The temperature of a place at noon on a certain day is 25%

[VJesus12]

The temperature of a place at noon on a certain day is 25% higher than the temperature of the same place at midnight on the same day. What is the temperature of the place at midnight?

(1) The temperature of the place at midnight is 20% lower than the temperature of the same place at noon.
(2) The temperature of the place at noon is 10 units greater than the temperature of the place at midnight.

The OA is the option B.

How can I get the temperature? I don't have any idea of how to solve this DS question? <i class="em em-sob"></i>

Source: e-GMAT

[[email protected]]

Hi All,

We're told that the temperature of a place at noon on a certain day is 25% higher than the temperature of the same place at midnight on the same day. We're asked for the temperature of the place at midnight. This question can be solved in a couple of different ways, but it's actually based on a 'math truism' (and knowing that truism can save you some time.

1) The temperature of the place at midnight is 20% lower than the temperature of the same place at noon.

The information in Fact 1 is the 'truism' that I mentioned earlier. If one number is 25% greater than a second number, then that second number is 20% less than the first. For example, consider the numbers 100 and 125..
125 = 25 more than 100 = 25/100 = 25% greater
100 = 25 less than 125 = 25/125 = 20% less

This is NOT 'new information'; it means the same as what the prompt gave us. As long as the temperature at noon is 25% higher than the temperature at midnight, then that measure is a possible answer to this question (for example, 4 and 5, 8 and 10, 12 and 15, etc.
Fact 1 is INSUFFICIENT

2) The temperature of the place at noon is 10 units greater than the temperature of the place at midnight.

The information in Fact 2 gives us a second unique equation, so we can set up a 'system' of equations. If X = the temperature at noon and Y = the temperature at midnight....
X = 1.25Y
X = Y + 10
With this 2 variable 'system', we can solve for Y (and there would be just one solution, so we don't actually have to do the math). If you did solve it though, you would end up with X=50 and Y=40
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich