DAT Question of the Day

Correct Answer: C. (13×12)/(52×51)

The number of ways 2 cards can be chosen from 52 is (52¦2) = (52×51) / 2, and the number of ways 2 cards can be picked from 13 diamonds is (13¦2) = (13×12) / 2. The ratio of the latter to the former is the required probability.

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Correct Answer: B. 5 to 3

If 3 out of every 8 people are women, then the remaining 5 are men. So the ratio of men to women is 5 to 3.

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Correct Answer: B. 40y²/x

If the answer is B, then the equation 25x/40y = 25y/B must be true, which yields B = 40y²/x

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Correct Answer: D. 720

This is clearly a permutation problem since the order of the books matters. The number of arrangements is ⁶P6 = 6! = 720.

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Correct Answer: C. 68%

This question doesn’t require any calculation, but rather knowledge of the standard deviation sets. Typically, about 68% is included in the first standard deviation, and 95% is included in the 2nd standard deviation. 99.5% of all people fall within three standard deviations of the mean in the normal curve.

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Correct Answer: A. 5:4

We need to figure out which numbers are primes and which ones are composite. The following shows primes in blue and composites in red: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Note that 1 is neither prime nor composite, it only has one factor. We have 5 reds and 4 blues. The correct answer is A.

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Correct Answer: E. (2√2)/π

There are several ways you can compute the area of the octagon. No matter which way you choose, all of them will be easier if you draw the picture.

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Correct Answer: B. √x.

It’s commonly known that logarithmic growth and s-curves can be used to represent populations, but these aren’t the only functions. In our question we have two key features, population growth and an upper limit. We can quickly rule out choice D and E. They will not cap out, in fact they will grow even faster never reaching an upper limit. Choice C is the negative absolute value. This is not growing but decreasing. The cosine is also bounded by a certain amplitude, in this case it has an amplitude of 1. It is possible to use this function to model a bounded population, but the cosine function is a periodic function. This means there are places where the function grows and there are places where the function decreases. The square root, on the other hand, is always growing even when it reaches its upper limit. This makes the square root function, choice B, the correct answer.

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Correct Answer: C. 128 cells

If the bacteria double every 15 minutes, then that means over the course of 2 hours, they will double 8 times. 500 x 2⁸ = 128,000 cells on the surface. Then we apply the anti bacterial wash, which kills 99.9% of cells, meaning 0.1%, or 0.001 of the cells remain. 128,000 x 0.001 = 128 cells.

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