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27 percent of p is 100. p is q percent of 100.
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03 Apr 2017, 02:26
03 Apr 2017, 02:26
Expert Reply
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Question Stats:
80% (01:16) correct
19% (01:07) wrong based on 109 sessions
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27 percent of p is 100.
p is q percent of 100.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
p is q percent of 100.
Quantity A |
Quantity B |
q |
400 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Drill 2
Question: 1
Page: 318
Question: 1
Page: 318
Re: 27 percent of p is 100. p is q percent of 100.
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03 Apr 2017, 05:21
03 Apr 2017, 05:21
Expert Reply
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Explanation
To find exact values for p and q, apply percent translation:
\(\frac{27}{100} \times p =100\), so
\(\frac{27p}{100} =100\),
\(27p = 10000\), and \(p = 370.37\);
p is q percent of 100, so q = 370.37 as well.
Hence Quantity B is greater.
Alternatively, you could avoid the calculation altogether and Ballpark this one all the way through: 100 is more than 25% (or \(\frac{1}{4}\)) of p, so p must be less than 400—and so must q.
To find exact values for p and q, apply percent translation:
\(\frac{27}{100} \times p =100\), so
\(\frac{27p}{100} =100\),
\(27p = 10000\), and \(p = 370.37\);
p is q percent of 100, so q = 370.37 as well.
Hence Quantity B is greater.
Alternatively, you could avoid the calculation altogether and Ballpark this one all the way through: 100 is more than 25% (or \(\frac{1}{4}\)) of p, so p must be less than 400—and so must q.
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27 percent of p is 100. p is q percent of 100.
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04 Apr 2017, 10:01
04 Apr 2017, 10:01
1
sandy wrote:
27 percent of p is 100.
p is q percent of 100.
p is q percent of 100.
Quantity A |
Quantity B |
q |
400 |
27 percent of p is 100
So, (27/100)(p) = 100
Multiply both sides by 100 to get: 27p = 10,000
Solve: p = 10,000/27
p is q percent of 100
In other words, p = (q/100)(100)
Simplify: p = q
Replace p with 10,000/27 to get: 10,000/27 = q
IMPORTANT: Since 10,000/25 = 400, we know that 10,000/27 will be a little less than 400
We get:
Quantity A: a number that's a little less than 400
Quantity B: 400
Answer: B
