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# m10 #22

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19 Apr 2012, 05:07
Easy C. just have to approx both top and bottom and see that it will be slightly less than 1.

What level are the daily gmat questions? It says from the GMAT club tests hardest questions but all the quantitative ones seem pretty easy.
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19 Apr 2012, 09:38
1
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Split the 998 and 1002 as 1000-2 and 1000+2 .

Hey, dont we have the GMAT club Timer available here?

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19 Apr 2012, 12:31
answer C. This is less than 1 and the numerator is very close to the denominator.
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20 Apr 2012, 02:28
x-1/x reaches to .5 for x=2;to .9 for x=10 ;to .95 for x=20.

so 24.93/25.07 > 24.93/25.93 >.95

C.
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21 Apr 2012, 02:30
(998/1002) * 0,02 = 19.96/20.04 which is 9.98 /10.02
The numbers that we add in both parts are 4.97/5.03 which is equal to 9.94/10.06

It is certain that we can not reach the ratio 1, because you increase upper part less than below part .So it is imposible to reach the ratio 1.
In order to reach 1 you have to increase upper part more than below part.
The ratio between than have to be [(19.96/20.04),(4.97/5.03)]

In general it is certain that (a+b)/(c+d) , the ratio will be between [a/c , b/d] and will be closer the ratio which's number are bigger.
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22 Apr 2013, 06:44
Which of the following is closest to $$\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}$$ ?

A. 0.50
B. 0.89
C. 0.98
D. 1.02
E. 1.05

Notice that the numerator is slightly less than the denominator: $$\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}\approx{\frac{20+4.97}{20+5.03}}$$, thus the fraction will be less, but very close to 1.

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22 Apr 2013, 18:51
After increasing the numerator i.e (1000*0.02 + 5) and decreasing the denominator i.e (1000*0.02 + 5), the resulting fraction is 1. Thus the answer should be 0.98.
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23 Apr 2013, 05:05
GMAT TIGER wrote:
tejal777 wrote:
Which of the following is closest to $$\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}$$ ?

(C) 2008 GMAT Club - m10#22

* 0.50
* 0.89
* 0.98
* 1.02
* 1.05

The OE is not clear..i did it without rounding it off and not getting the answer:(

Let’s use some logic..

By observation, numerator is very close too denominator.

D/E are out as numerator cannot be > denominator.
A is also out because numerator is substantially > 1/2(denominator).
B is equivalent to 90% i.e. numerator < 90% (denominator) where as .

So left with C.

Alternatively:

= $$\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}$$
= $$\frac{(1000 - 2) *0.02 + 4.97)}{(1000+2)*0.02 + 5.03)}$$
= $$\frac{(20 - 0.04) + 4.97)}{(20 + 0.04) + 5.03)}$$
= $$\frac{(19.96 + 4.97)}{(20.04) + 5.03)}$$
= $$\frac{(24.93)}{(25.07)}$$
= equivalent to 1 but < 1, which is 0.98....

In 30 second, it is known that OA is C....

Almost did it in similar fashion but with less computation i guess....

= $$\frac{(998*0.02 + 4.97)}{(1002*0.02 + 5.03)}$$
= $$\frac{(1000 - 2) *0.02 + (5 - .03)}{(1000+2)*0.02 + (5 + .03)]}$$

Now Let 1000 be replaced with 'X' and 5 with 'Y', then the resultant fraction is:

= $$\frac{(X - 0.04) + (Y - .03)}{(20 + 0.04) + 5.03)}$$
= $$\frac{(X + Y - .07)}{(X + Y + .07)}$$
= 1 - $$\frac{(.21)}{(X + Y + .07)}$$
= 1 - ~.0001 => 0.9998

So the closest value is 0.98...
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23 Apr 2013, 08:18
Which of the following is closest to ?

(C) 2008 GMAT Club - m10#22

* 0.50
* 0.89
* 0.98
* 1.02
* 1.05

{(998 x 0.02) + 4.97}/{(1002 x 0.02) + 5.03} can approximately be written as {(1000 x 0.02) + 5}/{(1000 x 0.02) + 5} keeping in mind that we increased the numerator overall and decreased the denominator overall, thereby increasing the value of the fraction.

However, after having done so, the value of the fraction becomes 1. We know the original fraction is close to 1. We have two options 1.02 and 0.98. We also know that while rewriting the fraction, we increased its value from the original, therefore the original has to be less than 1. So, I go with C.
Re: m10 #22   [#permalink] 23 Apr 2013, 08:18

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# m10 #22

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