Temperature on the Celsius scale (C) is related to temperature on the Fahrenheit scale (F) by the formula C = 5/9(F- 32). What is the difference between a certain pair of temperatures on the Celsius scale?
(1) The difference between the temperatures on the Fahrenheit scale is 45°.
(2) The greater of the two temperatures is 30° on the Celsius scale
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Temperature on the Celsius scale (C) is related
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GMATGuruNY
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I received a PM requesting that I comment.NandishSS wrote:Temperature on the Celsius scale (C) is related to temperature on the Fahrenheit scale (F) by the formula C = 5/9(F-32). What is the difference between a certain pair of temperatures on the Celsius scale?
(1) The difference between the temperatures on the Fahrenheit scale is 45°.
(2) The greater of the two temperatures is 30° on the Celsius scale
C = 5(F-32)/9.
To make the math easier, test values such that F-32 is a multiple of 9.
F-32 = 0, 9, 18...
F = 32, 41, 50...
Statement 1:
Case 1: lower F = 32, higher F = 32+45
Higher temperature on the Celsius scale = (5/9)(32+45-32) = 25.
Lower temperature on the Celsius scale = (5/9)(32-32) = 0.
Difference = 25-0 = 25.
Case 2: lower F = 41, higher F = 41+45
Higher temperature on the Celsius scale = (5/9)(41+45-32) = 30.
Lower temperature on the Celsius scale = (5/9)(41-32) = 5.
Difference = 30-5 = 25.
Since the difference is the same in each case, SUFFICIENT.
Statement 2:
Since the lower temperature can be any value, the difference between the higher temperature and the lower temperature cannot be determined.
INSUFFICIENT.
The correct answer is A.
Last edited by GMATGuruNY on Mon Sep 05, 2016 7:20 pm, edited 1 time in total.
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We're looking for the difference between two temperatures on the Celsius scale. Call them C1 and C2. So we want C2 - C1.
Statement 1: Algebraically, if we have a difference of 45 between the Fahrenheit temps, say C1= 5/9(F - 32) and C2= 5/9[(F + 45) - 32.]
C2 - C1 --> 5/9[(F + 45) - 32] - [5/9(F - 32).] The terms in red will cancel, leaving us with (5/9)F + (5/9)*45 - (5/9)F = (5/9) * 45 = 25. A 45 degree difference on the Fahrenheit scale is a 25 degree difference on the Celsius scale. Sufficient.
S2: only gives info about the greater temp, so clearly not sufficient.
Answer is A
Statement 1: Algebraically, if we have a difference of 45 between the Fahrenheit temps, say C1= 5/9(F - 32) and C2= 5/9[(F + 45) - 32.]
C2 - C1 --> 5/9[(F + 45) - 32] - [5/9(F - 32).] The terms in red will cancel, leaving us with (5/9)F + (5/9)*45 - (5/9)F = (5/9) * 45 = 25. A 45 degree difference on the Fahrenheit scale is a 25 degree difference on the Celsius scale. Sufficient.
S2: only gives info about the greater temp, so clearly not sufficient.
Answer is A
