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Cornfield problem

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by karthikpandian19 » Mon Dec 26, 2011 3:18 am
The corn crops of Moses, each of which is 27 acres, have been damaged by the rootworm pest.

3/11 of Cornfield A has been destroyed. While, 8/25 of the crop in cornfields B and C was lost. Cornfield D has been totally ruined and only 1/9 of cornfield E was left undamaged. 1/6 and 1/7 of cornfields F and G were damaged, respectively. Which of the following is the closest approximation for the number of unharmed acres in Moses' cornfields ?

57
84
105
111
126
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by rijul007 » Mon Dec 26, 2011 4:39 am
karthikpandian19 wrote:The corn crops of Moses, each of which is 27 acres, have been damaged by the rootworm pest.

3/11 of Cornfield A has been destroyed. While, 8/25 of the crop in cornfields B and C was lost. Cornfield D has been totally ruined and only 1/9 of cornfield E was left undamaged. 1/6 and 1/7 of cornfields F and G were damaged, respectively. Which of the following is the closest approximation for the number of unharmed acres in Moses' cornfields ?

57
84
105
111
126
3/11 of Cornfield A has been destroyed
Unharmed area in A = 8/11 of 27 acres

8/25 of the crop in cornfields B and C was lost.
UNharmed area = 2 * ( 17/25 of 27 acres) = 34/25 of 27
only 1/9 of cornfield E was left undamaged.
1/6 and 1/7 of cornfields F and G were damaged
Unharmed acres in F = 5/6 of 27
Unharmed acres in G = 6/7 of 27


Total acres of undamaged land = (8/11 + 34/25 + 1/9 +5/6 + 6/7 ) of 27
= (0.7 + 1.5 + 0.1 + 0.8 +0.9 ) of 27 approx
= 4 * 27 approx = 108

Option C is the closest
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by karthikpandian19 » Tue Dec 27, 2011 9:45 pm
OA is 105
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Why approximate such a way

by TusharV » Mon Jan 11, 2021 3:34 am
rijul007 wrote: ↑
Mon Dec 26, 2011 4:39 am
karthikpandian19 wrote:The corn crops of Moses, each of which is 27 acres, have been damaged by the rootworm pest.

3/11 of Cornfield A has been destroyed. While, 8/25 of the crop in cornfields B and C was lost. Cornfield D has been totally ruined and only 1/9 of cornfield E was left undamaged. 1/6 and 1/7 of cornfields F and G were damaged, respectively. Which of the following is the closest approximation for the number of unharmed acres in Moses' cornfields ?

57
84
105
111
126
3/11 of Cornfield A has been destroyed
Unharmed area in A = 8/11 of 27 acres

8/25 of the crop in cornfields B and C was lost.
UNharmed area = 2 * ( 17/25 of 27 acres) = 34/25 of 27
only 1/9 of cornfield E was left undamaged.
1/6 and 1/7 of cornfields F and G were damaged
Unharmed acres in F = 5/6 of 27
Unharmed acres in G = 6/7 of 27


Total acres of undamaged land = (8/11 + 34/25 + 1/9 +5/6 + 6/7 ) of 27
= (0.7 + 1.5 + 0.1 + 0.8 +0.9 ) of 27 approx
= 4 * 27 approx = 108

Option C is the closest
I found this question so difficult because you've to make so many approximations in such little time and these approximations aren't easy without any calculator because the uncertainty starts to become significant and the answers aren't spread out enough to eliminate that uncertainty. Even the answer approximated '108', is equally close to 105 as to 111 so I'm not quite sure why 105 was chosen over 111 as the answer.
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