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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 52% (02:10) correct 48% (02:28) wrong based on 86 sessions

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[GMAT math practice question]

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

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

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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

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
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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

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
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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

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

$${2 \over {100}} < x < {4 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,25 = {{100} \over 4} < {1 \over x} < {{100} \over 2} = 50\,\,\,\,\left( {\rm{I}} \right)$$

$$100 < y < 250\,\,\,\,\, \Rightarrow \,\,\,\,{1 \over {250}} < {1 \over y} < {1 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\, - {1 \over {100}} < - {1 \over y} < - {1 \over {250}}\,\,\,\,\left( {{\rm{II}}} \right)$$

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

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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8025
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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1
=>

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.
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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

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

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.

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GMAT 1: 640 Q44 V35 If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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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
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GMATH Teacher P
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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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1

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.
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Our high-level "quant" preparation starts here: https://gmath.net Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu   [#permalink] 15 Apr 2019, 05:42
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