Daily Practice

Solution

For the first celebrity, you have a 1/3 chance of picking the photo. Given you get the picture right, you now have a 1/2 chance of picking the next photo. If you get both of them right, you are guarenteed to get the third right. Thus the probability is 1/2*1/3 which is 1/6. -JasonDaGoat

Solution

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Solution

For an L-shaped figure with right angles and perimeter 24, working through the dimensions gives area = 20.

Solution

We will compute each expression. A) $2\; +\; 0\; +\; 1\; +\; 7\; =\; 10$ B) $2\; times\; 0\; +\; 1\; +\; 7\; =\; 8$ C) $2\; +\; 0\; times\; 1\; +\; 7\; =\; 9$ D) $2\; +\; 0\; +\; 1\; times\; 7\; =\; 9$ E) $2\; times\; 0\; times\; 1\; times\; 7\; =\; 0$ Ordering these, we get $10,\; 8,\; 9,\; 9,\; 0$. Out of these, $10$ is the largest number and option $(A)$ adds up to $10$. Therefore, the answer is $boxed\{textbf\{(A)\; \}\; 2+0+1+7\}$. - SBose

Solution

The 6 green marbles and yellow marbles form 1 - frac{1}{3} - frac{1}{4} = frac{5}{12} of the total marbles. Now, suppose the total number of marbles is x. We know the number of yellow marbles is frac{5}{12}x - 6 and a positive integer. Therefore, 12 must divide x. Trying the smallest multiples of 12 for x, we see that when x = 12, we get there are -1 yellow marbles, which is impossible. However when x = 24, there are frac{5}{12} cdot 24 - 6 = boxed{textbf{(D) }4} yellow marbles, which must be the smallest possible.