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There are 3 cards, each has a different number. Two of them are turned face down as shown. One is turned face up. When the numbers are added two at a time, the sums are 70, 85 and 95. Find the difference of the highest and lowest number on these 3 cards.

(A) 25 (B) 35 (C) 45 (D) 40

1 Answer

There are 3 cards, or 3 numbers, one of them is known to us as 55.
The sum of the cards, two numbers at a time is 70, 85 and 95.
Let the numbers be A, B and C.
So, A+B = 70, B+C = 85 and C+A = 95.
Let us assume that C = 55 for now.
If C = 55, then B + C = B + 55 = 85, which means that B = 85 - 55 = 30.
If C = 55, then C + A = 55 + A = 95, which means that A = 95 - 55 = 40.
We can see that A + B is then 40 + 30 = 70 which is already given. So, A, B and C must be 40, 30 and 55.
Therefore, the difference of the highest and lowest number on these 3 cards is 55 - 30 = 25.
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