split stringclasses 4
values | question_id stringlengths 26 43 | sample_index int16 0 15 | text stringlengths 103 7.74k ⌀ | token_ids listlengths 31 2.05k ⌀ | sampled_logprobs listlengths 31 2.05k ⌀ | self_certainty listlengths 31 2.05k ⌀ | finish_reason stringclasses 2
values | truncated bool 2
classes | generated_token_count int32 31 2.05k ⌀ | reference_chat_tokens int32 57 2.99k ⌀ | request_seed int64 12.8k 2.15B ⌀ | generation_identity stringclasses 4
values | native_generation_seconds_share float64 0.06 4.5 ⌀ | lowest_confidence float64 0.71 28.9 ⌀ | bottom10_confidence float64 2.98 32 ⌀ | extraction_inline_input_tokens int32 84 3.02k ⌀ | extraction_inline_output_tokens int32 1 128 ⌀ | extraction_inline_seconds_share float64 0 0.31 ⌀ | extraction_final_input_tokens int32 84 3.02k ⌀ | extraction_final_output_tokens int32 1 128 ⌀ | extraction_final_seconds_share float64 0 0.29 ⌀ | pred stringlengths 0 574 ⌀ | prediction stringlengths 0 475 ⌀ | extraction_failed bool 2
classes | embedding_valid bool 1
class | reasoning_mean_logprob float64 -0.66 -0 ⌀ | answer_mean_logprob float64 -6.94 0 ⌀ | reasoning_mean_entropy float64 0.01 0.76 ⌀ | reasoning_token_count int32 30 2.05k ⌀ | answer_token_count int32 0 125 ⌀ | feature_input_tokens int32 56 2.99k ⌀ | feature_seconds_share float64 0.01 0.21 ⌀ | correct bool 2
classes | raw_correct bool 2
classes |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
calibration | study_gsm8k_calibration_4a043e8d63be6481 | 0 | Let the total number of seats in the auditorium be $S = 500$.
The number of seats taken is $\frac{2}{5}$ of the total number of seats. So, the number of seats taken is
$$ \frac{2}{5} \times 500 = 2 \times 100 = 200 $$
The number of seats broken is $\frac{1}{10}$ of the total number of seats. So, the number of broken se... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 1 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats broken is $\frac{1}{10}$ of the total seats, so the number of seats broken is $\frac{1}{10} \tim... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 2 | Let the total number of seats in the auditorium be $S = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 3 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total number of seats, so the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats broken is $\frac{1}{10}$ of the total number of seats, so the number of broken seats i... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 4 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 5 | Let the total number of seats in the auditorium be 500.
The number of seats taken is $\frac{2}{5}$ of the total number of seats, so the number of seats taken is $\frac{2}{5} \times 500$.
$\frac{2}{5} \times 500 = 2 \times 100 = 200$ seats are taken.
The number of seats broken is $\frac{1}{10}$ of the total number of se... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 6 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is
$$ \frac{2}{5} \times 500 = 2 \times 100 = 200 $$
The number of seats broken is $\frac{1}{10}$ of the total seats, so the number of broken seats is
$$ \frac{1}{10}... | [
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34.84176635742... | length | true | 1,024 | 1,077 | 481,118,195 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.127802 | 10.058181 | 10.821692 | 1,100 | 5 | 0.002346 | 1,100 | 5 | 0.002367 | 250 | 250 | true | true | -0.12939 | 0 | 0.148833 | 1,024 | 0 | 1,075 | 0.030155 | true | true |
calibration | study_gsm8k_calibration_4a043e8d63be6481 | 7 | Let the total number of seats in the auditorium be $S = 500$.
The number of seats that are currently taken is $\frac{2}{5}$ of the total number of seats.
Number of taken seats = $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats that are broken is $\frac{1}{10}$ of the total number of seats.
Number of b... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 8 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats that are taken is $\frac{2}{5}$ of the total number of seats, so the number of taken seats is
$$ \frac{2}{5} \times 500 = 2 \times 100 = 200 $$
The number of seats that are broken is $\frac{1}{10}$ of the total number of seats, so the num... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 9 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 10 | Let the total number of seats in the auditorium be 500.
The number of seats that are taken is $\frac{2}{5}$ of the total seats.
Number of seats taken = $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats that are broken is $\frac{1}{10}$ of the total seats.
Number of broken seats = $\frac{1}{10} \times 5... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 11 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is
$S_t = \frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats broken is $\frac{1}{10}$ of the total seats, so the number of seats broken is
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 12 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats broken is $\frac{1}{10}$ of the total seats, so the number of broken seats is $\frac{1}{10} \tim... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 13 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats. So, the number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats broken is $\frac{1}{10}$ of the total seats. So, the number of broken seats is $\frac{1}{10} \t... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 14 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5}$ of the total seats, so the number of taken seats is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of broken seats is $\frac{1}{10}$ of the total seats, so the number of broken seats is $\frac{1}{10} \tim... | [
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calibration | study_gsm8k_calibration_4a043e8d63be6481 | 15 | Let the total number of seats in the auditorium be $T = 500$.
The number of seats taken is $\frac{2}{5} \times 500 = 2 \times 100 = 200$.
The number of seats broken is $\frac{1}{10} \times 500 = 50$.
The number of seats taken and broken is $200 + 50 = 250$.
The number of seats still available is the total number of sea... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 0 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given that $w_1 = 20$ pounds, $w_2 = 40$ pounds, $w_3 = 10$ pounds, $w_4 = 30$ pounds, and $w_5 = 50$ pounds.
For every 10 pounds they weigh, they need 1 pound of dog food per day.
We can find the amount of dog food needed for each dog by dividing th... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 1 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$. We are given that $w_1 = 20$ pounds, $w_2 = 40$ pounds, $w_3 = 10$ pounds, $w_4 = 30$ pounds, and $w_5 = 50$ pounds.
We are also given that for every 10 pounds a dog weighs, they need 1 pound of dog food per day.
We can find the amount of dog food needed fo... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 2 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$. We are given that:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds they weigh, they need 1 pound of dog food per day. We can find the amount of dog food needed for each dog by dividing their wei... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 3 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$. We are given that $w_1 = 20$ pounds, $w_2 = 40$ pounds, $w_3 = 10$ pounds, $w_4 = 30$ pounds, and $w_5 = 50$ pounds.
For every 10 pounds they weigh, they need 1 pound of dog food per day.
We can find the amount of dog food needed for each dog by dividing t... | [
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506,
18710,
529,
506,
3493,
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 4 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
Given:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds, the dogs need 1 pound of dog food per day.
This means that the ratio of weight to food is 10:1.
So, for $x$ pounds of dog food, we need $x... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 5 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$. We are given the weights as:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds of weight, a dog needs 1 pound of dog food per day. This means the amount of dog food needed per pound is $\frac{1}{1... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 6 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given that the weights are:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds they weigh, they need 1 pound of dog food per day. This means that the amount of dog food needed per pound is $... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 7 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
The weights are given as:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds of dog weight, they need 1 pound of dog food per day.
This means that the ratio of dog food needed to dog weight is $\fr... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 8 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given that:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds they weigh, they need 1 pound of dog food per day. This means that the amount of dog food needed is proportional to the weight ... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 9 | Let's calculate the dog food needed for each dog:
- The first dog weighs 20 pounds. Since they need 1 pound of food per 10 pounds of weight, the first dog needs 20/10 * 1 = 2 pounds of food.
- The second dog weighs 40 pounds. They need 40/10 * 1 = 4 pounds of food.
- The third dog weighs 10 pounds. They need 10/10 * 1 ... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 10 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given that $w_1 = 20$ pounds, $w_2 = 40$ pounds, $w_3 = 10$ pounds, $w_4 = 30$ pounds, and $w_5 = 50$ pounds.
For every 10 pounds, the dogs need 1 pound of dog food per day.
We can find the amount of food needed for each dog by dividing its weight by... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 11 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given that $w_1 = 20$ pounds, $w_2 = 40$ pounds, $w_3 = 10$ pounds, $w_4 = 30$ pounds, and $w_5 = 50$ pounds.
For every 10 pounds of dog weight, they need 1 pound of dog food per day. This means that the ratio of dog food to weight is $\frac{1 \text{... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 12 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given that the weights are:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds a dog weighs, they need 1 pound of dog food per day.
We can find the amount of dog food needed for each dog by d... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 13 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$.
We are given the weights of the dogs as follows:
$w_1 = 20$ pounds
$w_2 = 40$ pounds
$w_3 = 10$ pounds
$w_4 = 30$ pounds
$w_5 = 50$ pounds
For every 10 pounds they weigh, they need 1 pound of dog food per day.
We can find the food needed per dog by dividing... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 14 | Let the weights of the five dogs be $w_1, w_2, w_3, w_4, w_5$. We are given that $w_1 = 20$ pounds, $w_2 = 40$ pounds, $w_3 = 10$ pounds, $w_4 = 30$ pounds, and $w_5 = 50$ pounds.
For every 10 pounds of weight, a dog needs 1 pound of dog food per day.
We can find the food needed for each dog by dividing the weight of t... | [
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calibration | study_gsm8k_calibration_afb614dfb03558a1 | 15 | Let's calculate the dog food needed for each dog:
- Dog 1 weighs 20 pounds. Since they need 1 pound of food per 10 pounds of weight, they need $\frac{20}{10} = 2$ pounds of food.
- Dog 2 weighs 40 pounds. They need $\frac{40}{10} = 4$ pounds of food.
- Dog 3 weighs 10 pounds. They need $\frac{10}{10} = 1$ pound of food... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 0 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F.
We are given that $C_1 = 4$.
Let $C_2$ be the number of crickets Gilbert eats per week when the temperature averages 100 degrees F.
We are given that $C_2 = 2 \times C_1 = 2 \times 4 = 8$.
The temperature averages 90 d... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 1 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F per day, and $C_2$ be the number of crickets he eats per week when the temperature averages 100 degrees F per day.
We are given that $C_1 = 4$ crickets per week when the temperature averages 90 degrees F.
When the tempe... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 2 | Let $c_1$ be the number of crickets Gilbert eats per week at 90 degrees F, and $c_2$ be the number of crickets he eats per week at 100 degrees F.
We are given that $c_1 = 4$ and $c_2 = 2 \cdot c_1 = 2 \cdot 4 = 8$.
The temperature averages 90 degrees F for 80% of the time, and 100 degrees F for the remaining 20% of the... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 3 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F per day, and $C_2$ be the number of crickets he eats per week when the temperature averages 100 degrees F per day. We are given that $C_1 = 4$ and $C_2 = 2 \times C_1 = 2 \times 4 = 8$.
The temperature averages 90 degre... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 4 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F, and $C_2$ be the number of crickets he eats per week when the temperature averages 100 degrees F. We are given that $C_1 = 4$ and $C_2 = 2 \times C_1 = 2 \times 4 = 8$.
Let $T_1$ be the percentage of time the temperatu... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 5 | Let $c_1$ be the number of crickets Gilbert eats per week when the temperature is 90 degrees F. We are given that $c_1 = 4$.
Let $c_2$ be the number of crickets Gilbert eats per week when the temperature is 100 degrees F. We are given that $c_2 = 2 \times c_1 = 2 \times 4 = 8$.
The temperature averages 90 degrees F fo... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 6 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature is 90 degrees F, and let $C_2$ be the number of crickets he eats per week when the temperature is 100 degrees F.
We are given that $C_1 = 4$ crickets per week when the temperature is 90 degrees F.
We are also given that $C_2 = 2 \times C_1 =... | [
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14.14381980895... | stop | false | 576 | 677 | 1,554,080,883 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.127802 | 16.862566 | 17.783309 | 700 | 4 | 0.002346 | 700 | 4 | 0.002367 | 72 | 72 | false | true | -0.087854 | 0 | 0.094852 | 570 | 2 | 676 | 0.02142 | true | true |
calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 7 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F, so $C_1 = 4$.
Let $C_2$ be the number of crickets Gilbert eats per week when the temperature averages 100 degrees F, so $C_2 = 2 \cdot C_1 = 2 \cdot 4 = 8$.
The temperature averages 90 degrees F for 80% of the time. Th... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 8 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature is 90 degrees F, and $C_2$ be the number of crickets he eats per week when the temperature is 100 degrees F.
We are given that $C_1 = 4$ crickets per week when the temperature averages 90 degrees F.
We are also given that $C_2 = 2 \times C_1... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 9 | Let $c_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F.
We are given that $c_1 = 4$ crickets per week.
Let $c_2$ be the number of crickets Gilbert eats per week when the temperature averages 100 degrees F.
We are given that $c_2 = 2 \times c_1 = 2 \times 4 = 8$ crickets per... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 10 | Let $C_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F, and $C_2$ be the number of crickets he eats per week when the temperature averages 100 degrees F.
We are given that $C_1 = 4$ crickets per week when the temperature is 90 degrees F.
We are also given that $C_2 = 2 \tim... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 11 | Let $c_1$ be the number of crickets Gilbert eats per week when the temperature averages 90 degrees F per day, and $c_2$ be the number of crickets he eats per week when the temperature averages 100 degrees F per day. We are given that $c_1 = 4$ and $c_2 = 2c_1 = 2(4) = 8$.
The temperature averages 90 degrees F for 80% o... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 12 | Let $C_1$ be the number of crickets Gilbert eats per week when the average temperature is 90 degrees F.
$C_1 = 4$ crickets per week.
Let $C_2$ be the number of crickets Gilbert eats per week when the average temperature is 100 degrees F.
$C_2 = 2 \times C_1 = 2 \times 4 = 8$ crickets per week.
The temperature averages... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 13 | Let $C_1$ be the number of crickets Gilbert eats per week at 90 degrees F, and $C_2$ be the number of crickets he eats per week at 100 degrees F.
We are given that $C_1 = 4$ crickets per week when the temperature is 90 degrees F.
We are also given that $C_2 = 2 \times C_1 = 2 \times 4 = 8$ crickets per week when the te... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 14 | Let $c_1$ be the number of crickets Gilbert eats per week when the temperature is 90 degrees F, and $c_2$ be the number of crickets he eats per week when the temperature is 100 degrees F.
We are given that $c_1 = 4$ crickets per week when the temperature is 90 degrees F.
When the temperature is 100 degrees F, he eats t... | [
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calibration | study_gsm8k_calibration_7e3d9f62063a1d3d | 15 | Let $c_1$ be the number of crickets Gilbert eats per week when the temperature is 90 degrees F, and $c_2$ be the number of crickets he eats per week when the temperature is 100 degrees F.
We are given that $c_1 = 4$ crickets per week when the temperature averages 90 degrees F.
We are also given that $c_2 = 2c_1 = 2(4) ... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 0 | Let $N$ be the total number of beakers in the laboratory, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $N-C$ be the number of beakers without copper ions, which is $22 - 8 = 14$.
We are given that 3 drops of a solution turn the liquid in a beaker blue if there are copper ions present.... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 1 | Let $N$ be the total number of beakers in the laboratory, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $N - C$ be the number of beakers without copper ions, which is $22 - 8 = 14$.
Let $d$ be the number of drops used per beaker test, which is 3.
Let $T$ be the total number of drops us... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 2 | Let $B$ be the total number of beakers, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $N$ be the number of beakers without copper ions, so $N = B - C = 22 - 8 = 14$.
Let $d$ be the number of drops used per beaker. We are given that 3 drops turn the liquid blue if there are copper ions.... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 3 | Let $N$ be the total number of beakers, so $N = 22$.
Let $C$ be the number of beakers with copper ions, so $C = 8$.
Let $N - C$ be the number of beakers without copper ions, so $N - C = 22 - 8 = 14$.
We are given that 3 drops of a solution will turn the liquid in a beaker blue if there are copper ions present.
We are g... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 4 | Let $N$ be the total number of beakers in the laboratory, so $N = 22$.
Let $C$ be the number of beakers with copper ions, so $C = 8$.
Let $N - C$ be the number of beakers without copper ions, so $N - C = 22 - 8 = 14$.
Let $d$ be the number of drops used per beaker tested. Since the problem states "three drops of a solu... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 5 | Let $N$ be the total number of beakers, so $N = 22$.
Let $C$ be the number of beakers with copper ions, so $C = 8$.
Let $N - C$ be the number of beakers without copper ions, so $N - C = 22 - 8 = 14$.
Let $d$ be the number of drops used per beaker test. In this case, $d = 3$ drops.
The total number of drops used is 45.
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 6 | Let $N$ be the total number of beakers in the laboratory, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $W$ be the number of beakers without copper ions, so $W = N - C = 22 - 8 = 14$.
Each drop of the solution can turn a beaker blue if there are copper ions present.
We are given that 4... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 7 | Let $B$ be the total number of beakers in the laboratory, so $B = 22$.
Let $C$ be the number of beakers with copper ions, so $C = 8$.
Let $N$ be the number of beakers without copper ions, so $N = B - C = 22 - 8 = 14$.
Let $d$ be the number of drops used per beaker. In this case, $d=3$.
Let $D$ be the total number of dr... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 8 | Let $N$ be the total number of beakers in the lab, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $N-C$ be the number of beakers without copper ions, which is $22 - 8 = 14$.
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 9 | Let $N$ be the total number of beakers in the laboratory, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $N-C$ be the number of beakers without copper ions, which is $22-8 = 14$.
Let $d$ be the number of drops used to test each beaker. We are given that 3 drops are used to test each bea... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 10 | Let $N$ be the total number of beakers in the laboratory, so $N=22$.
Let $C$ be the number of beakers with copper ions, so $C=8$.
Let $N-C$ be the number of beakers without copper ions, so $N-C = 22-8 = 14$.
Let $d$ be the number of drops used per beaker test, so $d=3$.
Let $T$ be the total number of drops used before ... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 11 | Let $N$ be the total number of beakers in the laboratory. We are given that $N = 22$.
Let $C$ be the number of beakers with copper ions, so $C = 8$.
Let $W$ be the number of beakers without copper ions, so $W = N - C = 22 - 8 = 14$.
We are given that 3 drops of a solution are used to test a beaker.
We are also given th... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 12 | Let $N$ be the total number of beakers in the laboratory. We are given that $N = 22$.
Let $C$ be the number of beakers with copper ions in them. We are given that $C = 8$.
Let $N_0$ be the number of beakers without copper ions. Then $N_0 = N - C = 22 - 8 = 14$.
We are told that adding three drops of a solution will tur... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 13 | Let $N$ be the total number of beakers in the laboratory, so $N = 22$.
Let $C$ be the number of beakers with copper ions, so $C = 8$.
Let $N - C$ be the number of beakers without copper ions, so $N - C = 22 - 8 = 14$.
We are given that adding three drops of a solution will turn the liquid in a beaker blue if there are ... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 14 | Let $B$ be the total number of beakers in the laboratory, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $N$ be the number of beakers without copper ions, so $N = B - C = 22 - 8 = 14$.
Let $d$ be the number of drops needed to detect copper ions in a beaker. We are given that $d = 3$.
We... | [
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calibration | study_gsm8k_calibration_0106aacdd8f409e9 | 15 | Let $N$ be the total number of beakers, which is 22.
Let $C$ be the number of beakers with copper ions, which is 8.
Let $W$ be the number of beakers without copper ions, so $W = N - C = 22 - 8 = 14$.
We are given that 3 drops of a solution will turn the liquid in a beaker blue if there are copper ions present.
We are a... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 0 | Let $x$ be the length of the short sides of the rectangular plot.
The long sides of the plot are three times the length of the short sides, so the length of the long sides is $3x$.
The perimeter of the rectangular plot is $2(x) + 2(3x) = 2x + 6x = 8x$.
We are given that the total length of the fence is 640 feet. So, $8... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 1 | Let the length of the short side be $x$ feet. Then the length of the long side is $3x$ feet.
The perimeter of the rectangular plot is given by $2(x) + 2(3x) = 2x + 6x = 8x$.
We are given that the total length of the fence is 640 feet. Therefore, $8x = 640$.
Dividing both sides by 8, we get $x = \frac{640}{8} = 80$.
So ... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 2 | Let $l$ be the length of the long side and $s$ be the length of the short side of the rectangular plot.
We are given that the long sides are three times the length of the short sides, so $l = 3s$.
The perimeter of the rectangular plot is given by $2l + 2s$. We are given that the total length of the fence is 640 feet.
S... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 3 | Let the length of the short side of the rectangular plot be $x$ feet.
The long side is three times the length of the short side, so the length of the long side is $3x$ feet.
The perimeter of the rectangular plot is $2(\text{short side}) + 2(\text{long side}) = 2x + 2(3x) = 2x + 6x = 8x$.
We are given that the total len... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 4 | Let the short side of the rectangular plot be $x$ feet. The long side is three times the length of the short side, so the long side is $3x$ feet.
The perimeter of the rectangular plot is given by $2(\text{short side}) + 2(\text{long side})$.
We are given that the total length of the fence is 640 feet, so we have
$$2x +... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 5 | Let the length of the short side be $x$ feet.
Then the length of the long side is $3x$ feet.
The rectangular plot has two short sides of length $x$ and two long sides of length $3x$.
The total length of the fence is $2x + 2(3x) = 2x + 6x = 8x$.
We are given that the total length of the fence is 640 feet, so $8x = 640$.... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 6 | Let the length of the short side of the rectangular plot be $x$ feet.
The long side is three times the length of the short side, so the length of the long side is $3x$ feet.
The perimeter of the rectangular plot is given by $2(\text{short side}) + 2(\text{long side}) = 2x + 2(3x) = 2x + 6x = 8x$.
We are given that the ... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 7 | Let the length of the short side of the rectangular plot be $x$ feet.
The long side of the plot is three times the length of the short side, so the length of the long side is $3x$ feet.
The perimeter of the rectangular plot is given by $2(\text{short side}) + 2(\text{long side}) = 2x + 2(3x) = 2x + 6x = 8x$.
We are giv... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 8 | Let $x$ be the length of the short sides of the rectangular plot.
The long sides of the plot are three times the length of the short sides, so the length of the long sides is $3x$.
The perimeter of the rectangular plot is $2(\text{short side}) + 2(\text{long side}) = 2x + 2(3x) = 2x + 6x = 8x$.
We are given that the to... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 9 | Let $x$ be the length of the short side of the rectangular plot. Then the long side is $3x$. The perimeter of the rectangular plot is $2x + 2(3x) = 2x + 6x = 8x$.
We are given that the total length of the fence is 640 feet, so $8x = 640$. Dividing both sides by 8, we get $x = \frac{640}{8} = 80$.
Thus, the short side i... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 10 | Let the length of the short side of the rectangular plot be $x$ feet.
The long side of the plot is three times the length of the short side, so the length of the long side is $3x$ feet.
The perimeter of the rectangular plot is the total length of the fence, which is given by $2(\text{short side}) + 2(\text{long side}) ... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 11 | Let the length of the short side of the rectangular plot be $x$ feet. Then the length of the long side is $3x$ feet.
The perimeter of the rectangle is given by $2(\text{short side}) + 2(\text{long side})$.
We are given that the total length of the fence is 640 feet. So,
$$2x + 2(3x) = 640$$
$$2x + 6x = 640$$
$$8x = 640... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 12 | Let the length of the short side of the rectangular plot be $x$ feet.
The length of the long side is three times the length of the short side, so the length of the long side is $3x$ feet.
The perimeter of the rectangular plot is $2(x) + 2(3x) = 2x + 6x = 8x$.
We are given that the total length of the fence is 640 feet.... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 13 | Let $x$ be the length of the short side of the rectangular plot. Then the length of the long side is $3x$.
The perimeter of the rectangular plot is $2(x) + 2(3x) = 2x + 6x = 8x$.
We are given that the total length of the fence is 640 feet, so $8x = 640$.
Dividing both sides by 8, we get $x = \frac{640}{8} = 80$.
So the... | [
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calibration | study_gsm8k_calibration_5ed86699f1001353 | 14 | Let the length of the short side of the rectangular plot be $s$ feet. Then the length of the long side is $3s$ feet.
The perimeter of the rectangle is given by $2s + 2(3s) = 2s + 6s = 8s$.
We are given that the total length of the fence is 640 feet. So, $8s = 640$.
Dividing both sides by 8, we get $s = \frac{640}{8} = ... | [
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20.161699295... | stop | false | 395 | 483 | 1,170,626,759 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.127802 | 17.020575 | 18.445583 | 506 | 4 | 0.002346 | 506 | 4 | 0.002367 | 80 | 80 | false | true | -0.102052 | -0 | 0.106661 | 389 | 2 | 482 | 0.01496 | true | true |
calibration | study_gsm8k_calibration_5ed86699f1001353 | 15 | Let the length of the short side be $x$ feet.
Since the long sides are three times the length of the short sides, the length of the long side is $3x$ feet.
The rectangular plot has two short sides of length $x$ and two long sides of length $3x$.
The total length of the fence is $2x + 2(3x) = 2x + 6x = 8x$.
We are given... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 0 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each. So the total cost of the 4 tires is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36.
Let the amount saved on each tire be $s$. Then the total savings is $4s = 36$.
So, $s = \frac{36}{4} = 9$.
Therefore, Ga... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 1 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each. So the total cost of the 4 tires on sale is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36. This means the savings were $36.
The total amount saved is the difference between the original price and the sal... | [
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23.45426940... | stop | false | 621 | 694 | 1,259,279,715 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 12.543833 | 13.137669 | 717 | 4 | 0.002244 | 717 | 3 | 0.002542 | 84 | 84 | false | true | -0.143024 | -0 | 0.145364 | 615 | 2 | 693 | 0.025248 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 2 | Let the original price of each tire be $x$.
Gargamel bought 4 tires at $75 each, so the total cost of the tires is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36. This means that the total cost of the tires minus the actual cost is $36.
The actual cost of the tires is $300 - 36 = $264$.
Since ... | [
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23.45426940... | stop | false | 934 | 1,007 | 1,554,088,886 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 8.901742 | 10.327512 | 1,030 | 4 | 0.002244 | 1,030 | 4 | 0.002542 | 84 | 84 | false | true | -0.181715 | -0.000067 | 0.194598 | 928 | 2 | 1,006 | 0.040469 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 3 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each, so the total cost of the 4 tires on sale is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36. This means that the total amount he saved on the 4 tires is $36.
Since he saved the same amount on each tire, th... | [
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23.45426940... | stop | false | 394 | 467 | 1,241,282,659 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 12.8967 | 13.266397 | 490 | 4 | 0.002244 | 490 | 4 | 0.002542 | 84 | 84 | false | true | -0.20977 | -0 | 0.180965 | 388 | 2 | 466 | 0.014007 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 4 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each.
The total cost of the 4 tires on sale is $4 \times 75 = 300$.
The salesman told him that he saved a total of $36.
This means that the original cost of the 4 tires was $300 + 36 = 336$.
Since the original price of each tire was $x$... | [
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23.45426940... | stop | false | 561 | 634 | 205,621,702 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 11.509571 | 12.205468 | 657 | 3 | 0.002244 | 657 | 4 | 0.002542 | 84 | 84 | false | true | -0.168129 | -0.000093 | 0.168829 | 555 | 2 | 633 | 0.018252 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 5 | Let $p$ be the original price of each tire.
Gargamel bought 4 tires on sale for $75 each, so the total cost of the 4 tires on sale is $4 \times 75 = 300$.
The salesman told him that he saved a total of $36.
Since Gargamel bought 4 tires, and he saved the same amount on each tire, let $s$ be the amount saved on each tir... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 6 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each.
So, the total cost of the 4 tires is $4 \times 75 = 300$.
The salesman told Gargamel that he saved a total of $36.
The amount saved on each tire is the same. Let the amount saved on each tire be $s$.
Then, the total savings is $4s... | [
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23.45426940... | stop | false | 388 | 461 | 1,461,991,768 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 15.734561 | 16.111769 | 484 | 4 | 0.002244 | 484 | 4 | 0.002542 | 84 | 84 | false | true | -0.118331 | -0 | 0.127327 | 382 | 2 | 460 | 0.014007 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 7 | Let the original price of each tire be $p$.
Gargamel bought 4 tires on sale for $75 each, so the total cost of the 4 tires is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36.
So, the total original price of the 4 tires was $300 + 36 = $336$.
Since the original price of each tire was $p$, the to... | [
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23.829269409... | stop | false | 295 | 368 | 324,672,853 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 15.626513 | 16.216864 | 391 | 4 | 0.002244 | 391 | 4 | 0.002542 | 84 | 84 | false | true | -0.110219 | -0 | 0.109061 | 289 | 2 | 367 | 0.011711 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 8 | Let $p$ be the original price of each tire.
Gargamel bought 4 tires on sale for $75 each. So the total cost of the 4 tires is $4 \times 75 = $300$.
The salesman told Gargamel that he saved a total of $36. This means the total savings is $36.
Gargamel saved the same amount on each tire. Let $s$ be the amount he saved on... | [
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18.75426864... | stop | false | 360 | 433 | 1,033,312,836 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 13.85176 | 14.159165 | 456 | 4 | 0.002244 | 456 | 4 | 0.002542 | 84 | 84 | false | true | -0.179053 | -0 | 0.143552 | 354 | 2 | 432 | 0.015164 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 9 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each.
The total cost of the 4 tires on sale is $4 \times 75 = 300$.
The salesman told Gargamel that he saved a total of $36.
Since Gargamel bought 4 tires, the savings on each tire is the total savings divided by the number of tires, wh... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 10 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each, so the total cost of the 4 tires is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36.
So the total amount saved is $36.
Since he saved the same amount on each tire, the amount saved on each tire is $\frac{3... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 11 | Let $x$ be the original price of each tire.
Gargamel bought 4 tires on sale for $75 each, so the total cost of the 4 tires was $4 \times 75 = 300$.
The salesman told him that he saved a total of $36.
So, the total savings is $36.
Since he saved the same amount on each tire, the amount saved on each tire is $\frac{36}{4... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 12 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each. So the total cost of the 4 tires on sale is $4 \times 75 = 300$.
The salesman told him that he saved a total of $36. This means that the total original price of the 4 tires minus the actual cost of the 4 tires is $36.
So, $4x - 30... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 13 | Let the original price of each tire be $x$.
Gargamel bought 4 tires, and each tire was on sale for $75.
The total cost of the 4 tires on sale was $4 \times 75 = $300$.
The salesman told Gargamel that he saved a total of $36.
The total savings is the difference between the original price and the sale price.
The total or... | [
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23.45426940... | stop | false | 395 | 468 | 1,984,542,140 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.101184 | 14.267876 | 14.919466 | 491 | 4 | 0.002244 | 491 | 4 | 0.002542 | 84 | 84 | false | true | -0.076381 | -0 | 0.111168 | 389 | 2 | 467 | 0.015124 | true | true |
calibration | study_gsm8k_calibration_a939f32e46594df2 | 14 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each. The total cost of the tires was $4 \times 75 = $300$.
The salesman told Gargamel that he saved a total of $36.
Since Gargamel bought 4 tires, the amount saved on each tire is $\frac{36}{4} = 9$.
So, Gargamel saved $9 on each tire.... | [
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calibration | study_gsm8k_calibration_a939f32e46594df2 | 15 | Let the original price of each tire be $x$.
Gargamel bought 4 tires on sale for $75 each.
So the total cost of 4 tires on sale is $4 \times 75 = $300$.
The salesman told him that he saved a total of $36.
Since he bought 4 tires, the saving on each tire is $\frac{36}{4} = 9$.
So Gargamel saved $9 on each tire.
The sale ... | [
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calibration | study_gsm8k_calibration_175747f138207840 | 0 | Let $n$ be the number of Santana's brothers, which is 7.
The number of brothers born in March is 3.
The number of brothers born in October is 1.
The number of brothers born in November is 1.
The number of brothers born in December is 2.
The total number of brothers is $3 + 1 + 1 + 2 = 7$, which is correct.
The first h... | [
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15.4292926788... | length | true | 1,024 | 1,120 | 171,224,024 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.159544 | 7.742449 | 8.722331 | 1,143 | 3 | 0.002346 | 1,143 | 3 | 0.002367 | 2 | 2 | true | true | -0.178299 | 0 | 0.191089 | 1,024 | 0 | 1,118 | 0.028064 | false | false |
calibration | study_gsm8k_calibration_175747f138207840 | 1 | Let $N$ be the number of Santana's brothers. We are given that $N = 7$.
The number of brothers with birthdays in March is 3.
The number of brothers with birthdays in October is 1.
The number of brothers with birthdays in November is 1.
The number of brothers with birthdays in December is 2.
The total number of brothers... | [
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calibration | study_gsm8k_calibration_175747f138207840 | 2 | Let $n$ be the number of Santana's brothers.
We are given that Santana has 7 brothers, so $n=7$.
The number of brothers with birthdays in March is 3.
The number of brothers with birthdays in October is 1.
The number of brothers with birthdays in November is 1.
The number of brothers with birthdays in December is 2.
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5.63427543640... | length | true | 1,024 | 1,120 | 153,995,153 | 67b4f7efa6a927768d976765a81a1e612321f23eadd4f1e5bc4b904b29ecdb3c | 0.127802 | 5.286273 | 7.668738 | 1,143 | 2 | 0.002346 | 1,143 | 2 | 0.002367 | 0 | 0 | true | true | -0.195433 | 0 | 0.212762 | 1,024 | 0 | 1,118 | 0.026774 | false | false |
calibration | study_gsm8k_calibration_175747f138207840 | 3 | Let the number of Santana's brothers be $N = 7$.
The number of brothers with birthdays in March is 3.
The number of brothers with birthdays in October is 1.
The number of brothers with birthdays in November is 1.
The number of brothers with birthdays in December is 2.
The total number of brothers is $3 + 1 + 1 + 2 = 7$... | [
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