answers listlengths 1 1 | datasets listlengths 1 1 | id stringlengths 64 64 | messages listlengths 1 1 | prompt stringlengths 10 2.99k | reference_answer_raw stringlengths 3 1.22k | source stringclasses 1
value | source_records stringlengths 116 1.08k | verifiability dict |
|---|---|---|---|---|---|---|---|---|
[
"115"
] | [
"deepscaler"
] | b5d3bd84d793e842d3c4b1ea95898088cf5b0ef6e4c467f6ac43cf468c77ff8e | [
{
"content": "Find a positive integral solution to the equation $\\frac{1+3+5+\\dots+(2n-1)}{2+4+6+\\dots+2n}=\\frac{115}{116}$.",
"role": "user"
}
] | Find a positive integral solution to the equation $\frac{1+3+5+\dots+(2n-1)}{2+4+6+\dots+2n}=\frac{115}{116}$. | "115" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:965"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"x"
] | [
"deepscaler"
] | a9e6a68c46d49347912be096444dee9bc162e6cf42f406cfa23301d2a16633da | [
{
"content": "If $x$ and $y$ are non-zero numbers such that $x=1+\\frac{1}{y}$ and $y=1+\\frac{1}{x}$, then $y$ equals",
"role": "user"
}
] | If $x$ and $y$ are non-zero numbers such that $x=1+\frac{1}{y}$ and $y=1+\frac{1}{x}$, then $y$ equals | "x" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:966"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | a28ff010e9f6bfbd79dcd0364ae406277184a4ce967039b53275aae336a2dc4e | [
{
"content": "Point $P$ is outside circle $C$ on the plane. At most how many points on $C$ are $3$ cm from $P$?",
"role": "user"
}
] | Point $P$ is outside circle $C$ on the plane. At most how many points on $C$ are $3$ cm from $P$? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:967"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}"
] | [
"deepscaler"
] | fe770ac92bcf791ba30e5350147781d2f8e204aeabe816409818b88b1767f79d | [
{
"content": "A particular $12$-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a $1$, it mistakenly displays a $9$. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?",
... | A particular $12$-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a $1$, it mistakenly displays a $9$. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time? | "\\frac{1}{2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:968"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2662"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"26"
] | [
"deepscaler"
] | 71058751a2d61d6c2d4ea4b979d859fd113ad1926b6cd27c91f86538e4ad6e89 | [
{
"content": "$(2 \\times 3 \\times 4)\\left(\\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4}\\right) = $",
"role": "user"
}
] | $(2 \times 3 \times 4)\left(\frac{1}{2} + \frac{1}{3} + \frac{1}{4}\right) = $ | "26" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:969"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"40"
] | [
"deepscaler"
] | f16fbc20777328042ebb1e24a4499881b8587395070e541cc147e5b337d82a95 | [
{
"content": "Two subsets of the set $S=\\{a, b, c, d, e\\}$ are to be chosen so that their union is $S$ and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter?",
"role": "user"
}
] | Two subsets of the set $S=\{a, b, c, d, e\}$ are to be chosen so that their union is $S$ and their intersection contains exactly two elements. In how many ways can this be done, assuming that the order in which the subsets are chosen does not matter? | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:970"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{3}"
] | [
"deepscaler"
] | 833bdd9999e222cd2fc4452fbddd0f61a51ff8bcd2576b1f5eae179ca9b4bb69 | [
{
"content": "Given that the ratio of $3x - 4$ to $y + 15$ is constant, and $y = 3$ when $x = 2$, then, when $y = 12$, $x$ equals:",
"role": "user"
}
] | Given that the ratio of $3x - 4$ to $y + 15$ is constant, and $y = 3$ when $x = 2$, then, when $y = 12$, $x$ equals: | "\\frac{7}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:972"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{3}(4+\\sqrt{2})"
] | [
"deepscaler"
] | f75490a78948f8f1eacfeb09e1a929d8b88b2cf1f0aa6aa29f4be8b722a86dd9 | [
{
"content": "A line initially 1 inch long grows according to the following law, where the first term is the initial length.\n\\[1+\\frac{1}{4}\\sqrt{2}+\\frac{1}{4}+\\frac{1}{16}\\sqrt{2}+\\frac{1}{16}+\\frac{1}{64}\\sqrt{2}+\\frac{1}{64}+\\cdots\\]\nIf the growth process continues forever, the limit of the le... | A line initially 1 inch long grows according to the following law, where the first term is the initial length.
\[1+\frac{1}{4}\sqrt{2}+\frac{1}{4}+\frac{1}{16}\sqrt{2}+\frac{1}{16}+\frac{1}{64}\sqrt{2}+\frac{1}{64}+\cdots\]
If the growth process continues forever, the limit of the length of the line is: | "\\frac{1}{3}(4+\\sqrt{2})" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:973"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3a - 2b"
] | [
"deepscaler"
] | 3dadd54f103ae361cb569029eebd32a1b0de988542c2c45f341d9a9c9a779d92 | [
{
"content": "When a bucket is two-thirds full of water, the bucket and water weigh $a$ kilograms. When the bucket is one-half full of water the total weight is $b$ kilograms. In terms of $a$ and $b$, what is the total weight in kilograms when the bucket is full of water?",
"role": "user"
}
] | When a bucket is two-thirds full of water, the bucket and water weigh $a$ kilograms. When the bucket is one-half full of water the total weight is $b$ kilograms. In terms of $a$ and $b$, what is the total weight in kilograms when the bucket is full of water? | "3a - 2b" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:974"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2331"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"deepscaler"
] | 4f97f537d4926ec9061e9b70c2238697450df42a6961f50686480e3fb85f8b9c | [
{
"content": "The 16 squares on a piece of paper are numbered as shown in the diagram. While lying on a table, the paper is folded in half four times in the following sequence:\n(1) fold the top half over the bottom half\n(2) fold the bottom half over the top half\n(3) fold the right half over the left half\n(... | The 16 squares on a piece of paper are numbered as shown in the diagram. While lying on a table, the paper is folded in half four times in the following sequence:
(1) fold the top half over the bottom half
(2) fold the bottom half over the top half
(3) fold the right half over the left half
(4) fold the left half over... | "9" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:975"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"67"
] | [
"deepscaler"
] | e5fafc49904b65ec3e08edaba365dcf3d2870693616a5d90896506e8c53c20e8 | [
{
"content": "Sam drove $96$ miles in $90$ minutes. His average speed during the first $30$ minutes was $60$ mph (miles per hour), and his average speed during the second $30$ minutes was $65$ mph. What was his average speed, in mph, during the last $30$ minutes?",
"role": "user"
}
] | Sam drove $96$ miles in $90$ minutes. His average speed during the first $30$ minutes was $60$ mph (miles per hour), and his average speed during the second $30$ minutes was $65$ mph. What was his average speed, in mph, during the last $30$ minutes? | "67" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:976"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:998"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"deepscaler"
] | aeeaecf68a7048f607bb9a97add1c8ac6d6b36eb84e2988617b00e6dda7bddce | [
{
"content": "The product of the two $99$-digit numbers\n$303,030,303,...,030,303$ and $505,050,505,...,050,505$\nhas thousands digit $A$ and units digit $B$. What is the sum of $A$ and $B$?",
"role": "user"
}
] | The product of the two $99$-digit numbers
$303,030,303,...,030,303$ and $505,050,505,...,050,505$
has thousands digit $A$ and units digit $B$. What is the sum of $A$ and $B$? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:977"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"125"
] | [
"deepscaler"
] | f731a20033f0f1b61339c45178aa6a5e9b78e23b37ea91e5ac7795b50db827a4 | [
{
"content": "One hundred students at Century High School participated in the AHSME last year, and their mean score was 100. The number of non-seniors taking the AHSME was $50\\%$ more than the number of seniors, and the mean score of the seniors was $50\\%$ higher than that of the non-seniors. What was the mea... | One hundred students at Century High School participated in the AHSME last year, and their mean score was 100. The number of non-seniors taking the AHSME was $50\%$ more than the number of seniors, and the mean score of the seniors was $50\%$ higher than that of the non-seniors. What was the mean score of the seniors? | "125" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:978"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{912}{119}"
] | [
"deepscaler"
] | fcdeae6087eb346f1770c30c43223245a3b161fb1fa7e2467317a06329ec2e7e | [
{
"content": "Circles with centers $(2,4)$ and $(14,9)$ have radii $4$ and $9$, respectively. The equation of a common external tangent to the circles can be written in the form $y=mx+b$ with $m>0$. What is $b$?",
"role": "user"
}
] | Circles with centers $(2,4)$ and $(14,9)$ have radii $4$ and $9$, respectively. The equation of a common external tangent to the circles can be written in the form $y=mx+b$ with $m>0$. What is $b$? | "\\frac{912}{119}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:979"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"deepscaler"
] | 0f0fdfdb6b80b9746473c0a16fe4aad20f409bc964a5a06504e4a61aed83d53d | [
{
"content": "Each integer 1 through 9 is written on a separate slip of paper and all nine slips are put into a hat. Jack picks one of these slips at random and puts it back. Then Jill picks a slip at random. Which digit is most likely to be the units digit of the sum of Jack's integer and Jill's integer?",
... | Each integer 1 through 9 is written on a separate slip of paper and all nine slips are put into a hat. Jack picks one of these slips at random and puts it back. Then Jill picks a slip at random. Which digit is most likely to be the units digit of the sum of Jack's integer and Jill's integer? | "0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:980"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{6}"
] | [
"deepscaler"
] | 23e7473292e518a559cbb4a28fba8f4fb0f20ab828fcda1ffb5954b30338b772 | [
{
"content": "A triangle with vertices as $A=(1,3)$, $B=(5,1)$, and $C=(4,4)$ is plotted on a $6\\times5$ grid. What fraction of the grid is covered by the triangle?",
"role": "user"
}
] | A triangle with vertices as $A=(1,3)$, $B=(5,1)$, and $C=(4,4)$ is plotted on a $6\times5$ grid. What fraction of the grid is covered by the triangle? | "\\frac{1}{6}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:981"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"deepscaler"
] | da82d92fd2c54dd7260ee8fc1c9d7dddf9b0dfc9373d60ffabe67f85ec1cda49 | [
{
"content": "Triangle $ABC$ and point $P$ in the same plane are given. Point $P$ is equidistant from $A$ and $B$, angle $APB$ is twice angle $ACB$, and $\\overline{AC}$ intersects $\\overline{BP}$ at point $D$. If $PB = 3$ and $PD= 2$, then $AD\\cdot CD =$",
"role": "user"
}
] | Triangle $ABC$ and point $P$ in the same plane are given. Point $P$ is equidistant from $A$ and $B$, angle $APB$ is twice angle $ACB$, and $\overline{AC}$ intersects $\overline{BP}$ at point $D$. If $PB = 3$ and $PD= 2$, then $AD\cdot CD =$ | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:982"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"83"
] | [
"deepscaler"
] | 0273bb2c65c2573743ed818954a60a627e1f9dfd149f9685040083651d7827ed | [
{
"content": "When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.\n\nFor example, starting with an input of $N=7,$ the machine will output $3 \\cdot 7 +1 = 22.$ Then if the output is repeatedly inserted into the machine five more times, the fin... | When a positive integer $N$ is fed into a machine, the output is a number calculated according to the rule shown below.
For example, starting with an input of $N=7,$ the machine will output $3 \cdot 7 +1 = 22.$ Then if the output is repeatedly inserted into the machine five more times, the final output is $26.$ $7 \t... | "83" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:983"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | 1a735447fb6f3049c53e8e8d58dd173808f626bc28f7a110b2d2894555465788 | [
{
"content": "Each principal of Lincoln High School serves exactly one $3$-year term. What is the maximum number of principals this school could have during an $8$-year period?",
"role": "user"
}
] | Each principal of Lincoln High School serves exactly one $3$-year term. What is the maximum number of principals this school could have during an $8$-year period? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:984"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"deepscaler"
] | 46ac12ea22958c32f7520fcb40d01063c35ddae49a6e295a30e0addae39e47ee | [
{
"content": "A rectangular grazing area is to be fenced off on three sides using part of a $100$ meter rock wall as the fourth side. Fence posts are to be placed every $12$ meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence... | A rectangular grazing area is to be fenced off on three sides using part of a $100$ meter rock wall as the fourth side. Fence posts are to be placed every $12$ meters along the fence including the two posts where the fence meets the rock wall. What is the fewest number of posts required to fence an area $36$ m by $60... | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:985"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{12}"
] | [
"deepscaler"
] | e6a6f04ecc5852c08af55225b8c62b0c4d7b27ac64d52326287e1e73d77d806c | [
{
"content": "What number is one third of the way from $\\frac14$ to $\\frac34$?",
"role": "user"
}
] | What number is one third of the way from $\frac14$ to $\frac34$? | "\\frac{5}{12}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:986"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-5"
] | [
"deepscaler"
] | 92e59edec4f81a4ef2fd0f3274c29bd504d7dc9d8eb53dd11a40d744f5341453 | [
{
"content": "What is the sum of all real numbers $x$ for which the median of the numbers $4,6,8,17,$ and $x$ is equal to the mean of those five numbers?",
"role": "user"
}
] | What is the sum of all real numbers $x$ for which the median of the numbers $4,6,8,17,$ and $x$ is equal to the mean of those five numbers? | "-5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:987"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1877"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"h(10x+5h-2)"
] | [
"deepscaler"
] | 1b44aef4a58ab2c2f6aa40b65772baa4b2288405afe2b79fdf5bc50f065a488a | [
{
"content": "If $f(x) = 5x^2 - 2x - 1$, then $f(x + h) - f(x)$ equals:",
"role": "user"
}
] | If $f(x) = 5x^2 - 2x - 1$, then $f(x + h) - f(x)$ equals: | "h(10x+5h-2)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:988"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"99"
] | [
"deepscaler"
] | 0c9f3dc8d632f65eb6af9ac2d14ecaf1207dfa6078e835a86dd2687a14b74370 | [
{
"content": "The difference between a two-digit number and the number obtained by reversing its digits is $5$ times the sum of the digits of either number. What is the sum of the two digit number and its reverse?",
"role": "user"
}
] | The difference between a two-digit number and the number obtained by reversing its digits is $5$ times the sum of the digits of either number. What is the sum of the two digit number and its reverse? | "99" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:989"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16:3"
] | [
"deepscaler"
] | 436bc3fd042aecfa4675f72891fae06fc680f05d4fa45ff1904818e596b32cd8 | [
{
"content": "The ratio of $w$ to $x$ is $4:3$, the ratio of $y$ to $z$ is $3:2$, and the ratio of $z$ to $x$ is $1:6$. What is the ratio of $w$ to $y?$",
"role": "user"
}
] | The ratio of $w$ to $x$ is $4:3$, the ratio of $y$ to $z$ is $3:2$, and the ratio of $z$ to $x$ is $1:6$. What is the ratio of $w$ to $y?$ | "16:3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:990"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2436"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"253"
] | [
"deepscaler"
] | 4ca9abf8f8f1d0ed22c7036e96d69f31bd24d3c9c040665c22237742a705d10a | [
{
"content": "Let $a$, $b$, and $c$ be positive integers with $a\\ge$ $b\\ge$ $c$ such that\n$a^2-b^2-c^2+ab=2011$ and\n$a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$.\nWhat is $a$?",
"role": "user"
}
] | Let $a$, $b$, and $c$ be positive integers with $a\ge$ $b\ge$ $c$ such that
$a^2-b^2-c^2+ab=2011$ and
$a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$.
What is $a$? | "253" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:991"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2735"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4a"
] | [
"deepscaler"
] | 4d8385e2070e066cb9b2ecd2c7c590bb6d66131ecf2596041a5ccd11aee6cf3a | [
{
"content": "Let $r$ be the result of doubling both the base and exponent of $a^b$, and $b$ does not equal to $0$. \nIf $r$ equals the product of $a^b$ by $x^b$, then $x$ equals:",
"role": "user"
}
] | Let $r$ be the result of doubling both the base and exponent of $a^b$, and $b$ does not equal to $0$.
If $r$ equals the product of $a^b$ by $x^b$, then $x$ equals: | "4a" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:992"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | 437d86aba433e58ee961f052efa26ebe236a4f9a26d10e6f4b7058c2107d1466 | [
{
"content": "Let $S$ be a set of $6$ integers taken from $\\{1,2,\\dots,12\\}$ with the property that if $a$ and $b$ are elements of $S$ with $a<b$, then $b$ is not a multiple of $a$. What is the least possible value of an element in $S$?",
"role": "user"
}
] | Let $S$ be a set of $6$ integers taken from $\{1,2,\dots,12\}$ with the property that if $a$ and $b$ are elements of $S$ with $a<b$, then $b$ is not a multiple of $a$. What is the least possible value of an element in $S$? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:994"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2690"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"deepscaler"
] | f6e8f3a90ba2eb81d2ece2bc0d9d39bbb202008deca77daac39ce51e4d7b38c3 | [
{
"content": "There is a positive integer $n$ such that $(n+1)! + (n+2)! = n! \\cdot 440$. What is the sum of the digits of $n$?",
"role": "user"
}
] | There is a positive integer $n$ such that $(n+1)! + (n+2)! = n! \cdot 440$. What is the sum of the digits of $n$? | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:995"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1889"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | 5e3cdcfcf9af80b8fd88b23f1f5336177020e025bf562694eb265f217192fc32 | [
{
"content": "A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic progression. The inner rectangle is one foot wide, and each of the two shaded regions is $1$ foot wide on all four sides. What is the length in feet of the inner rectangle?",
... | A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic progression. The inner rectangle is one foot wide, and each of the two shaded regions is $1$ foot wide on all four sides. What is the length in feet of the inner rectangle? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:996"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1.5"
] | [
"deepscaler"
] | dd43e59e5c6c45d0fc1bde5f9e320e8714fee6871484c18c9f2f1d546e514a21 | [
{
"content": "An inverted cone with base radius $12 \\mathrm{cm}$ and height $18 \\mathrm{cm}$ is full of water. The water is poured into a tall cylinder whose horizontal base has radius of $24 \\mathrm{cm}$. What is the height in centimeters of the water in the cylinder?",
"role": "user"
}
] | An inverted cone with base radius $12 \mathrm{cm}$ and height $18 \mathrm{cm}$ is full of water. The water is poured into a tall cylinder whose horizontal base has radius of $24 \mathrm{cm}$. What is the height in centimeters of the water in the cylinder? | "1.5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:997"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1429"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"234"
] | [
"deepscaler"
] | 11fe977616dcd766772d6b8b1ded743eb7920ae9e84dbb7b8bf8d5813a84764b | [
{
"content": "At one of George Washington's parties, each man shook hands with everyone except his spouse, and no handshakes took place between women. If $13$ married couples attended, how many handshakes were there among these $26$ people?",
"role": "user"
}
] | At one of George Washington's parties, each man shook hands with everyone except his spouse, and no handshakes took place between women. If $13$ married couples attended, how many handshakes were there among these $26$ people? | "234" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:999"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
".088 m^2"
] | [
"deepscaler"
] | 5473b40cd6ba4198c26e28c561c8bd8e8ca069a25331061bef65ed983e3166ac | [
{
"content": "The area of the rectangular region is",
"role": "user"
}
] | The area of the rectangular region is | ".088 m^2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1002"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2367"
] | [
"deepscaler"
] | a7a84b9f5207ec1981c297b0c21ac3d4beb577722be41d9e270a274e37f009ae | [
{
"content": "Let $a$, $b$, $c$, and $d$ be positive integers with $a < 2b$, $b < 3c$, and $c<4d$. If $d<100$, the largest possible value for $a$ is",
"role": "user"
}
] | Let $a$, $b$, $c$, and $d$ be positive integers with $a < 2b$, $b < 3c$, and $c<4d$. If $d<100$, the largest possible value for $a$ is | "2367" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1003"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{32}{5}"
] | [
"deepscaler"
] | 002520135eeac2bee7728231550bcc21febc7d40db8a66e70f162edd780d0ba3 | [
{
"content": "Square $PQRS$ lies in the first quadrant. Points $(3,0), (5,0), (7,0),$ and $(13,0)$ lie on lines $SP, RQ, PQ$, and $SR$, respectively. What is the sum of the coordinates of the center of the square $PQRS$?",
"role": "user"
}
] | Square $PQRS$ lies in the first quadrant. Points $(3,0), (5,0), (7,0),$ and $(13,0)$ lie on lines $SP, RQ, PQ$, and $SR$, respectively. What is the sum of the coordinates of the center of the square $PQRS$? | "\\frac{32}{5}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1004"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"deepscaler"
] | 1c1f044d2fc45c26b1eed0deb03a20ac13c4335aff206c78a08b7d24041e86de | [
{
"content": "Two is $10 \\%$ of $x$ and $20 \\%$ of $y$. What is $x - y$?",
"role": "user"
}
] | Two is $10 \%$ of $x$ and $20 \%$ of $y$. What is $x - y$? | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1005"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{15}{x}"
] | [
"deepscaler"
] | 32cc49b5f3c15ee7d5b3f8264e32bea446e7bf917fc297086a81feca93c514be | [
{
"content": "When simplified, the third term in the expansion of $(\\frac{a}{\\sqrt{x}} - \\frac{\\sqrt{x}}{a^2})^6$ is:",
"role": "user"
}
] | When simplified, the third term in the expansion of $(\frac{a}{\sqrt{x}} - \frac{\sqrt{x}}{a^2})^6$ is: | "\\frac{15}{x}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1006"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"$\\{0, -\\frac{1}{n}\\}$"
] | [
"deepscaler"
] | 87432bee136cd9368b8a3449cb6276c201c1549f1750569d8fe217268da2eeee | [
{
"content": "Let $f(n) = \\frac{x_1 + x_2 + \\cdots + x_n}{n}$, where $n$ is a positive integer. If $x_k = (-1)^k, k = 1, 2, \\cdots, n$, the set of possible values of $f(n)$ is:",
"role": "user"
}
] | Let $f(n) = \frac{x_1 + x_2 + \cdots + x_n}{n}$, where $n$ is a positive integer. If $x_k = (-1)^k, k = 1, 2, \cdots, n$, the set of possible values of $f(n)$ is: | "$\\{0, -\\frac{1}{n}\\}$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1007"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"deepscaler"
] | d8f84acc8bc3fb28743bfdf300613d0bc243486aeafe483526b824535c8c37a8 | [
{
"content": "Pablo buys popsicles for his friends. The store sells single popsicles for $1 each, 3-popsicle boxes for $2 each, and 5-popsicle boxes for $3. What is the greatest number of popsicles that Pablo can buy with $8?",
"role": "user"
}
] | Pablo buys popsicles for his friends. The store sells single popsicles for $1 each, 3-popsicle boxes for $2 each, and 5-popsicle boxes for $3. What is the greatest number of popsicles that Pablo can buy with $8? | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1008"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | 9dc9cacbab2503adefbc84232d4f7fdfd1a88ffb45c972befaf9675e9b208dd3 | [
{
"content": "Three primes $p, q$, and $r$ satisfy $p + q = r$ and $1 < p < q$. Then $p$ equals",
"role": "user"
}
] | Three primes $p, q$, and $r$ satisfy $p + q = r$ and $1 < p < q$. Then $p$ equals | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1010"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"19"
] | [
"deepscaler"
] | 9469ae03dd1e7eabb9be3513625d51e1f276ba535f21521fac578817e04813e0 | [
{
"content": "Let $n$ be the number of ways $10$ dollars can be changed into dimes and quarters, with at least one of each coin being used. Then $n$ equals:",
"role": "user"
}
] | Let $n$ be the number of ways $10$ dollars can be changed into dimes and quarters, with at least one of each coin being used. Then $n$ equals: | "19" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1011"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9902"
] | [
"deepscaler"
] | 006500e2d875620539ee07f2f871fe2ceb7bba0d6b75e975830e113c63651971 | [
{
"content": "If the sequence $\\{a_n\\}$ is defined by\n$a_1=2$\n$a_{n+1}=a_n+2n$\nwhere $n\\geq1$.\nThen $a_{100}$ equals",
"role": "user"
}
] | If the sequence $\{a_n\}$ is defined by
$a_1=2$
$a_{n+1}=a_n+2n$
where $n\geq1$.
Then $a_{100}$ equals | "9902" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1013"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"deepscaler"
] | 66951bb78cb55b9d877dff0e1c485f969782a5606b91a61698a5d4fb2abed5c7 | [
{
"content": "Let $s_k$ denote the sum of the $k$th powers of the roots of the polynomial $x^3-5x^2+8x-13$. In particular, $s_0=3$, $s_1=5$, and $s_2=9$. Let $a$, $b$, and $c$ be real numbers such that $s_{k+1} = a s_k + b s_{k-1} + c s_{k-2}$ for $k = 2$, $3$, $....$ What is $a+b+c$?",
"role": "user"
}
] | Let $s_k$ denote the sum of the $k$th powers of the roots of the polynomial $x^3-5x^2+8x-13$. In particular, $s_0=3$, $s_1=5$, and $s_2=9$. Let $a$, $b$, and $c$ be real numbers such that $s_{k+1} = a s_k + b s_{k-1} + c s_{k-2}$ for $k = 2$, $3$, $....$ What is $a+b+c$? | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1014"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$y = x$, $y = x-2$"
] | [
"deepscaler"
] | bf49f3a543529123f7b0cd559d91d19e6a07473088ece3122ac22a924857b03f | [
{
"content": "The roots of the equation $x^{2}-2x = 0$ can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:\n[Note: Abscissas means x-coordinate.]",
"role": "user"
}
] | The roots of the equation $x^{2}-2x = 0$ can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:
[Note: Abscissas means x-coordinate.] | "$y = x$, $y = x-2$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1016"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"deepscaler"
] | 5e8a2bb47f222508af143271213fcaf24c3194f37cc32389064dedec4866ec3b | [
{
"content": "A ray of light originates from point $A$ and travels in a plane, being reflected $n$ times between lines $AD$ and $CD$ before striking a point $B$ (which may be on $AD$ or $CD$) perpendicularly and retracing its path back to $A$ (At each point of reflection the light makes two equal angles as indi... | A ray of light originates from point $A$ and travels in a plane, being reflected $n$ times between lines $AD$ and $CD$ before striking a point $B$ (which may be on $AD$ or $CD$) perpendicularly and retracing its path back to $A$ (At each point of reflection the light makes two equal angles as indicated in the adjoining... | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1017"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | ff5437a96068b6a9885c77a273d6e8ba1f9a1426f39530007e2ccc2aa7b8dd0f | [
{
"content": "If $a \\otimes b = \\dfrac{a + b}{a - b}$, then $(6\\otimes 4)\\otimes 3 =$",
"role": "user"
}
] | If $a \otimes b = \dfrac{a + b}{a - b}$, then $(6\otimes 4)\otimes 3 =$ | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1018"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"deepscaler"
] | ee9b535b181cde74ea181fcafd0ee367691cb9e908a611ac9cbba1f0e4109399 | [
{
"content": "Kiana has two older twin brothers. The product of their three ages is 128. What is the sum of their three ages?",
"role": "user"
}
] | Kiana has two older twin brothers. The product of their three ages is 128. What is the sum of their three ages? | "18" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1019"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1122"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{p^2}{4}"
] | [
"deepscaler"
] | 686960762c55424ea32a37e96d23bb6f667855b123e752cb407c02a0d941446e | [
{
"content": "If $y=x^2+px+q$, then if the least possible value of $y$ is zero $q$ is equal to:",
"role": "user"
}
] | If $y=x^2+px+q$, then if the least possible value of $y$ is zero $q$ is equal to: | "\\frac{p^2}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1020"}] | {
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"reference_components": 1,
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} |
[
"1"
] | [
"deepscaler"
] | 23ba506d0411ba0cf18a834a10f2b85a24f5fabea66a5b865c67a3331b8bd7b1 | [
{
"content": "If $g(x)=1-x^2$ and $f(g(x))=\\frac{1-x^2}{x^2}$ when $x\\not=0$, then $f(1/2)$ equals",
"role": "user"
}
] | If $g(x)=1-x^2$ and $f(g(x))=\frac{1-x^2}{x^2}$ when $x\not=0$, then $f(1/2)$ equals | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1021"}] | {
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} |
[
"36"
] | [
"deepscaler"
] | 7505554514b9c2654a00676b8635e222efa8e427de7a868f64e7476b89dee5b4 | [
{
"content": "How many ways are there to place $3$ indistinguishable red chips, $3$ indistinguishable blue chips, and $3$ indistinguishable green chips in the squares of a $3 \\times 3$ grid so that no two chips of the same color are directly adjacent to each other, either vertically or horizontally?",
"rol... | How many ways are there to place $3$ indistinguishable red chips, $3$ indistinguishable blue chips, and $3$ indistinguishable green chips in the squares of a $3 \times 3$ grid so that no two chips of the same color are directly adjacent to each other, either vertically or horizontally? | "36" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1022"}] | {
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"plain_numeric_reference": true,
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} |
[
"4\\frac{1}{2}"
] | [
"deepscaler"
] | e8dd32d387aa8b665f523e8dc42a5b7a636d40d983631db21b1bbd5e2e9f5700 | [
{
"content": "George and Henry started a race from opposite ends of the pool. After a minute and a half, they passed each other in the center of the pool. If they lost no time in turning and maintained their respective speeds, how many minutes after starting did they pass each other the second time?",
"role... | George and Henry started a race from opposite ends of the pool. After a minute and a half, they passed each other in the center of the pool. If they lost no time in turning and maintained their respective speeds, how many minutes after starting did they pass each other the second time? | "4\\frac{1}{2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1023"}] | {
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} |
[
"14\\frac{14}{23}"
] | [
"deepscaler"
] | db416ede073980924eea0e9cd0d33dba3d25aca85bc41d7a9b01fe74acbd6674 | [
{
"content": "A watch loses $2\\frac{1}{2}$ minutes per day. It is set right at $1$ P.M. on March 15. Let $n$ be the positive correction, in minutes, to be added to the time shown by the watch at a given time. When the watch shows $9$ A.M. on March 21, $n$ equals:",
"role": "user"
}
] | A watch loses $2\frac{1}{2}$ minutes per day. It is set right at $1$ P.M. on March 15. Let $n$ be the positive correction, in minutes, to be added to the time shown by the watch at a given time. When the watch shows $9$ A.M. on March 21, $n$ equals: | "14\\frac{14}{23}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1024"}] | {
"all_reference_components_parse": true,
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} |
[
"37"
] | [
"deepscaler"
] | eedf6189cb4aae62f50db22c807557edeed7aa53ea3f116349097ae8620c860d | [
{
"content": "Leah has $13$ coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth?",
"role": "user"
}
] | Leah has $13$ coins, all of which are pennies and nickels. If she had one more nickel than she has now, then she would have the same number of pennies and nickels. In cents, how much are Leah's coins worth? | "37" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1025"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2622"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"91"
] | [
"deepscaler"
] | c54eb2e1f7bbb9924265bded6f2a1b9ef9b0694f7a405789115ec6b141360f8a | [
{
"content": "Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members... | Members of the Rockham Soccer League buy socks and T-shirts. Socks cost $4 per pair and each T-shirt costs $5 more than a pair of socks. Each member needs one pair of socks and a shirt for home games and another pair of socks and a shirt for away games. If the total cost is $2366, how many members are in the League? | "91" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1026"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1349"}] | {
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} |
[
"9"
] | [
"deepscaler"
] | d0fe3925da60a70f1d31cd2e71d607aba7fb0cbecac4330449d3e5b1b7c4956c | [
{
"content": "The perimeter of one square is $3$ times the perimeter of another square. The area of the larger square is how many times the area of the smaller square?",
"role": "user"
}
] | The perimeter of one square is $3$ times the perimeter of another square. The area of the larger square is how many times the area of the smaller square? | "9" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1027"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16:3"
] | [
"deepscaler"
] | ec891ee26bf00ea8c12f81cdfa563d60e3a5878fb3eb2f90e9e4cb72fe692930 | [
{
"content": "The ratio of $w$ to $x$ is $4:3$, of $y$ to $z$ is $3:2$ and of $z$ to $x$ is $1:6$. What is the ratio of $w$ to $y$?",
"role": "user"
}
] | The ratio of $w$ to $x$ is $4:3$, of $y$ to $z$ is $3:2$ and of $z$ to $x$ is $1:6$. What is the ratio of $w$ to $y$? | "16:3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1028"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
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} |
[
"3"
] | [
"deepscaler"
] | f2001392a81d0abba10de3016a630afe33fc1d7f652f5d72705085b31d70826a | [
{
"content": "The number of scalene triangles having all sides of integral lengths, and perimeter less than $13$ is:",
"role": "user"
}
] | The number of scalene triangles having all sides of integral lengths, and perimeter less than $13$ is: | "3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1029"}] | {
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} |
[
"\\frac{8}{9}"
] | [
"deepscaler"
] | 05810cdc7270943c399d1cb9952936045e2d40391258eaa4d389e6c2c5512d6b | [
{
"content": "If the area of $\\triangle ABC$ is $64$ square units and the geometric mean (mean proportional) between sides $AB$ and $AC$ is $12$ inches, then $\\sin A$ is equal to",
"role": "user"
}
] | If the area of $\triangle ABC$ is $64$ square units and the geometric mean (mean proportional) between sides $AB$ and $AC$ is $12$ inches, then $\sin A$ is equal to | "\\frac{8}{9}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1030"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"deepscaler"
] | 5b8e3abf2c0d3a03eb1202ea7e57c1bf5384f6ce832d1c94b245b4b927e6806c | [
{
"content": "Walter gets up at 6:30 a.m., catches the school bus at 7:30 a.m., has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours additional time at school. He takes the bus home and arrives at 4:00 p.m. How many minutes has he spent on the bus?",
"role": "user"
}
] | Walter gets up at 6:30 a.m., catches the school bus at 7:30 a.m., has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours additional time at school. He takes the bus home and arrives at 4:00 p.m. How many minutes has he spent on the bus? | "60" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1031"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"50"
] | [
"deepscaler"
] | 4b0b74aff14843e7da9775f0f059d21fed8bbb99c849fa1153348b68152fe7b6 | [
{
"content": "Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?",
"role": "us... | Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet? | "50" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1032"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2419"
] | [
"deepscaler"
] | 50d31906d1ee2d0633a77ee7885a6d7a2f3610022c1a65f8c6aadc8a5563e6d3 | [
{
"content": "The sequence $1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2,\\ldots$ consists of $1$’s separated by blocks of $2$’s with $n$ $2$’s in the $n^{th}$ block. The sum of the first $1234$ terms of this sequence is",
"role": "user"
}
] | The sequence $1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2,\ldots$ consists of $1$’s separated by blocks of $2$’s with $n$ $2$’s in the $n^{th}$ block. The sum of the first $1234$ terms of this sequence is | "2419" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1033"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"deepscaler"
] | 0a7133b61c23a6bbbe75ab369634114f217a78b4227a36058b562dc741c5a05f | [
{
"content": "Call a number prime-looking if it is composite but not divisible by $2, 3,$ or $5.$ The three smallest prime-looking numbers are $49, 77$, and $91$. There are $168$ prime numbers less than $1000$. How many prime-looking numbers are there less than $1000$?",
"role": "user"
}
] | Call a number prime-looking if it is composite but not divisible by $2, 3,$ or $5.$ The three smallest prime-looking numbers are $49, 77$, and $91$. There are $168$ prime numbers less than $1000$. How many prime-looking numbers are there less than $1000$? | "100" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1034"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"728"
] | [
"deepscaler"
] | ae9fbbfbbb14a4145d8a6bdd0bd1ee5626d4282881c7cccfb6bde65d02536033 | [
{
"content": "How many whole numbers between 1 and 1000 do not contain the digit 1?",
"role": "user"
}
] | How many whole numbers between 1 and 1000 do not contain the digit 1? | "728" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1035"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{16}"
] | [
"deepscaler"
] | 8b5c647ced53fdde9551f5922e8850e0a09b3e9ace4ae6a0429a620aa57805db | [
{
"content": "A quadratic polynomial with real coefficients and leading coefficient $1$ is called $\\emph{disrespectful}$ if the equation $p(p(x))=0$ is satisfied by exactly three real numbers. Among all the disrespectful quadratic polynomials, there is a unique such polynomial $\\tilde{p}(x)$ for which the sum... | A quadratic polynomial with real coefficients and leading coefficient $1$ is called $\emph{disrespectful}$ if the equation $p(p(x))=0$ is satisfied by exactly three real numbers. Among all the disrespectful quadratic polynomials, there is a unique such polynomial $\tilde{p}(x)$ for which the sum of the roots is maximiz... | "\\frac{5}{16}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1036"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1328"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"$6$"
] | [
"deepscaler"
] | d0eb02f4d9a9d533d1037c1ae43d5a06156c5d87241bfe6bef8cf458af5da6c7 | [
{
"content": "A circle with center $O$ has area $156\\pi$. Triangle $ABC$ is equilateral, $\\overline{BC}$ is a chord on the circle, $OA = 4\\sqrt{3}$, and point $O$ is outside $\\triangle ABC$. What is the side length of $\\triangle ABC$?",
"role": "user"
}
] | A circle with center $O$ has area $156\pi$. Triangle $ABC$ is equilateral, $\overline{BC}$ is a chord on the circle, $OA = 4\sqrt{3}$, and point $O$ is outside $\triangle ABC$. What is the side length of $\triangle ABC$? | "$6$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1037"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"826"
] | [
"deepscaler"
] | 9e95080b4c9903f744b5570d1d3d952eb8f929f747cb79ffc1043b2eaaa16dd1 | [
{
"content": "When $10^{93}-93$ is expressed as a single whole number, the sum of the digits is",
"role": "user"
}
] | When $10^{93}-93$ is expressed as a single whole number, the sum of the digits is | "826" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1039"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"20 seconds"
] | [
"deepscaler"
] | 1bd1b8f2dc6f451eaf006ce0bf041eb0c4bd0737775a025069685eb4808e8bc9 | [
{
"content": "The rails on a railroad are $30$ feet long. As the train passes over the point where the rails are joined, there is an audible click. \nThe speed of the train in miles per hour is approximately the number of clicks heard in:",
"role": "user"
}
] | The rails on a railroad are $30$ feet long. As the train passes over the point where the rails are joined, there is an audible click.
The speed of the train in miles per hour is approximately the number of clicks heard in: | "20 seconds" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1040"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2x-2"
] | [
"deepscaler"
] | f1cd919d61f6dc860a7e274b371e3d0d4c8f3e83f485d5985b8a558f2e1877e6 | [
{
"content": "When the polynomial $x^3-2$ is divided by the polynomial $x^2-2$, the remainder is",
"role": "user"
}
] | When the polynomial $x^3-2$ is divided by the polynomial $x^2-2$, the remainder is | "2x-2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1041"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-\\frac{1}{64}"
] | [
"deepscaler"
] | 48abe3aa081884759a2bfc023ab2a52c47758ffbc89fa874eb5a58a13b5f3197 | [
{
"content": "\\frac{3}{2} + \\frac{5}{4} + \\frac{9}{8} + \\frac{17}{16} + \\frac{33}{32} + \\frac{65}{64} - 7 =",
"role": "user"
}
] | \frac{3}{2} + \frac{5}{4} + \frac{9}{8} + \frac{17}{16} + \frac{33}{32} + \frac{65}{64} - 7 = | "-\\frac{1}{64}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1042"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2017"
] | [
"deepscaler"
] | 87179e4b5e3bda1c1956fc957fb912d054b9c463775563b7d4bd7e08dbfb7edf | [
{
"content": "Marvin had a birthday on Tuesday, May 27 in the leap year $2008$. In what year will his birthday next fall on a Saturday?",
"role": "user"
}
] | Marvin had a birthday on Tuesday, May 27 in the leap year $2008$. In what year will his birthday next fall on a Saturday? | "2017" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1043"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{xy}"
] | [
"deepscaler"
] | a56e9e275e64a627ae296ac12d006abb05dde16fdb9dc7074b72cd9b40fe6ec8 | [
{
"content": "If $x, y$ and $2x + \\frac{y}{2}$ are not zero, then\n$\\left( 2x + \\frac{y}{2} \\right)^{-1} \\left[(2x)^{-1} + \\left( \\frac{y}{2} \\right)^{-1} \\right]$ equals",
"role": "user"
}
] | If $x, y$ and $2x + \frac{y}{2}$ are not zero, then
$\left( 2x + \frac{y}{2} \right)^{-1} \left[(2x)^{-1} + \left( \frac{y}{2} \right)^{-1} \right]$ equals | "\\frac{1}{xy}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1044"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"deepscaler"
] | 949d0625e0075c2417e39ff630d50ca84893f7cb5732dbc3ad21023248e807f4 | [
{
"content": "There are $52$ people in a room. what is the largest value of $n$ such that the statement \"At least $n$ people in this room have birthdays falling in the same month\" is always true?",
"role": "user"
}
] | There are $52$ people in a room. what is the largest value of $n$ such that the statement "At least $n$ people in this room have birthdays falling in the same month" is always true? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1045"}] | {
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} |
[
"\\frac{1}{9}"
] | [
"deepscaler"
] | 433f4a76f6fedd4ea43514c18f630ef569c56d2b050f431e6499045eb2e583cf | [
{
"content": "Three fair dice are tossed at random (i.e., all faces have the same probability of coming up). What is the probability that the three numbers turned up can be arranged to form an arithmetic progression with common difference one?",
"role": "user"
}
] | Three fair dice are tossed at random (i.e., all faces have the same probability of coming up). What is the probability that the three numbers turned up can be arranged to form an arithmetic progression with common difference one? | "\\frac{1}{9}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1046"}] | {
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} |
[
"20"
] | [
"deepscaler"
] | 1d70eba63fbdeb557c6d36d848729def59868788dd7d283f7a6725b08004877d | [
{
"content": "All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $7$ smallest triangles has area $1,$ and $\\triangle ABC$ has area $40$. What is the area of trapezoid $DBCE$?",
"role": "user"
}
] | All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB=AC$. Each of the $7$ smallest triangles has area $1,$ and $\triangle ABC$ has area $40$. What is the area of trapezoid $DBCE$? | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1047"}] | {
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"reference_components": 1,
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} |
[
"34"
] | [
"deepscaler"
] | ff97c92934cc6df8af3c909825906f8dc38eaad2c0b17d46b397c780258b77cd | [
{
"content": "The average age of the $6$ people in Room A is $40$. The average age of the $4$ people in Room B is $25$. If the two groups are combined, what is the average age of all the people?",
"role": "user"
}
] | The average age of the $6$ people in Room A is $40$. The average age of the $4$ people in Room B is $25$. If the two groups are combined, what is the average age of all the people? | "34" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1048"}] | {
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} |
[
"60"
] | [
"deepscaler"
] | 18fb051eb6cfdd32aa6cabda3946f6fdba551815e6434073fd232a7e5fcb010e | [
{
"content": "Find the degree measure of an angle whose complement is 25% of its supplement.",
"role": "user"
}
] | Find the degree measure of an angle whose complement is 25% of its supplement. | "60" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1049"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"500"
] | [
"deepscaler"
] | a046c48f2757c88979ffe6b9b2f97c3a084912a71592c4b40892279c87268d2a | [
{
"content": "A quadrilateral is inscribed in a circle of radius $200\\sqrt{2}$. Three of the sides of this quadrilateral have length $200$. What is the length of the fourth side?",
"role": "user"
}
] | A quadrilateral is inscribed in a circle of radius $200\sqrt{2}$. Three of the sides of this quadrilateral have length $200$. What is the length of the fourth side? | "500" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1050"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2874"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"deepscaler"
] | 5b89ca77ec542bd6a9ac7b8c2f8f8723c304daf29353088f922ef9088f08546c | [
{
"content": "Jim starts with a positive integer $n$ and creates a sequence of numbers. Each successive number is obtained by subtracting the largest possible integer square less than or equal to the current number until zero is reached. For example, if Jim starts with $n = 55$, then his sequence contains $5$ n... | Jim starts with a positive integer $n$ and creates a sequence of numbers. Each successive number is obtained by subtracting the largest possible integer square less than or equal to the current number until zero is reached. For example, if Jim starts with $n = 55$, then his sequence contains $5$ numbers:
$\begin{array... | "3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1052"}] | {
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} |
[
"11110"
] | [
"deepscaler"
] | 40f3271e83fa92bbf7ed1192402920e2ba587a1db690a418d870efbd4412d098 | [
{
"content": "What is the value of $1234 + 2341 + 3412 + 4123$",
"role": "user"
}
] | What is the value of $1234 + 2341 + 3412 + 4123$ | "11110" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1053"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1718"}] | {
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"reference_components": 1,
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} |
[
"-16"
] | [
"deepscaler"
] | 753a7034c0ba33e4dcc6eb133bba1ebac8915688f26095cef0d29e1c96be5412 | [
{
"content": "If $y$ varies directly as $x$, and if $y=8$ when $x=4$, the value of $y$ when $x=-8$ is:",
"role": "user"
}
] | If $y$ varies directly as $x$, and if $y=8$ when $x=4$, the value of $y$ when $x=-8$ is: | "-16" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1054"}] | {
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"reference_components": 1,
"reference_present": true
} |
[
"4032"
] | [
"deepscaler"
] | 594dcba3d079ab27fb3832f93e620622b7d506462742a4e6198d60a1905819e8 | [
{
"content": "Let $x=-2016$. What is the value of $|| |x|-x|-|x||-x$ ?",
"role": "user"
}
] | Let $x=-2016$. What is the value of $|| |x|-x|-|x||-x$ ? | "4032" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1055"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2363"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.5"
] | [
"deepscaler"
] | b25344a5fa6ea3eb36bc99bf45e17bdd37af7413631703f6bbcb6190dc338d38 | [
{
"content": "If $9^{x + 2} = 240 + 9^x$, then the value of $x$ is:",
"role": "user"
}
] | If $9^{x + 2} = 240 + 9^x$, then the value of $x$ is: | "0.5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1056"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | 01c199d02ad480d4ecc9c7c1177bfb3980c8190236e565e36abf04011ab51a9d | [
{
"content": "What is the value of \\(\\frac{\\log_2 80}{\\log_{40}2}-\\frac{\\log_2 160}{\\log_{20}2}\\)?",
"role": "user"
}
] | What is the value of \(\frac{\log_2 80}{\log_{40}2}-\frac{\log_2 160}{\log_{20}2}\)? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1059"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"72"
] | [
"deepscaler"
] | 3c3a698499c7adf5c7ef28e00bec9c759a8a5c0adc0f10fa252885fc8c6e99a0 | [
{
"content": "A wooden cube has edges of length $3$ meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. The entire surface area including the inside, in square meters, is",
"role": "user"
}
] | A wooden cube has edges of length $3$ meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. The entire surface area including the inside, in square meters, is | "72" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1060"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"80"
] | [
"deepscaler"
] | 5bb3a0deb2adf339a8de1103eff6db79568d2e8a3b7b14d92750267e4cc10a39 | [
{
"content": "If an integer $n > 8$ is a solution of the equation $x^2 - ax+b=0$ and the representation of $a$ in the base-$n$ number system is $18$, then the base-n representation of $b$ is",
"role": "user"
}
] | If an integer $n > 8$ is a solution of the equation $x^2 - ax+b=0$ and the representation of $a$ in the base-$n$ number system is $18$, then the base-n representation of $b$ is | "80" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1061"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"deepscaler"
] | c190d304e83a9458c6fdc0d93e39fc2568b14ed4f17ada8dd29976c597a786c2 | [
{
"content": "How many $4$-digit positive integers (that is, integers between $1000$ and $9999$, inclusive) having only even digits are divisible by $5?$",
"role": "user"
}
] | How many $4$-digit positive integers (that is, integers between $1000$ and $9999$, inclusive) having only even digits are divisible by $5?$ | "100" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1062"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1712"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"33"
] | [
"deepscaler"
] | fe2d1928c7da33d3e2ccc066c1c52758173ddc8ee9697e94997b7172d2d20476 | [
{
"content": "The number of solution-pairs in the positive integers of the equation $3x+5y=501$ is:",
"role": "user"
}
] | The number of solution-pairs in the positive integers of the equation $3x+5y=501$ is: | "33" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1063"}] | {
"all_reference_components_parse": true,
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} |
[
"1"
] | [
"deepscaler"
] | 601dd2969a6c8b57f2025d0ab262daca046dc1e2d5b5e19d4f843cdadb221fd4 | [
{
"content": "Let $c = \\frac{2\\pi}{11}.$ What is the value of\n\\[\\frac{\\sin 3c \\cdot \\sin 6c \\cdot \\sin 9c \\cdot \\sin 12c \\cdot \\sin 15c}{\\sin c \\cdot \\sin 2c \\cdot \\sin 3c \\cdot \\sin 4c \\cdot \\sin 5c}?\\]",
"role": "user"
}
] | Let $c = \frac{2\pi}{11}.$ What is the value of
\[\frac{\sin 3c \cdot \sin 6c \cdot \sin 9c \cdot \sin 12c \cdot \sin 15c}{\sin c \cdot \sin 2c \cdot \sin 3c \cdot \sin 4c \cdot \sin 5c}?\] | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1064"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"deepscaler"
] | bc4dc196f0a73745341d1abc332fafbeb88245b283824b3d267e357851a7c210 | [
{
"content": "An insect lives on the surface of a regular tetrahedron with edges of length 1. It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? (Note: Two edges of a tetrahedron are opposite if ... | An insect lives on the surface of a regular tetrahedron with edges of length 1. It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? (Note: Two edges of a tetrahedron are opposite if they have no common en... | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1065"}] | {
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} |
[
"15"
] | [
"deepscaler"
] | 938ce9444cfbcd8239a183dffd63b178dbc005fefbffcb3f07e57b3f15d25229 | [
{
"content": "If $2x+1=8$, then $4x+1=$",
"role": "user"
}
] | If $2x+1=8$, then $4x+1=$ | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1066"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"deepscaler"
] | f4fef2c00daa8f4363687ff2cd121c60bea5b85c93844802bd2f4ce4583271f6 | [
{
"content": "A list of integers has mode 32 and mean 22. The smallest number in the list is 10. The median m of the list is a member of the list. If the list member m were replaced by m+10, the mean and median of the new list would be 24 and m+10, respectively. If m were instead replaced by m-8, the medi... | A list of integers has mode 32 and mean 22. The smallest number in the list is 10. The median m of the list is a member of the list. If the list member m were replaced by m+10, the mean and median of the new list would be 24 and m+10, respectively. If m were instead replaced by m-8, the median of the new list wou... | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1067"}] | {
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"reference_components": 1,
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} |
[
"66"
] | [
"deepscaler"
] | 1a07381fd1069d0453a1904b15ec0f0a6c4ee6be4a655f6b4c599f96ebfc7802 | [
{
"content": "A box contains $3$ shiny pennies and $4$ dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is $a/b$ that it will take more than four draws until the third shiny penny appears and $a/b$ is in lowest terms, then $a+b=$",
"role": "user"
}
] | A box contains $3$ shiny pennies and $4$ dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is $a/b$ that it will take more than four draws until the third shiny penny appears and $a/b$ is in lowest terms, then $a+b=$ | "66" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1068"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
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} |
[
"13"
] | [
"deepscaler"
] | 63afe0fc3cb17e9c70191df455b15bd17b54c78cb844986d27a1f9e804663d59 | [
{
"content": "The lines with equations $ax-2y=c$ and $2x+by=-c$ are perpendicular and intersect at $(1, -5)$. What is $c$?",
"role": "user"
}
] | The lines with equations $ax-2y=c$ and $2x+by=-c$ are perpendicular and intersect at $(1, -5)$. What is $c$? | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1069"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"deepscaler"
] | 97407a7f14b6583a277a80406be935c3068bb1a6ec20df8ab24729bc4cb70891 | [
{
"content": "In one of the adjoining figures a square of side $2$ is dissected into four pieces so that $E$ and $F$ are the midpoints of opposite sides and $AG$ is perpendicular to $BF$. These four pieces can then be reassembled into a rectangle as shown in the second figure. The ratio of height to base, $XY /... | In one of the adjoining figures a square of side $2$ is dissected into four pieces so that $E$ and $F$ are the midpoints of opposite sides and $AG$ is perpendicular to $BF$. These four pieces can then be reassembled into a rectangle as shown in the second figure. The ratio of height to base, $XY / YZ$, in this rectangl... | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1070"}] | {
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"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"20"
] | [
"deepscaler"
] | 6eff131483495e93be1440e7fbce789eb7f0969e272c56de789c1a293c95d06b | [
{
"content": "In rectangle $ABCD$, $\\overline{AB}=20$ and $\\overline{BC}=10$. Let $E$ be a point on $\\overline{CD}$ such that $\\angle CBE=15^\\circ$. What is $\\overline{AE}$?",
"role": "user"
}
] | In rectangle $ABCD$, $\overline{AB}=20$ and $\overline{BC}=10$. Let $E$ be a point on $\overline{CD}$ such that $\angle CBE=15^\circ$. What is $\overline{AE}$? | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1071"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6:00"
] | [
"deepscaler"
] | 430dd633a13d380edf69bcba05decad1868752215d1af664068ca53c97c4ec91 | [
{
"content": "The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his... | The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at hi... | "6:00" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1073"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"deepscaler"
] | 620f62482f0e7c86cef2971394c80db4e585d351c30266e712feb9c098a4bc7e | [
{
"content": "Mientka Publishing Company prices its bestseller Where's Walter? as follows:\n$C(n) = \\begin{cases} 12n, & \\text{if } 1 \\le n \\le 24 \\\\ 11n, & \\text{if } 25 \\le n \\le 48 \\\\ 10n, & \\text{if } 49 \\le n \\end{cases}$\nwhere $n$ is the number of books ordered, and $C(n)$ is the cost in do... | Mientka Publishing Company prices its bestseller Where's Walter? as follows:
$C(n) = \begin{cases} 12n, & \text{if } 1 \le n \le 24 \\ 11n, & \text{if } 25 \le n \le 48 \\ 10n, & \text{if } 49 \le n \end{cases}$
where $n$ is the number of books ordered, and $C(n)$ is the cost in dollars of $n$ books. Notice that $25$ b... | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1074"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"deepscaler"
] | 1419db21603a320e6ffc32626de9a8708dc1e5d610fd913e3389a6dccac30dab | [
{
"content": "The value of $\\frac{1}{16}a^0+\\left (\\frac{1}{16a} \\right )^0- \\left (64^{-\\frac{1}{2}} \\right )- (-32)^{-\\frac{4}{5}}$ is:",
"role": "user"
}
] | The value of $\frac{1}{16}a^0+\left (\frac{1}{16a} \right )^0- \left (64^{-\frac{1}{2}} \right )- (-32)^{-\frac{4}{5}}$ is: | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1075"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"[201,400]"
] | [
"deepscaler"
] | 0802c555ba1cccc7e27918d5e8d5e0fa912c314a324e3710ee18457eca087323 | [
{
"content": "For a certain positive integer $n$ less than $1000$, the decimal equivalent of $\\frac{1}{n}$ is $0.\\overline{abcdef}$, a repeating decimal of period of $6$, and the decimal equivalent of $\\frac{1}{n+6}$ is $0.\\overline{wxyz}$, a repeating decimal of period $4$. In which interval does $n$ lie?"... | For a certain positive integer $n$ less than $1000$, the decimal equivalent of $\frac{1}{n}$ is $0.\overline{abcdef}$, a repeating decimal of period of $6$, and the decimal equivalent of $\frac{1}{n+6}$ is $0.\overline{wxyz}$, a repeating decimal of period $4$. In which interval does $n$ lie? | "[201,400]" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1076"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"deepscaler"
] | f355cd60058c599ae304428f3e7e0a3acb10be9bfe2d62a2b4aa1e3bba41a5df | [
{
"content": "In a sign pyramid a cell gets a \"+\" if the two cells below it have the same sign, and it gets a \"-\" if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produc... | In a sign pyramid a cell gets a "+" if the two cells below it have the same sign, and it gets a "-" if the two cells below it have different signs. The diagram below illustrates a sign pyramid with four levels. How many possible ways are there to fill the four cells in the bottom row to produce a "+" at the top of the ... | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1077"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
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