Is 11x/23

Question

Is 11x/23 < 7x/13 ?

(1) x is an integer.
(2) x > 0

Kudos for a correct  solution .

camlan1990 · Answer

11x/23 < 7x/13 if x > 0
(1) x is an integer. 
Do not know the sign of x
INSUF
(2) x > 0
SUFF

Ans: B

farzana87 · Answer

Answer c. if x>0, it can be a fraction as well. Hence B is not suff. x>0 and an integer turns the answer to a definitive yes.

Hemavakade · Answer

The Question stem can be simplified as

143x < 161x

143 < 161

But we don't know the value of x.
1) If x is negative, say -1 then the statement is not true
2) If x = 0 then again statement is not true.
3) but for all positive values of x (x >0) the above statement will be true.

statement 1  
Not sufficient - Because of reason (1) and (2)

statement 2  
Sufficient - Because of Reason (3)

Answer = B

BrainLab · Answer

we have 143x<161x ? The answer is (B) because even if x is a fraction let's say 2/5 both numbers share the same denominator but the numerator of 161x is more than of 143x

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No . This type asks whether 11x/23 is less than 7x/13.

Given information from the question stem: You can think of the question stem as asking whether 11x/23 is less than 7x/13. 11/23 is slightly less than 1/2 and 7/13 is slightly more than 1/2. Since both numbers are multiplied by the same variable, x, it would appear that the answer will be “yes” 11x/23 is less than 7x/13, at least if x is a positive integer. However, if x is a negative number or a fraction it may not be the case.

Statement 1 : “x is an integer.” With this information you know that x is not a fraction. However, x could still be negative. If x is negative then 7x/13 will be
“more negative” (further to the left on the number line) and therefore a smaller number than 11x/23 . This would give the answer of “no.” You can also get a “yes” from Statement 1 if x is a positive integer. For this reason Statement 1 is not sufficient. Eliminate choices A and D.

Statement 2 : “x is positive.” This eliminates the possibility of x being negative (and also eliminates the possibility of x being 0, which would also have given a “no” answer to the question). However, Statement 2 does allow for x to be a noninteger—a fraction or decimal. Does it matter if x is a non-integer? It does not. Even if x is 1/2, 7x/13 will still be a larger number than 11x/23 . The number property at work in this question is “positive/negative” and the fact that x cannot be negative and cannot be zero is enough to ensure that the answer to the question is always yes” 11x/23 is smaller than 7x/13. This statement is sufficient and  the answer is B .

The important takeaways from this question: When a problem deals with the combination of inequalities and variables and/or when a statement specifically defines a variable as positive (>0) or negative (<0), be certain to check positive/negative number properties as part of your analysis.

bumpbot · Answer

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Is 11x/23 < 7x/13 ?

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