If 0.02

Question

If  0.02<x<0.04  and  100<y<250 , which of the following could be the value of  \frac{(y-x)}{(xy)} ?

A. 10  
 B. 20  
 C. 30  
 D. 50  
 E. 100

Archit3110 · Answer

x = 0.03
and y = 100 to 250 ~ 150 values
now 
 \frac{(y-x)}{(xy)} 
upon doing substiution of values of any value of y and x = 0.03 
we would observe that we get = y/x*y = 1/x = 1/0.03 ~ 33 nearest ~ 30 
IMO C

NandishSS · Answer

Let x= 0.03

and y=101

\frac{(y-x)}{(xy)}  =  \frac{(101-0.03)}{(101*0.03)}

Numerator 0.03 is negligible as compared to 101 we can ignore 0.03 & denominator would be almost 3.xxx

So 101/3 =33.333

Hence C

fskilnik · Answer

?\,\,\,:\,\,\,\frac{{y - x}}{{xy}} = \frac{1}{x} - \frac{1}{y}\,\,\,\,\,\underline {{	ext{could}}\,\,{	ext{be}}}

{2 \over {100}} < x < {4 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,25 = {{100} \over 4} < {1 \over x} < {{100} \over 2} = 50\,\,\,\,\left( {m{I}} ight)

100 < y < 250\,\,\,\,\, \Rightarrow \,\,\,\,{1 \over {250}} < {1 \over y} < {1 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\, - {1 \over {100}} < - {1 \over y} < - {1 \over {250}}\,\,\,\,\left( {{m{II}}} ight)

\left( {m{I}} ight) + \left( {{m{II}}} ight)\,\,\,25 - {1 \over {100}} < {1 \over x} - {1 \over y} < 50 - {1 \over {250}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {m{C}} ight)

We follow the notations and rationale taught in the  GMATH  method.

Regards, 
Fabio.

MathRevolution · Answer

=> Note that \frac{(y-x)}{(xy)} = \frac{1}{x} – \frac{1}{y}. 0.02 < x < 0.04 => \frac{1}{0.02} > \frac{1}{x} > \frac{1}{0.04} => 50 > \frac{1}{x} > 25 => 25 < \frac{1}{x} < 50 100 < y < 250 => \frac{1}{100} > \frac{1}{y} > \frac{1}{250} => 0.01 > \frac{1}{y} > 0.004 => 0.004 < \frac{1}{y} < 0.01 So, 25 – 0.01 < \frac{1}{x} – \frac{1}{y} < 50 – 0.004 24.99 < \frac{(y-x)}{(xy)} < 49.996 The only possible value of \frac{(y-x)}{(xy)} listed is 30 . Therefore, the answer is C. Answer: C

ScottTargetTestPrep · Answer

Simplifying the expression, we have:

(y - x)/(xy) = y/(xy) - x/(xy) = 1/x - 1/y

We see that 1/x ranges from 1/0.04 = 25 to 1/0.02 = 50, and 1/y ranges from 1/250 = 0.004 to 1/100 = 0.01. Therefore, 1/x - 1/y ranges from 25 - 0.01 = 24.99 to 50 - 0.004 = 49.996. We see that only 30 falls into this range; thus, the correct choice is C.

Answer: C

foryearss · Answer

guys , what am I donig wrong ?
2/100 < x < 4/100 .....................(1)
-4/100 < -x < -2/100..................(2)
100< y < 250...................(3)
(1) +(2)............ : 100-4/100 < y-x < 250-2/100 (4)

now , by multiblying (1) and (3) , since all values are positive :

100*2/100 < xy < 250* 4/100
2 < xy < 10
that means : 1/10< 1/xy < 1/2 ....................(5)

by multiblying (4) and (5) : we got : ( 100-4/100 ) *1/10 < ( y-x) /xy < 1/2 * ( 250-2/100)
that means : 10< ( y-x) /xy < 125
so where is my mistake ?

MathRevolution
fskilnik

MathRevolution fskilnik

fskilnik · Answer

Hi  foryearss  ,

There were no mistakes. The inferior and superior bounds you found are correct, but unfortunately, they are not good enough for the alternative choices offered.

Regards,
Fabio.

shaurya_gmat · Answer

y-x / yx can be approximately written as y / yx (x is very small in comparison to y ; Answer choices are far apart so this should work)
So we are basically looking for the range of 1/x
Only 25 fits the range.

nayanq2001 · Answer

Hi, can you please tell, me how can I solve this by conventional rules? Like first, 0.02 -x>-0.04. Now, subtracting y-x ---> 100-0.02

KarishmaB · Answer

Responding to a pm: \frac{(y-x)}{xy}= \frac{y}{xy} - \frac{x}{xy} = \frac{1}{x} - \frac{1}{y} We can easily find the ranges of 1/x and 1/y by taking the reciprocal of the inequality. 0.02\frac{1}{x}>\frac{100}{4} (the inequality sign flips) 25 < \frac{1}{x} < 50 and \frac{1}{250} < \frac{1}{y} < \frac{1}{100} 1/x lies between 25 and 50 and 1/y is a very small value. So 30 lies in this range and is acceptable. 50 is not because 1/x cannot be 50 and then 1/y needs to be subtracted from it too. Answer (C)

Bunuel · Answer

0.02<x<0.04  gives  -0.04<-x<-0.02  and when  added to   100<y<250  we get  99.96 < y - x < 249.98 . However,  99.96 < y - x < 249.98  and  2 < xy < 10  won't given you the correct answer. You'd need to do the way shown above.

nayanq2001 · Answer

But, I would like to know if my method is correct even if the answer does not suffice the need?

pappal · Answer

since y>>>x, so y-x ~ y 
so the expression reduces to y/xy =1/x as all given values are positive
lets find the boundary values 1/0.02=50 and 1/0.04=25
so the value of the expression is between 25 to 50 & only value that satisfies is 30.
C

If 0.02<x<0.04 and 100<y<250, which of the following could be the valu

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