Answer: A

prateekchugh · Answer

Is 10 – 6x < 0? 10<6x \frac{10}{6} 3 x^3 5 x^2 -3 x^3 >0 x^2 (5-3x)>0 x^2 is always positive------ (5-3x)>0----5>3x---- \frac{5}{3} >x Answer is No This statement is sufficient (2) 4 > \frac{ 3}{x} \frac{4}{3}>\frac{1}{x} Case 1) x is positive x> \frac{3}{4} .....Answer is yes or no Case 2) x is negative x< \frac{3}{4} Answer is No This statement is insufficient

bumpbot · Answer

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Is 10–6x<0?

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