DAT Question of the Day

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: B. 10

The ratio of “change in degrees Fahrenheit” to “change in degrees Celsius” is simply 9 to 5, and therefore, (18×5) / 9 = 10. If you were converting a temperature of 18^o Fahrenheit to degrees Celsius, then it would be ((18-32) × 5) / 9 = -7.78^o Celsius.

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Correct Answer: A. 15

If the mean is 15, the sum of the 4 numbers must be 12 + 14 + 19 + x = 15 × 4 = 60, which yields x = 15. The standard deviation is not required here.

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Correct Answer: B. 3/8

There are 2⁴=16 different outcomes than can be observed from flipping a coin 4 times (e.g. HHHH, HHHT, HHTH, etc.), out of which only 6 arrangements contain exactly two heads. Therefore, the probability is 6 out of 16, i.e. 3/8.

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Correct Answer: D. 15.5

If the mean of 15, x, 17 and 12 is 15, then

If the four values are arranged in ascending order (a descending order will also work), we have,

For an odd number of values, the one right in the middle would be the median. In this case, there is an even number of values; so we take the mean of the two values in the middle, i.e. of 15 an 16, which is 15.5.

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Correct Answer: D. cos x (tan x * sin x + cos x)

This problem is solved through the use of trigonometric identities. It should be known that sin²x + cos²x = 1. Thus, we are looking for an answer that simplifies to that identity. Answers A and E are not correct because the square of the sum of sin x +/- cos x results in a sin x * cos x term. Thus, although they may seem initially correct, multiplying out the equation shows that it is not. In answer D, we first see that tan x = sinx/cosx. Thus, cosx * tanx = sinx, and cosx * tanx *sinx = sin²x. Thus, multiplying through the equation, we come to the correct identity of sin²x + cos²x = 1.

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Correct Answer: A. 1.11 x 10^-2

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Correct Answer: C. 16.1

1 mile equals 1.60934 km or roughly about 1.61 km which is 1610 meters. One hundredth of a mile is 16.1 meters.

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