For what percent of real number values of x between 0 and 100

Question

For what   approximate percent  of real positive integer values of x between 0 and 100 is  x^{2}-11x+28<0  ?

(A) 2
(B) 3
(C) 5
(D) 7
(E) 10

AnkurChakrabarty · Answer

Someone please explain. I got A.
(x-4)(x-7)<0
So, 4<x<7. 
x=5,6. So, 2%. Where am I wrong?

chetan2u · Answer

x^{2}-11x+28<0.....(x-7)(x-4)<0......4<x<7 ....

Now between 0 and 100, there are 100 gaps, leaving extreme integers...0<x<1, 1<x<2...99<x<100, and 99 integers -- 1, 2, ..99
Between 4<x<7, there are 3 gaps and 4-5, 5-6, 6-7 and 2 integers 5, 6...
So  \frac{3G+2}{100G+99}  will be closer to 3%, but not exact 3%.

So either ..
1) the question should ask for approximate percent.
2) Ask for 'positive integer values', and answer will change accordingly.

Not the language that you would see on GMAT.

Ravixxx · Answer

Hi  chetan2u ,
thank for your answer and for your comments, I modify the question

chetan2u · Answer

Now we are looking for approximate percentage..

As real values can be any fraction etc, we look for similar ranges......
we can take 0-1, 1-2, and so on as one range each, so 0 to 100, we have 100 ranges..
 x^{2}-11x+28<0...(x-7)(x-4)<0....4<x<7  gives us 3 ranges 4-5, 5-6, and 6-7

Approx % =  \frac{3}{100 }*100 = 3%

AnkurChakrabarty , hope it helps

Shrey1 · Answer

Hi  chetan2u

Question mentions real positive integer, so in that case there would be no need for following the ranges logic. There would be 100 real positive integer between 0 and 100.

Only 2 real positive integers, satisfy the equation.

So, the answer would be 2%

Help me understand, if there is a gap in my approach ?

Shrey1 · Answer

Ravixxx  I guess you have updated the question, by mentioning the positive integer condition. However, you have missed to update the answer.

Please check.

chetan2u · Answer

As you have also realized, my response talking of ranges was for the initial question posted. With the question edited, the answer will change.

For what percent of real number values of x between 0 and 100

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