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# GMAT Diagnostic Test Question 7

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GMAT Diagnostic Test Question 7 [#permalink]  06 Jun 2009, 20:53
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GMAT Diagnostic Test Question 7
Field: Arithmetic, Fractions
Difficulty: 650

Which of the following numbers is the greatest?

A. $$\frac{1876452}{1876455}$$

B. $$\frac{1883446}{1883449}$$

C. $$\frac{1883453}{1883456}$$

D. $$\frac{1883456}{1883459}$$

E. $$\frac{1883491}{1883494}$$
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Last edited by Bunuel on 06 Oct 2013, 23:06, edited 4 times in total.
Updated
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Re: GMAT Diagnostic Test Question 7 [#permalink]  12 Jun 2009, 06:37
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Explanation:

You have to notice that the difference between a numerator and denominator of any fraction equals 3. Thus, the greater the numerator/denominator, the greater the fraction. In this case, the greatest numerator is in the third fraction. The answer is E.

You might think of these two fractions as an extreme example:

$$\frac{997}{1000}$$ and $$\frac{1}{4}$$

The difference between numerator and denominator is the same for both fractions, as you can see. There's no doubt, though, that the first fraction is very close to 1, unlike the second one. So, having in mind the same difference between numerators and denominators of the fractions in the answer choices, the greater numerator (denominator) of the fraction, the greater the fraction.
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Last edited by bb on 28 Sep 2013, 10:48, edited 2 times in total.
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Re: GMAT Diagnostic Test Question 7 [#permalink]  10 Aug 2009, 02:59
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You might think of these two fractions as an extreme example:

$$\frac{997}{1000}$$ and $$\frac{1}{4}$$

The difference between numerator and denominator is the same for both fractions, as you can see. There's no doubt, though, that the first fraction is very close to 1, unlike the second one. So, having in mind the same difference between numerators and denominators of the fractions in the answer choices, the greater numerator (denominator) of the fraction, the greater the fraction.

Hope this helps .
tejal777 wrote:
I noticed the difference bt was'nt able to conclude anything..So basically this is like comparing 1/4 , 5/8 and 7/10...since the last one has the highest numerator it will be the largest fraction..hmm..intresting..can somebody please elaborate on this ??

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Re: GMAT Diagnostic Test Question 7 [#permalink]  06 Sep 2009, 22:52
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1876452/1876455 = 1876455/1876455 - 3/1876455 = 1- 3/1876455
1883456/1883459 = 1883459/1883459 - 3/1883459 = 1- 3/1883459
1883491/1883494 = 1883494/1883494 - 3/1883494 = 1- 3/1883494 = LARGEST
(3/1883494 - SMALLEST)
1883446/1883449 = 1883449/1883449 - 3/1883449 = 1- 3/1883449
1883453/1883456 = 1883456/1883456 - 3/1883456 = 1- 3/1883456

Last edited by manojmakkatt on 22 Nov 2009, 07:14, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 7 [#permalink]  09 Dec 2010, 11:49
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Guys, not sure if this has been said before, but I noticed this mistake (at least it appears to me as a mistake) in the OE:

The fifth fraction has the biggest numerator, not the third. I hope this helps. Awesome job, by the way, guys!
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Re: Greatest value [#permalink]  09 Feb 2013, 18:04
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In each of the answer choices, the difference between the numerator and denominator is the same i.e 3. Hence the number with the largest numerator and largest denominator will be the highest.

To illustrate this point :

$$\frac{1}{2} = 0.5$$

$$\frac{9}{10} = 0.9$$

$$\frac{99}{100} = 0.99$$
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Re: GMAT Diagnostic Test Question 7 [#permalink]  18 Sep 2009, 14:51
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I doubt the actual GMAT would ever arrange the answer choices in such order.

It would most likely do such as:

a. 1876452/1876455
b. 1876456/1876459
c. 1876460/1876463
d. 1876464/1876467
e. 1876468/1876471
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Re: GMAT Diagnostic Test Question 7 [#permalink]  08 Oct 2009, 15:41
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In general,

we can see in each variant regularity n/[n+3] = [n+3-3]/[n+3] = 1-3/[n+3].

So n/[n+3] is greatest when n is greatest. Two inverse dependences (1/[n] and -n) give direct dependence.

The greatesr n = 1883491. And the best answer is C.
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Re: GMAT Diagnostic Test Question 7 [#permalink]  20 May 2010, 10:31
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When I see this question, I see:
$$\frac{1}{2}<\frac{3}{4}<\frac{5}{6}....$$
as the denominator gets larger, the fraction gets closer to 1

So not too difficult ..600 level
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Re: GMAT Diagnostic Test Question 7 [#permalink]  09 Aug 2009, 20:48
I noticed the difference bt was'nt able to conclude anything..So basically this is like comparing 1/4 , 5/8 and 7/10...since the last one has the highest numerator it will be the largest fraction..hmm..intresting..can somebody please elaborate on this ??
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Re: GMAT Diagnostic Test Question 7 [#permalink]  10 Aug 2009, 07:17
Quote:
You might think of these two fractions as an extreme example:

and

The difference between numerator and denominator is the same for both fractions, as you can see. There's no doubt, though, that the first fraction is very close to 1, unlike the second one. So, having in mind the same difference between numerators and denominators of the fractions in the answer choices, the greater numerator (denominator) of the fraction, the greater the fraction.

Hope this helps .

Thanks for elaborating, this actually helps a lot
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Re: GMAT Diagnostic Test Question 7 [#permalink]  10 Aug 2009, 08:24
Welcome to the forum, shaknon!

We hope you like our community and will become an active participant . Good luck with your GMAT journey!
shaknon wrote:
Quote:
You might think of these two fractions as an extreme example:

and

The difference between numerator and denominator is the same for both fractions, as you can see. There's no doubt, though, that the first fraction is very close to 1, unlike the second one. So, having in mind the same difference between numerators and denominators of the fractions in the answer choices, the greater numerator (denominator) of the fraction, the greater the fraction.

Hope this helps .

Thanks for elaborating, this actually helps a lot

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Re: GMAT Diagnostic Test Question 7 [#permalink]  08 Oct 2009, 21:17
Expert's post
linfongyu wrote:
I doubt the actual GMAT would ever arrange the answer choices in such order.

It would most likely do such as:

a. 1876452/1876455
b. 1876456/1876459
c. 1876460/1876463
d. 1876464/1876467
e. 1876468/1876471

Thanks! That's right. Need to rearrange (though only one is 187... - others are 188...)
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Re: GMAT Diagnostic Test Question 7 [#permalink]  09 Oct 2009, 04:31
I've updated the PDF, Answers Sheet and the online version of the test.
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Re: GMAT Diagnostic Test Question 7 [#permalink]  09 Oct 2009, 05:28
dzyubam wrote:

Guess its E. This spun me around for some time
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Re: GMAT Diagnostic Test Question 7 [#permalink]  09 Oct 2009, 09:40
We've reordered the answer choices per linfongyu's suggestion. The answer is E now, as stated in the OE.
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Re: GMAT Diagnostic Test Question 7 [#permalink]  19 Dec 2009, 12:24
this is a good concept to learn. I got it wrong because I thought it's the other way around.
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Re: GMAT Diagnostic Test Question 7 [#permalink]  14 Jan 2010, 19:41
My answer was D. I compared fractions. 2/5 was smaller than 6/9, 6/9 was greater than 3/6 & = to 6/9 but > than 1/4. I guess I should have known that the correct answer wouldn't be either of the numbers w/ 6/9. Still don't understand how it's E though..
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Re: GMAT Diagnostic Test Question 7 [#permalink]  16 Feb 2010, 19:14
manojmakkatt wrote:
1876452/1876455 = 1876455/1876455 - 3/1876455 = 1- 3/1876455
1883456/1883459 = 1883459/1883459 - 3/1883459 = 1- 3/1883459
1883491/1883494 = 1883494/1883494 - 3/1883494 = 1- 3/1883494 = LARGEST
(3/1883494 - SMALLEST)
1883446/1883449 = 1883449/1883449 - 3/1883449 = 1- 3/1883449
1883453/1883456 = 1883456/1883456 - 3/1883456 = 1- 3/1883456

if you look at it this way, it all makes sense seems like a piece of cake, however when you're doing it in a test, I for one, stump and get nervous and just counting seconds on my mind when handing too many similar looking numbers like this one.
anyone has a tip for me in how to go about taking control of this stress?
also does anyone know how to go training your mind to thinking this way in the exam?

thanks
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Re: GMAT Diagnostic Test Question 7 [#permalink]  02 Apr 2010, 05:23
meganbaxter1 wrote:
manojmakkatt wrote:
1876452/1876455 = 1876455/1876455 - 3/1876455 = 1- 3/1876455
1883456/1883459 = 1883459/1883459 - 3/1883459 = 1- 3/1883459
1883491/1883494 = 1883494/1883494 - 3/1883494 = 1- 3/1883494 = LARGEST
(3/1883494 - SMALLEST)
1883446/1883449 = 1883449/1883449 - 3/1883449 = 1- 3/1883449
1883453/1883456 = 1883456/1883456 - 3/1883456 = 1- 3/1883456

if you look at it this way, it all makes sense seems like a piece of cake, however when you're doing it in a test, I for one, stump and get nervous and just counting seconds on my mind when handing too many similar looking numbers like this one.
anyone has a tip for me in how to go about taking control of this stress?
also does anyone know how to go training your mind to thinking this way in the exam?

thanks

The only way I know is to practice, practice, and practice; that way, you become familiar with a lot
of concepts tested on the exam, and your confidence level boosts while, at the same
time, your time of solving questions shrinks...
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Re: GMAT Diagnostic Test Question 7   [#permalink] 02 Apr 2010, 05:23

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# GMAT Diagnostic Test Question 7

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