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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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06 Mar 2019, 02:03
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65% (hard)

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 18 Aug 2017 Posts: 5026 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu [#permalink] ### Show Tags 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 Director Joined: 06 Jan 2015 Posts: 689 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu [#permalink] ### Show Tags 06 Mar 2019, 03:26 1 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 _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu [#permalink] ### Show Tags 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. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Math Revolution GMAT Instructor 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] ### Show Tags 08 Mar 2019, 02:39 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. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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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.

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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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14 Apr 2019, 15:14
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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Re: If 0.02<x<0.04 and 100<y<250, which of the following could be the valu  [#permalink]

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15 Apr 2019, 05:42
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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