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04 Feb 2022, 08:45
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Difficulty:
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92% (01:21) correct
8%
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wrong
based on 51
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In a poll of 44,000 dentists, only 30 percent responded; of these, 20 percent claimed to prefer Toothpaste A. How many of the dentists who responded did not claim a preference for Toothpaste A?
A. 2,200
B. 2,640
C. 6,160
D. 8,800
E. 10,560
A. 2,200
B. 2,640
C. 6,160
D. 8,800
E. 10,560
04 Feb 2022, 10:43
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Before you jump into just "DO THE MATH OKAY 30% of 44,000, let's calculate that... 30/100 * 44,000 okay that's 30 * 440 OKAY SO that's..."
Take some time to *understand the situation first*.
30% of the dentists responded. Of those 20% preferred A. We're asked how many of the dentist who responded and did NOT prefer A. So that's the other 80% of the respondents.
Okay so that's 80% of the 30% of the total.
When dealing with 'sub-portions of a portion,' you can treat the 'portion' as its own whole. That is, just think of 80% of **30**. That's (4/5)*30 = 24.
So 80% of 30% of a total is **24% of the total**.
So what is 24% of 44,000?
BUT WAIT DON'T DO MATH FOR GOD'S SAKE.
I'm looking for an answer slightly less than 1/4 (44,000). So a little less than 11,000.
E.
I'm pretty fast with arithmetic, and I still avoid it any chance I can.
IMPORTANT TAKEAWAYS:
--Understand the whole situation before doing a bunch of calculations (a few easy ones are fine, but as soon as you groan inside... WAIT. It'll be there if you need to do it later)
--"Percents of a (percent of a total)" are often easier thought of as "(Percents of a percent) of a total"
--Use nearby, easy percents to estimate (in this problem, 25% is close to 24%), and narrow down answers, sometimes to the only one.
Take some time to *understand the situation first*.
30% of the dentists responded. Of those 20% preferred A. We're asked how many of the dentist who responded and did NOT prefer A. So that's the other 80% of the respondents.
Okay so that's 80% of the 30% of the total.
When dealing with 'sub-portions of a portion,' you can treat the 'portion' as its own whole. That is, just think of 80% of **30**. That's (4/5)*30 = 24.
So 80% of 30% of a total is **24% of the total**.
So what is 24% of 44,000?
BUT WAIT DON'T DO MATH FOR GOD'S SAKE.
I'm looking for an answer slightly less than 1/4 (44,000). So a little less than 11,000.
E.
I'm pretty fast with arithmetic, and I still avoid it any chance I can.
IMPORTANT TAKEAWAYS:
--Understand the whole situation before doing a bunch of calculations (a few easy ones are fine, but as soon as you groan inside... WAIT. It'll be there if you need to do it later)
--"Percents of a (percent of a total)" are often easier thought of as "(Percents of a percent) of a total"
--Use nearby, easy percents to estimate (in this problem, 25% is close to 24%), and narrow down answers, sometimes to the only one.
vaibhav1221
Joined: 19 Nov 2017
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Schools: IIMA '25 (A) Columbia CBS'26 (D) Fuqua '26 (D) ISB '25 (WL) Darden '26 (D) Kenan-Flagler '26 (WL)
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Schools: IIMA '25 (A) Columbia CBS'26 (D) Fuqua '26 (D) ISB '25 (WL) Darden '26 (D) Kenan-Flagler '26 (WL)
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07 Feb 2022, 09:52
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If 20% of the respondents like toothpaste A, then 80% did not like toothpaste A.
Number of people who did not like toothpaste A = \(44,000*(\frac{30}{100})*(\frac{80}{100})\)
\(= 440*24\\
= 440(20+4)\\
= 8800 + 440*4\)
You can stop at this point and mark E or calculate further and then mark E.
\(= 8800 + 1760\\
= 10,560\)
Number of people who did not like toothpaste A = \(44,000*(\frac{30}{100})*(\frac{80}{100})\)
\(= 440*24\\
= 440(20+4)\\
= 8800 + 440*4\)
You can stop at this point and mark E or calculate further and then mark E.
\(= 8800 + 1760\\
= 10,560\)
