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If |d - 9| = 2d, then d =
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$${C}{n \choose m}=\frac{m!}{[(m-n)!n!]}$$ for nonnegative integers m and n, $$m \ge n$$. If $${C}{3 \choose 5}={C}{x \choose 5}$$ and $$x \neq 3$$, what is the value of x?
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 The figure above represents a square garden that is divided into 9 rectangular regions with indicated dimensions in meters. The shaded regions are planted with peas, and the unshaded regions are planted with tomatoes. If the sum of the areas of the regions planted with peas is equal to the sum of the areas of the regions planted with tomatoes, what is the value of x?
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If the number 52,1n9, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
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OG12 OG15
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For which of the following values of n is $$\frac{(100+n)}{n}$$ NOT an integer?
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OG12 OG15 OG16 OG17
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A bakery opened yesterday with its daily supply of 40 dozen rolls. Half of the rolls were sold by noon, and 80 percent of the remaining rolls were sold between noon and closing time. How many dozen rolls had not been sold when the bakery closed yesterday?
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OG12 OG15
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If 4 is one solution of the equation $${x}^{2} + 3x + k = 10$$, where k is a constant, what is the other solution?
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OG12 OG15 OG16 OG17 OG18
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If n is a prime number greater than 3, what is the remainder when $${n}^{2}$$ is divided by 12 ?
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OG12 OG15 OG16
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A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by $1, 10 fewer of the towels could be bought for $120, excluding sales tax. What is the current price of each towel?
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If a is a positive integer, and if the units digit of $$\mathbf{a}^{2}$$ is 9 and the units digit of $$\mathbf({a}+{1})^{2}$$ is 4, what is the units digit of $$\mathbf({a}+{2})^{2}$$ ?
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$${(R^{c})(R^{d})(R^{e})}=R^{-12}$$, if R>0 and c, d, and e are each different negative integers, what is the smallest that c could be?
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What is the remainder, after division by 100, of $$7^{10}$$?
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How many different sets of positive square integers, each greater than 1, add up to 75?
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If$$2^{x}+2^{y}=x^{2}+y^{2}$$ , where x and y are nonnegative integers, what is the greatest possible value of |x-y|?
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Which of the following is not a divisor of 52?
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If u,v and w are single-digit integers and 1,000(u) + 10,000(v) + 10(w) = N, what is the tens digit of the number N?
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OG17 OG18 OG19 OG20 OG2022
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Last year Joe grew 1 inch and Sally grew 200 percent more than Joe grew. How many inches did Sally grow last year?
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PREP07 Test 2
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A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?
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PREP07 Test 2
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According to a financial analyst, if Company C sets the unit selling price of its product at x dollars, then its monthly profit P, in dollars, is given by the formula P = 1,000(4x - x^2 - 2). According to this formula, at what amount should Company C set the unit selling price of its product so that its monthly profit is $2,000 ?
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PREP07 Test 2
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For which of the following values of x is $$\sqrt{(1-\sqrt{(2 - \sqrt{x})}}$$ NOT defined as a real number?
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