DAT Question of the Day

Correct Answer: C. 4

After the first ball is picked, the second may not be the same color. After two balls picked, the third may still be a different color than the first two (since there are a total of 3 colors). But when the fourth ball is picked, it must match one of the prior colors. Therefore, picking 4 balls will ensure that you have at least one set of 2 balls with the same color.

The numbers 5, 7, 8 do not matter here (they could matter if these numbers were lower, or the number of balls picked were higher).

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Correct Answer: D. 13

If we denote the hypotenuse of the triangle as c and the two other sides as a and b, then the values of the area and perimeter can be written as (1/2)ab = 30 and a + b + c = 30. We have three unknowns but two equations so far. However, a right triangle also follows the relation a² + b² = c². We can now solve these three equations and obtain c = 13.

However, the “spirit” of the problem is not checking whether you can solve this system of 3 equations (which is pretty complicated!) – instead, this problem is trying to see if you can come up with a “shortcut” to get to the right answer. Since both the perimeter and area are both nice, whole numbers, we can conclude that the lengths of the sides are also nice, whole numbers, most likely from one of the “special” triangles that we know about (eg. 3-4-5, 5-12-13) or a similar triangle. We can immediately see that the sides of the 5-12-13 triangle add up to 30. The area of the 5-12-13 triangle is 30 as well, and we can thus get to the correct answer without doing any solving at all. The work is shown below for your convenience, however.

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Correct Answer: B. 20√2

As can be seen from the figure below, the diagonal of the square is equal to the diameter of the circle, which is 5×2=10 cm. If the length of one side of the square is x, the diagonal is given by √2 x. Therefore, √2(x) = 10 -> x = 5√2 and the perimeter is 4 × 5√2 = 20√2.

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