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a = 4 6 < b < 8
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04 Mar 2018, 13:50
04 Mar 2018, 13:50
Expert Reply
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Question Stats:
83% (00:42) correct
16% (00:37) wrong based on 56 sessions
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\(a = 4\)
\(6 < b < 8\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
\(6 < b < 8\)
Quantity A |
Quantity B |
0.6 |
\(\frac{a}{b}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Drill 1
Question: 12
Page: 495
Question: 12
Page: 495
Re: a = 4 6 < b < 8
[#permalink]
04 Mar 2018, 14:19
04 Mar 2018, 14:19
1
Expert Reply
Explanation
Start by combining the 2 given equations:
If \(a = 4\) and \(6 < b < 8\), then the acceptable range for \(\frac{a}{b}\) is \(\frac{4}{6}>\frac{a}{b}>\frac{4}{8}\), which can be reduced to or, in decimal form, \(0.5 <\frac{a}{b}< 0.67\).
Select choice (D) because can be either larger or smaller than 0.6.
Start by combining the 2 given equations:
If \(a = 4\) and \(6 < b < 8\), then the acceptable range for \(\frac{a}{b}\) is \(\frac{4}{6}>\frac{a}{b}>\frac{4}{8}\), which can be reduced to or, in decimal form, \(0.5 <\frac{a}{b}< 0.67\).
Select choice (D) because can be either larger or smaller than 0.6.
Re: a = 4 6 < b < 8
[#permalink]
05 Mar 2018, 18:26
05 Mar 2018, 18:26
1
answer D
we calculate the minimum and maximum of a/b
min : 4/8 = 1/2 with is less than 0.6
max : 4/6 = 2/3 with is more than 0.6
also, we have:
6<b<8
1/8 < 1/b < 1/6
a/8 < a/b < a/6
4/8 < a/b < 4/6
1/2 < a/b < 2/3
so the range of a/b is less than 0.6 from 1/2 to 0.6 and is more than 0.6 from 0.6 to 2/3 and thus D is correct.
we calculate the minimum and maximum of a/b
min : 4/8 = 1/2 with is less than 0.6
max : 4/6 = 2/3 with is more than 0.6
also, we have:
6<b<8
1/8 < 1/b < 1/6
a/8 < a/b < a/6
4/8 < a/b < 4/6
1/2 < a/b < 2/3
so the range of a/b is less than 0.6 from 1/2 to 0.6 and is more than 0.6 from 0.6 to 2/3 and thus D is correct.
