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Difficulty:
75%
(hard)
Question Stats:
63% (02:17) correct
38%
(02:33)
wrong
based on 1248
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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 15062 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 15062 times ]
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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.
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General Discussion
gmatophobia
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Joined: 22 Dec 2016
Last visit: 09 Sep 2026
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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
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Bunuel, I was able to find the difference 0.0065, however, I couldn't deduce the range for this difference and hence ended up selecting A.
How I can check which range this number in?
How I can check which range this number in?
babyulikeit
Joined: 04 Jul 2024
Last visit: 14 May 2025
Posts: 24
Location: India
GMAT Focus 1: 695 Q85 V85 DI83 
GMAT Focus 1: 695 Q85 V85 DI83
Posts: 24
AnkurGMAT20
AnkurGMAT20
A simple way would be to add zeros at the end of the decimal value as it makes it easier to check.
eg. - you got .0065 and want to test whether it falls under the .005 to .01 range, add zeros in front of the range numbers so that the digits after the decimal are equal between your answer (.0065) and the range.
.0050 and .0100 - so now you can directly compare as you would any number - here 65 falls between 50 and 100 so that's the answer.
GMAT Focus 1: 575 Q77 V81 DI78 
Posts: 106
AnkurGMAT20
Multiply 0.0065 by 1000 to get 6.5 and now answer choice figures multiplied by 1000 should give us the lower/upper ranges, multiply C by 1000 to get the 5-10 range and 6.5 falls within this range. Ans C.
Reading the question, we see the answer choices are in decimals, which is a clue that working with decimals may be easier. Converting the fractions to decimals:
\(4\frac{7}{8}\) = 4.875
\(5\frac{1}{4}\) = 5.250
\(4\frac{3}{5}\) = 4.600
\(5\frac{1}{8}\) = 5.125
The greatest difference would be the biggest - smallest: 5.250 - 4.600 = 0.650
Since these are percents, we need to move the decimal place two places to the left: 0.0065
or
\(4\frac{7}{8}\) = 0.04875
\(5\frac{1}{4}\) = 0.05250
\(4\frac{3}{5}\) = 0.04600
\(5\frac{1}{8}\) = 0.05125
0.05250 - 0.04600 = 0.00650
\(4\frac{7}{8}\) = 4.875
\(5\frac{1}{4}\) = 5.250
\(4\frac{3}{5}\) = 4.600
\(5\frac{1}{8}\) = 5.125
The greatest difference would be the biggest - smallest: 5.250 - 4.600 = 0.650
Since these are percents, we need to move the decimal place two places to the left: 0.0065
or
\(4\frac{7}{8}\) = 0.04875
\(5\frac{1}{4}\) = 0.05250
\(4\frac{3}{5}\) = 0.04600
\(5\frac{1}{8}\) = 0.05125
0.05250 - 0.04600 = 0.00650
guddo
The greatest difference between any two rates will be between the smallest and the greatest rates.
Diff between 4(3/5) and 5 (1/4) is 2/5 + 1/4 = 13/20 (Think about them on the number line)
13/20 is 0.65 so 0.65% is .0065. Note that .006 lies between .005 and .01.
Answer (C)
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how i did was
5& 2/8 > 5 & 1/8 > 4 & 7/8
now 4 & 7/8 os nothing but 4 & 35/40 and compare it with 4 & 24/40 we get farthest are 4 & 24/40 and 5 & 2/8
read them as 4+0.6 and 5 + .25
subtract these = 0.65%
In decimal this is 0.0065
5& 2/8 > 5 & 1/8 > 4 & 7/8
now 4 & 7/8 os nothing but 4 & 35/40 and compare it with 4 & 24/40 we get farthest are 4 & 24/40 and 5 & 2/8
read them as 4+0.6 and 5 + .25
subtract these = 0.65%
In decimal this is 0.0065
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