DAT Question of the Day

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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Correct Answer: C. 79

For a grade of B, either the condition 85 × 0.4 + x × 0.6 ≥ 82 needs to be met under the first policy, or the condition 85 × 0.5 + x × 0.5 ≥ 82 needs to be met under the second policy. These two conditions yield x ≥ 80 and x ≥ 79, respectively. Since the minimum value of x is to be computed, we pick the lower of these two bounds, which is 79.

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Correct Answer: D. {60, 61, 59}

This can be done by computing the variance of each of these expressions. Also, by inspection, it can be seen that the numbers in D vary by the least amount from each other.

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Correct Answer: D. 198

The volume of a cylinder is πr² × h = π × 3² × 7 = 63π. If π is approximated as 22/7, then 63π = 63 × 22/7 = 198.

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Correct Answer: A. 10

We are given a regression equation, which is Y = 25 +0.5X – 2ZX, where X is 10 years and Z is 1 lion per year. This means that the equation can be substituted as Y = 25 +0.5(10) – 2(10)(1) = 10 lions remaining after 10 years.

Y=25+0.5X-2Z
X=10 years, Z=1 lion death per year
Y=25+0.5(10)-2(10)(1)= 10 lions remaining

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Correct Answer: D. 16.8 minutes

At a 50% reduced speed, the first program will take (6×100)/(100-50)=12 minutes to complete, and at a 40% reduced speed, the second program will take (12×100)/(100-40)=20 minutes to complete. However, if they are started together, the first program will be completed after the first 12 minutes, and the second program will run alone at the regular speed. In 12 minutes, only (12×100)/20=60% of the second program will be complete. For the remaining 40%, it will run at its full speed and take another (12×40)/100=4.8 minutes to complete. The total time required to finish both the programs is 12+4.8=16.8 minutes.

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Correct Answer: A. 11 AM

Let x be the number of hours it takes Jason to pass Mark. During this time, Jason travels 40x miles. Mark started an hour earlier, so he has driven for x+1 hours, during which he travels 30(x+1) miles. Therefore,

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Correct Answer: B. X is divisible by B.

Given that X is a multiple of A, we know that X is always divisible by A. Following, if A is always divisible by B, then A must be a multiple of B. Thus, it logically follows that if A is divisible by B, and X is divisible by A, then X must be divisible by B.

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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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