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Four banks offered home equity loans at the rates of \(4 \frac{7}{8}\) percent, \(5 \frac{1}{4}\) percent, \(4 \frac{3}{5}\) percent, and \(5 \frac{1}{8}\) percent, respectively. The greatest difference between any two of these rates, expressed as a decimal, is between
A. 0.0001 and 0.0005
B. 0.001 and 0.005
C. 0.005 and 0.01
D. 0.01 and 0.05
E. 0.05 and 0.1
2024-01-29_22-15-56.png [ 47.67 KiB | Viewed 12664 times ]
A. 0.0001 and 0.0005
B. 0.001 and 0.005
C. 0.005 and 0.01
D. 0.01 and 0.05
E. 0.05 and 0.1
Attachment:
2024-01-29_22-15-56.png [ 47.67 KiB | Viewed 12664 times ]
29 Jan 2024, 13:11
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guddo
The greatest difference would be between the largest and smallest numbers, so it would be:
- \(5 \frac{1}{4}\% - 4 \frac{3}{5}\% = \)
\(=\frac{21}{4}\% - \frac{23}{5}\%=\)
\(=\frac{105}{20}\% - \frac{92}{20}\%=\)
\(= \frac{13}{20}\% = \)
\(= \frac{65}{100}\% = \)
\(= 0.65 \% \)
Expressed as decimal, 0.65%, is 0.65/100 = 0.0065, which is between 0.005 and 0.01.
Answer: C.
29 Jan 2024, 23:12
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guddo
\(4 \frac{7}{8} = \frac{39}{8}\)
\(5 \frac{1}{4} = \frac{42}{8}\)
\(4 \frac{3}{5} = \frac{23}{5}\)
\(5 \frac{1}{8} = \frac{41}{8}\)
The LCM of the denominator = 40
\(4 \frac{7}{8} = \frac{39*5}{8*5} = \frac{195}{40}\)
\(5 \frac{1}{4} = \frac{42}{8}= \frac{210}{40}\)
\(4 \frac{3}{5} = \frac{23}{5}= \frac{184}{40}\)
\(5 \frac{1}{8} = \frac{41}{8}= \frac{205}{40}\)
The greatest number is \(\frac{210}{40}\) and the least number is \(\frac{184}{40}\)
\(\frac{210}{40} - \frac{184}{40} = \frac{26}{40}\)
All the above numbers are in percentage.
Hence, \(\frac{26}{40}* \frac{1}{100} = \frac{26}{4}*10^{-3} = 6.5 * 10^{-3} = 0.0065\)
Option C
