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# M10-22

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Math Expert
Joined: 02 Sep 2009
Posts: 58396

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16 Sep 2014, 00:42
2
3
00:00

Difficulty:

25% (medium)

Question Stats:

80% (00:44) correct 20% (00:43) wrong based on 80 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 58396

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16 Sep 2014, 00:42
1
1
Official Solution:

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 than, but very close to 1.

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Intern
Joined: 21 Oct 2015
Posts: 45
GMAT 1: 620 Q47 V28

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17 May 2016, 21:43
What's the harm in ignoring 0.02 in numerator/denominator? I suppose minimal. Also, let's approximate other numbers.

4.97 -> 5
5.03 -> 5

Equation becomes:
(998+5)/(1002+5) = 1003/1007

Too close. C would be the best approximation.

Cheers.

Posted from my mobile device
Intern
Joined: 05 Oct 2017
Posts: 43
Concentration: Accounting, Social Entrepreneurship

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18 Oct 2018, 04:23
1
Bunuel wrote:
Official Solution:

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 than, but very close to 1.

after a little bit calculation I got 24.93 as numerator and 25.07 as denominator. then I ended up selecting answer choice D.
The numerator is slightly greater than 25. why don't you consider that?
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Math Expert
Joined: 02 Sep 2009
Posts: 58396

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18 Oct 2018, 04:26
1
rashedBhai wrote:
Bunuel wrote:
Official Solution:

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 than, but very close to 1.

after a little bit calculation I got 24.93 as numerator and 25.07 as denominator. then I ended up selecting answer choice D.
The numerator is slightly greater than 25. why don't you consider that?

even according to your calculations the numerator (24.93) is LESS than the denominator (25.07), so the fraction must be less than 1.
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Intern
Joined: 05 Oct 2017
Posts: 43
Concentration: Accounting, Social Entrepreneurship

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18 Oct 2018, 05:10
got it. Thanks.

Posted from my mobile device
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Re: M10-22   [#permalink] 18 Oct 2018, 05:10
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# M10-22

Moderators: chetan2u, Bunuel