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A certain thermometer measured the temperature in City X in degreed Fa
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Hoozan
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A certain thermometer measured the temperature in City X in degreed Fa [#permalink] New post  07 Feb 2021, 02:44
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A certain thermometer measured the temperature in City X in degreed Fahrenheit every day for one month, and found that the range of temperatures was 21 degrees. If, subsequently, it was discovered that the thermometer always overstated the temperature by 15%, what would the approximate range of measurements have been, in degrees, if the temperatures had been measured accurately?

(A) 15
(B) 17
(C) 18
(D) 21
(E) 24
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Abdul29
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Re: A certain thermometer measured the temperature in City X in degreed Fa [#permalink] New post  07 Feb 2021, 03:21
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There's probably a quicker way to do this, but I opted for a manual way. 0.15 * 21 = 3.15. Because of overestimation, we subtract 3.15 from 21, resulting in approximately 18.
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stne
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A certain thermometer measured the temperature in City X in degreed Fa [#permalink] New post  15 Feb 2021, 08:04
Hoozan wrote:
A certain thermometer measured the temperature in City X in degreed Fahrenheit every day for one month, and found that the range of temperatures was 21 degrees. If, subsequently, it was discovered that the thermometer always overstated the temperature by 15%, what would the approximate range of measurements have been, in degrees, if the temperatures had been measured accurately?

(A) 15
(B) 17
(C) 18
(D) 21
(E) 24


Let lower temp. be 100 and higher 121

Now these are 15% more than actual reading. Hence actual reading:

\(100= \frac{115}{100}x\) and \(121= \frac{115}{100}y\)

Where \(x\) is the actual lower temp. and \(y\) is the actual higher temp.

\(x= \frac{2000}{23}\) and \(y= \frac{2420}{23}\)

Actual range:

\(\frac{2420}{23} - \frac{2000}{23} = \frac{420}{23} =18.26 \approx 18\)

Ans-C

Hope it helps.
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