question stringlengths 4k 7.76k | answer stringlengths 17 3.06k | input_ids sequencelengths 8.19k 8.19k | attention_mask sequencelengths 8.19k 8.19k |
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Given that the average of a set of 10 numbers is 85, what is the average of the remaining numbers if the numbers 70 and 76 are excluded from the set? The sum of the 10 numbers is $10 \times 85 = 850$.
If we exclude the numbers 70 and 76, we subtract their sum from the total sum, so we have $850 - (70 + 76) = 850 - 146 ... | Out of 25 students, 60% are girls, so there are 25 * 0.6 = 15 girls in the class.
The remaining students are boys, so there are 25 - 15 = 10 boys in the class.
40% of the boys like playing basketball, so there are 10 * 0.4 = 4 boys who like playing basketball.
The rest of the boys don't like playing basketball, so ther... | [
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Acute-angled $\triangle ABC$ is inscribed in a circle with center at $O$; $\stackrel \frown {AB} = 120^\circ$ and $\stackrel \frown {BC} = 72^\circ$.
A point $E$ is taken in minor arc $AC$ such that $OE$ is perpendicular to $AC$. Then the ratio of the magnitudes of $\angle OBE$ and $\angle BAC$ is:
$\textbf{(A)}\ \frac... | We want to find the value of $X$ in the given situation.
To solve this problem, we can use the concept of permutations.
Since each friend can receive more than one problem, we need to find the number of ways to distribute $X$ pieces of paper among 10 friends.
The number of ways to distribute $X$ pieces of paper among 1... | [
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"Beth had x students in her 10th-grade class. The following year 30 more students join. In her fin(...TRUNCATED) | "The school uses 200 sheets of paper per class per day, so in one week, each class uses 200 sheets/d(...TRUNCATED) | [33,2788,550,2124,2444,287,607,838,400,12,9526,1398,13,220,383,1708,614,1542,517,2444,4654,13,220,55(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"If Adam's father deposited $2000 in the bank, with 8% interest paid annually and the interest being(...TRUNCATED) | "To solve this problem, we need to determine the value of x, which represents the width of the sidew(...TRUNCATED) | [1532,7244,338,2988,27163,720,11024,287,262,3331,11,351,807,4,1393,3432,13844,290,262,1393,852,23019(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"Nina wants to give presents to her children. She buys three toys at $10 each, two packs of basketba(...TRUNCATED) | "Let's assume the cost of the sandwich is x.\nThe juice is two times more expensive than the sandwic(...TRUNCATED) | [45,1437,3382,284,1577,10969,284,607,1751,13,1375,24779,1115,14958,379,720,940,1123,11,734,15186,286(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"In the diagram, the rectangle has a width $w$, a length of X$, and a perimeter of $24$. What is the(...TRUNCATED) | "The jar of grape candy had 5 more pieces of candy than the jar of banana candy, so it had 43 + 5 = (...TRUNCATED) | [818,262,16362,11,262,35991,468,257,9647,720,86,47113,257,4129,286,1395,47113,290,257,25317,286,720,(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"How many two-digit positive integers are congruent to X (mod 3)?\nIf we know the answer to the abov(...TRUNCATED) | "The cost of the new computer is $600 and it lasts for 6 years, so the cost per year is $600 / 6 = $(...TRUNCATED) | [2437,867,734,12,27003,3967,37014,389,369,48929,298,284,1395,357,4666,513,19427,198,1532,356,760,262(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"After Daragh took out her favorite 8 bears from her initial collection of 20 stuffed bears and divi(...TRUNCATED) | "Jimmy makes 8 sandwiches in total, using x slices of bread each, so the total number of slices of b(...TRUNCATED) | [3260,7491,10471,1718,503,607,4004,807,13062,422,607,4238,4947,286,1160,22259,13062,290,9086,262,563(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"For a project, a builder purchased 7 boxes of bolts with each box containing 11 bolts. He purchase(...TRUNCATED) | "The increase in price is $102 - $85 = $17.\nTo find the percent increase, we divide the increase by(...TRUNCATED) | [1890,257,1628,11,257,27098,8155,767,10559,286,24667,351,1123,3091,7268,1367,24667,13,220,679,8155,2(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
"There are 28 garden gnomes in a yard. Three-fourths of them have red hats, and the rest have blue h(...TRUNCATED) | "Jason eats an omelet made using x eggs every morning.\nIn two weeks, there are 14 days.\nSo the tot(...TRUNCATED) | [1858,389,2579,11376,19967,2586,287,257,12699,13,7683,12,14337,9998,286,606,423,2266,23910,11,290,26(...TRUNCATED) | [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1(...TRUNCATED) |
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