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

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Math Revolution GMAT Instructor
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If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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New post 06 Mar 2019, 02:03
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (02:02) correct 43% (02:16) wrong based on 37 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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New post 06 Mar 2019, 03:21
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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New post 06 Mar 2019, 03:26
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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New post 07 Mar 2019, 18:39
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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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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New post 08 Mar 2019, 02:39
=>

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
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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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New post 08 Mar 2019, 08:09
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.

Answer: 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] 08 Mar 2019, 08:09
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If 0.02<x<0.04 and 100<y<250, which of the following could be the valu

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