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math_qa__Wj6ldsSFLvjELbEF
If a: b :: 3 : 7, then what is (5a+6b): (a-2b)? Choose the correct choice from the following answers: A) 57 : 11 B) - 57 : 11 C) 11 : 10 D) - 11 : 10 E) - 1 : 10
<gadget id="calculator">5 * 3</gadget> <output>15</output> <gadget id="calculator">7 * 6</gadget> <output>42</output> <gadget id="calculator">15 + 42</gadget> <output>57</output> <gadget id="calculator">2 * 7</gadget> <output>14</output> <gadget id="calculator">3 - 14</gadget> <output>-11</output> <gadget id="calculator">57 / (-11)</gadget> <output>-57/11 = around -5.181818</output> <result>B</result>
B
-5.181818
If a: b :: 3 : 7, then what is (5a+6b): (a-2b)?
{ "A": "57 : 11", "B": "- 57 : 11", "C": "11 : 10", "D": "- 11 : 10", "E": "- 1 : 10" }
divide(add(multiply(5, 3), multiply(7, 6)), subtract(3, multiply(2, 7)))
multiply(n0,n2)|multiply(n1,n3)|multiply(n1,n4)|add(#0,#1)|subtract(n0,#2)|divide(#3,#4)
a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 6 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 6 ] / [ ( 3 / 7 ) - 2 ] = - 57 / 11 answer : b
general
math_qa__T47FRQ2e6laWT9hO
A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 30 percent. Pick one: A) 145 B) 90 C) 175 D) 160 E) 130
<gadget id="calculator">30 / 20</gadget> <output>3/2 = around 1.5</output> <gadget id="calculator">(3/2) * 60</gadget> <output>90</output> <result>B</result>
B
90
A mobile battery in 1 hour charges to 20 percent.How much time (in minute) will it require more to charge to 30 percent.
{ "A": "145", "B": "90", "C": "175", "D": "160", "E": "130" }
multiply(divide(30, 20), const_60)
divide(n2,n1)|multiply(#0,const_60)|
1 hr = 20 percent . thus 15 min = 5 percent . now to charge 30 percent 90 min . answer : b
physics
math_qa__xEcSZ1zXG7TJtdDu
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 5 can be used only once? Select: A) 20 B) 150 C) 225 D) 300 E) 304
<gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">5 * 5</gadget> <output>25</output> <gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">25 * 16</gadget> <output>400</output> <gadget id="calculator">25 * 4</gadget> <output>100</output> <gadget id="calculator">400 - 100</gadget> <output>300</output> <result>E</result>
E
304
How many 4 digit numbers are there, if it is known that the first digit is even, the second is odd, the third is prime, the fourth (units digit) is divisible by 3, and the digit 5 can be used only once?
{ "A": "20", "B": "150", "C": "225", "D": "300", "E": "304" }
subtract(multiply(multiply(add(4, const_1), add(4, const_1)), multiply(4, 4)), multiply(multiply(add(4, const_1), add(4, const_1)), 4))
add(n0,const_1)|multiply(n0,n0)|multiply(#0,#0)|multiply(#2,#1)|multiply(#2,n0)|subtract(#3,#4)|
"4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with five 5 - s , 5 x 5 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : e ."
physics
math_qa__B6tNgk6AtaXUA0i5
Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 6/7 and that of Ravi is 1/5. Find the probability that both of them are selected. Options. A) 2 / 35 B) 2 / 3 C) 6 / 35 D) 5 / 7 E) 7 / 5
<gadget id="calculator">6 / 7</gadget> <output>6/7 = around 0.857143</output> <gadget id="calculator">1 / 5</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">(6/7) * (1/5)</gadget> <output>6/35 = around 0.171429</output> <result>C</result>
C
0.171429
Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 6/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
{ "A": "2 / 35", "B": "2 / 3", "C": "6 / 35", "D": "5 / 7", "E": "7 / 5" }
multiply(divide(6, 7), divide(1, 5))
divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)|
"let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 6 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 6 / 7 x 1 / 5 = 6 / 35 answer : c"
general
math_qa__5uZB3Ljm1BZFEkP4
One hour after Yolanda started walking from X to Y, a distance of 31 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 1 miles per hour and Bobâs was 2 miles per hour, how many miles had Bob walked when they met? Pick: A) 19 B) 20 C) 22 D) 21 E) 19.5
<gadget id="calculator">31 - 1</gadget> <output>30</output> <gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">30 / 3</gadget> <output>10</output> <gadget id="calculator">10 * 2</gadget> <output>20</output> <result>B</result>
B
20
One hour after Yolanda started walking from X to Y, a distance of 31 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 1 miles per hour and Bobâs was 2 miles per hour, how many miles had Bob walked when they met?
{ "A": "19", "B": "20", "C": "22", "D": "21", "E": "19.5" }
multiply(divide(subtract(31, 1), add(1, 2)), 2)
add(n1,n2)|subtract(n0,n1)|divide(#1,#0)|multiply(n2,#2)|
"let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked ( t + 1 ) miles . these distances must sum to 31 miles , so 2 t + ( t + 1 ) = 31 , which may be solved for t as follows 2 t + ( t + 1 ) = 31 2 t + t + 1 = 31 3 t = 30 t = 10 ( hours ) therefore , bob had walked 2 t = 2 ( 10 ) = 20 miles when they met . the best answer is b ."
physics
math_qa__Xvc6HuNlyPO7oIUQ
If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC? Answers. A) 9 B) 18 − 3 √ 3 C) 18 D) 18 + 3 √ 3 E) 27
<gadget id="calculator">3 * 2</gadget> <output>6</output> <gadget id="calculator">3 ** (1/2)</gadget> <output>sqrt(3) = around 1.732051</output> <gadget id="calculator">3 - (sqrt(3))</gadget> <output>3 - sqrt(3) = around 1.267949</output> <gadget id="calculator">6 * (3 - sqrt(3))</gadget> <output>18 - 6*sqrt(3) = around 7.607695</output> <gadget id="calculator">(18 - 6*sqrt(3)) / (3 - sqrt(3))</gadget> <output>(18 - 6*sqrt(3))/(3 - sqrt(3)) = around 6</output> <gadget id="calculator">3 * ((18 - 6*sqrt(3))/(3 - sqrt(3)))</gadget> <output>3*(18 - 6*sqrt(3))/(3 - sqrt(3)) = around 18</output> <result>C</result>
C
18
If the perimeter of ΔACD is 9+3√3, what is the perimeter of equilateral triangle ΔABC?
{ "A": "9", "B": "18 − 3 √ 3", "C": "18", "D": "18 + 3 √ 3", "E": "27" }
multiply(3, divide(multiply(multiply(3, const_2), subtract(const_3, sqrt(const_3))), subtract(const_3, sqrt(const_3))))
multiply(n1,const_2)|sqrt(const_3)|subtract(const_3,#1)|multiply(#0,#2)|divide(#3,#2)|multiply(n1,#4)
the altitude of an equilateral triangle is side * √ 3 / 2 . as perimeter of triangle acd is 9 + 3 √ 3 , ac + cd + ad = ( side + side / 2 + side * √ 3 / 2 ) = 9 + 3 √ 3 or side = 6 . perimeter of equilateral triangle , abc is 3 ( side ) or 18 . answer : ( optionc )
geometry
math_qa__wimuaIMXplaUZUsj
If 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes Choose the correct choice from the following options: A) 41 B) 28 C) 43 D) 44 E) 45
<gadget id="calculator">factorial(8)</gadget> <output>40_320</output> <gadget id="calculator">8 - 2</gadget> <output>6</output> <gadget id="calculator">factorial(6)</gadget> <output>720</output> <gadget id="calculator">factorial(2)</gadget> <output>2</output> <gadget id="calculator">720 * 2</gadget> <output>1_440</output> <gadget id="calculator">40_320 / 1_440</gadget> <output>28</output> <result>B</result>
B
28
If 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
{ "A": "41", "B": "28", "C": "43", "D": "44", "E": "45" }
divide(factorial(8), multiply(factorial(subtract(8, const_2)), factorial(const_2)))
factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)|
"n ( n - 1 ) / 2 = 8 * 7 / 2 = 28 answer : b"
general
math_qa__aK8NNupZXf5ZnFQZ
A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of : Choose the correct option: A) 45 hours B) 47 hours C) 48 hours D) 50 hours E) none
<gadget id="calculator">25 - 20</gadget> <output>5</output> <gadget id="calculator">20 / 40</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">100 + 25</gadget> <output>125</output> <gadget id="calculator">125 / 100</gadget> <output>5/4 = around 1.25</output> <gadget id="calculator">(1/2) * (5/4)</gadget> <output>5/8 = around 0.625</output> <gadget id="calculator">5 / (5/8)</gadget> <output>8</output> <gadget id="calculator">8 + 40</gadget> <output>48</output> <result>C</result>
C
48
A man's basic pay for a 40 hour week is Rs.20. Overtime is paid for at 25% above the basic rate. In a certain week he worked overtime and his total wage was Rs.25. He therefore worked for a total of :
{ "A": "45 hours", "B": "47 hours", "C": "48 hours", "D": "50 hours", "E": "none" }
add(divide(subtract(25, 20), multiply(divide(20, 40), divide(add(const_100, 25), const_100))), 40)
add(n2,const_100)|divide(n1,n0)|subtract(n2,n1)|divide(#0,const_100)|multiply(#1,#3)|divide(#2,#4)|add(n0,#5)
explanation : basic rate per hour = rs . ( 20 / 40 ) = rs . 1 / 2 overtime per hour = 125 % of rs . 1 / 2 = 125 / 100 × 1 / 2 = rs . 5 / 8 suppose he worked x hours overtime . then , 20 + 5 / 8 x = 25 or 5 / 8 x = 5 x = 5 × 8 / 5 = 8 hours so he worked in all for ( 40 + 8 ) hours = 48 hours . correct option : c
gain
math_qa__KLr0IuOTbrpdQOUJ
It takes six minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video? Options: A) 13.8 B) 14.1 C) 14.4 D) 14.6 E) 14.8
<gadget id="calculator">2 + 3</gadget> <output>5</output> <gadget id="calculator">5 + 4</gadget> <output>9</output> <gadget id="calculator">9 * 60</gadget> <output>540</output> <gadget id="calculator">1 / 540</gadget> <output>1/540 = around 0.001852</output> <gadget id="calculator">3 * 4</gadget> <output>12</output> <gadget id="calculator">12 + 3</gadget> <output>15</output> <gadget id="calculator">1 / 15</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">(1/540) + (1/15)</gadget> <output>37/540 = around 0.068519</output> <gadget id="calculator">1 / (37/540)</gadget> <output>540/37 = around 14.594595</output> <gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">16 * 3</gadget> <output>48</output> <gadget id="calculator">48 - 2</gadget> <output>46</output> <gadget id="calculator">100 * 100</gadget> <output>10_000</output> <gadget id="calculator">46 / 10_000</gadget> <output>23/5_000 = around 0.0046</output> <gadget id="calculator">(540/37) - (23/5_000)</gadget> <output>2_699_149/185_000 = around 14.589995</output> <result>C</result>
C
14.4
It takes six minutes to load a certain video on a cellphone, and fifteen seconds to load that same video on a laptop. If the two devices were connected so that they operated in concert at their respective rates, how many seconds would it take them to load the video?
{ "A": "13.8", "B": "14.1", "C": "14.4", "D": "14.6", "E": "14.8" }
subtract(inverse(add(inverse(multiply(add(add(const_2, const_3), const_4), const_60)), inverse(add(multiply(const_3, const_4), const_3)))), divide(subtract(multiply(multiply(const_4, const_4), const_3), const_2), multiply(const_100, const_100)))
add(const_2,const_3)|multiply(const_3,const_4)|multiply(const_4,const_4)|multiply(const_100,const_100)|add(#0,const_4)|add(#1,const_3)|multiply(#2,const_3)|inverse(#5)|multiply(#4,const_60)|subtract(#6,const_2)|divide(#9,#3)|inverse(#8)|add(#11,#7)|inverse(#12)|subtract(#13,#10)|
"the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 6 ) = 1 / 360 of the video per second . the combined rate is 1 / 15 + 1 / 360 = 25 / 360 of the video per second . the time required to load the video is 360 / 25 = 14.4 seconds . the answer is c ."
physics
math_qa__JSHS96COcMmM4O9w
For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 12, then v= Choose the correct choice from the following answers: A) 15 B) 18 C) 21 D) 24 E) 27
<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 - (1/3)</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">12 / (2/3)</gadget> <output>18</output> <gadget id="calculator">18 / (2/3)</gadget> <output>27</output> <result>E</result>
E
27
For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 12, then v=
{ "A": "15", "B": "18", "C": "21", "D": "24", "E": "27" }
divide(divide(12, subtract(const_1, divide(const_1, 3))), subtract(const_1, divide(const_1, 3)))
divide(const_1,n0)|subtract(const_1,#0)|divide(n1,#1)|divide(#2,#1)
( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 12 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 27 the answer is e .
general
math_qa__cjFhZaSjlvPG3Sh4
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions. Choose the correct choice from the following answers. A) 287 m B) 704 m C) 168 m D) 278 m E) 107 m
<gadget id="calculator">3 + 4</gadget> <output>7</output> <gadget id="calculator">7 * 3</gadget> <output>21</output> <gadget id="calculator">21 + 1</gadget> <output>22</output> <gadget id="calculator">22 / 7</gadget> <output>22/7 = around 3.142857</output> <gadget id="calculator">(22/7) * 22.4</gadget> <output>70.4</output> <gadget id="calculator">70.4 * 2</gadget> <output>140.8</output> <gadget id="calculator">140.8 * 500</gadget> <output>70_400</output> <gadget id="calculator">70_400 / 100</gadget> <output>704</output> <result>B</result>
B
704
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
{ "A": "287 m", "B": "704 m", "C": "168 m", "D": "278 m", "E": "107 m" }
divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 500), const_100)
add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)|
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : b"
physics
math_qa__6IxCoJ6dYUcc11HU
20 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ? Choose the most appropriate option: A) 40 % B) 50 % C) 60 % D) 70 % E) 80 %
<gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">100 - 40</gadget> <output>60</output> <gadget id="calculator">(4/5) * 60</gadget> <output>48</output> <gadget id="calculator">60 - 48</gadget> <output>12</output> <gadget id="calculator">40 - 12</gadget> <output>28</output> <gadget id="calculator">28 / 40</gadget> <output>7/10 = around 0.7</output> <gadget id="calculator">(7/10) * 100</gadget> <output>70</output> <result>D</result>
D
70
20 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ?
{ "A": "40 %", "B": "50 %", "C": "60 %", "D": "70 %", "E": "80 %" }
multiply(divide(subtract(40, subtract(60, multiply(divide(subtract(const_100, 20), const_100), subtract(const_100, 40)))), 40), const_100)
subtract(const_100,n0)|subtract(const_100,n2)|divide(#0,const_100)|multiply(#2,#1)|subtract(n1,#3)|subtract(n2,#4)|divide(#5,n2)|multiply(#6,const_100)
science majors make up 0.4 of the class . 60 % of the class are women and 0.2 * 0.6 = 0.12 of the class are female science majors . then 0.28 of the class are male science majors . 0.4 x = 0.28 x = 0.7 = 70 % the answer is d .
gain
math_qa__tki3pvVq5coTxJJb
A grocer has a sale of Rs. 8435, Rs. 8927, Rs. 8855, Rs. 9230 and Rs. 8562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 8500? Choose the correct choice from the following options: A) s . 1991 B) s . 2991 C) s . 3991 D) s . 4991 E) s . 6991
<gadget id="calculator">5 + 1</gadget> <output>6</output> <gadget id="calculator">6 * 8_500</gadget> <output>51_000</output> <gadget id="calculator">8_435 + 8_927</gadget> <output>17_362</output> <gadget id="calculator">17_362 + 8_855</gadget> <output>26_217</output> <gadget id="calculator">26_217 + 9_230</gadget> <output>35_447</output> <gadget id="calculator">35_447 + 8_562</gadget> <output>44_009</output> <gadget id="calculator">51_000 - 44_009</gadget> <output>6_991</output> <result>E</result>
E
6,991
A grocer has a sale of Rs. 8435, Rs. 8927, Rs. 8855, Rs. 9230 and Rs. 8562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 8500?
{ "A": "s . 1991", "B": "s . 2991", "C": "s . 3991", "D": "s . 4991", "E": "s . 6991" }
subtract(multiply(add(5, const_1), 8500), add(add(add(add(8435, 8927), 8855), 9230), 8562))
add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)|
"explanation : total sale for 5 months = rs . ( 8435 + 8927 + 8855 + 9230 + 8562 ) = rs . 44009 . required sale = rs . [ ( 8500 x 6 ) â € “ 44009 ] = rs . ( 51000 â € “ 44009 ) = rs . 6991 . answer e"
general
math_qa__yb9sZa0EgQXJ9B6M
In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 4 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders? Choose the correct choice from the following options: A) 3 B) 6 C) 8 D) 9 E) 12
<gadget id="calculator">36 * 12</gadget> <output>432</output> <gadget id="calculator">432 * 4</gadget> <output>1_728</output> <gadget id="calculator">1_728 / 72</gadget> <output>24</output> <gadget id="calculator">24 / 4</gadget> <output>6</output> <result>B</result>
B
6
In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 4 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 12 standard orders?
{ "A": "3", "B": "6", "C": "8", "D": "9", "E": "12" }
divide(divide(multiply(multiply(36, 12), 4), 72), 4)
multiply(n0,n4)|multiply(#0,n1)|divide(#1,n3)|divide(#2,n2)|
"the choices give away the answer . . 36 machines take 4 hours to fill 4 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 4 = 6 ans b"
physics
math_qa__3k6mnfqdboHV4jla
If the cost price is 90% of the selling price, then what is the profit percent? Select the correct option. A) 5 % B) 11 % C) 13 % D) 21 % E) 19 %
<gadget id="calculator">100 - 90</gadget> <output>10</output> <gadget id="calculator">10 / 90</gadget> <output>1/9 = around 0.111111</output> <gadget id="calculator">(1/9) * 100</gadget> <output>100/9 = around 11.111111</output> <result>B</result>
B
11
If the cost price is 90% of the selling price, then what is the profit percent?
{ "A": "5 %", "B": "11 %", "C": "13 %", "D": "21 %", "E": "19 %" }
multiply(divide(subtract(const_100, 90), 90), const_100)
subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)|
"let s . p . = $ 100 c . p . = $ 90 profit = $ 10 profit % = 10 / 90 * 100 = 25 / 6 = 11 % approximately answer is b"
gain
math_qa__AU3aRlRd46o8a81Y
7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9. Choose the most appropriate option: A) 200 B) 300 C) 400 D) 500 E) 470
<gadget id="calculator">9 * 9</gadget> <output>81</output> <gadget id="calculator">3 * 81</gadget> <output>243</output> <gadget id="calculator">3 * 9</gadget> <output>27</output> <gadget id="calculator">27 * 2</gadget> <output>54</output> <gadget id="calculator">243 + 54</gadget> <output>297</output> <gadget id="calculator">297 + 3</gadget> <output>300</output> <result>B</result>
B
300
7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.
{ "A": "200", "B": "300", "C": "400", "D": "500", "E": "470" }
add(add(multiply(const_3, multiply(9, 9)), multiply(multiply(const_3, 9), const_2)), const_3)
multiply(n7,n7)|multiply(n7,const_3)|multiply(#0,const_3)|multiply(#1,const_2)|add(#2,#3)|add(#4,const_3)
1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the third digit . therefore , there will be 3 * 81 = 243 numbers ( 1 - digit , 2 - digits and 3 - digits ) in which 7 will appear only once . in each of these numbers , 7 is written once . therefore , 243 times . 2 . the numbers in which 7 will appear twice . e . g 772 or 377 or 747 or 77 in these numbers , one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7 ) . there will be 9 such numbers . however , this digit which is not 7 can appear in the first or second or the third place . so there are 3 * 9 = 27 such numbers . in each of these 27 numbers , the digit 7 is written twice . therefore , 7 is written 54 times . 3 . the number in which 7 appears thrice - 777 - 1 number . 7 is written thrice in it . therefore , the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300 option b
general
math_qa__lFC9xOhIHZl0ioyz
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 16km? Choose the correct option: A) 3 B) 6 C) 8 D) 9 E) 7
<gadget id="calculator">4 - 2</gadget> <output>2</output> <gadget id="calculator">16 / 2</gadget> <output>8</output> <result>C</result>
C
8
A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 16km?
{ "A": "3", "B": "6", "C": "8", "D": "9", "E": "7" }
divide(16, subtract(4, 2))
subtract(n0,n1)|divide(n2,#0)|
"m = 4 s = 2 us = 4 - 2 = 2 d = 16 t = 16 / 2 = 8 answer : c"
physics
math_qa__i6ccF2vuSGqkDmIs
Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance. Answers A) 4 km B) 5 km C) 6 km D) 7 km E) 8 km
<gadget id="calculator">4 * 10</gadget> <output>40</output> <gadget id="calculator">100 - 40</gadget> <output>60</output> <gadget id="calculator">24 / 60</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">1 + (2/5)</gadget> <output>7/5 = around 1.4</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/3) / 5</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <gadget id="calculator">(2/3) / 4</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/15) + (1/6)</gadget> <output>7/30 = around 0.233333</output> <gadget id="calculator">(7/5) / (7/30)</gadget> <output>6</output> <result>C</result>
C
6
Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the rest at 5 kmph. Find the total distance.
{ "A": "4 km", "B": "5 km", "C": "6 km", "D": "7 km", "E": "8 km" }
divide(add(1, divide(24, subtract(const_100, multiply(const_4, const_10)))), add(divide(divide(1, const_3), 5), divide(divide(const_2, const_3), const_4)))
divide(n0,const_3)|divide(const_2,const_3)|multiply(const_10,const_4)|divide(#0,n3)|divide(#1,const_4)|subtract(const_100,#2)|add(#3,#4)|divide(n1,#5)|add(n0,#7)|divide(#8,#6)
time = distance / speed let total distance travelled be x in 84 / 60 hrs 2 / 3 rd of x travelled in 4 km / hr 1 / 3 rd of distance travelled in 5 km / hr 2 x / ( 3 * 4 ) + x / ( 3 * 5 ) = 84 / 60 x = 6 km answer : c
physics
math_qa__VDFlwaDVlP5K2DKR
If the area of a circle decreases by 20%, then the radius of a circle decreases by Pick one: A) 20 % B) 18 % C) 36 % D) 11 % E) none of these
<gadget id="calculator">100 - 20</gadget> <output>80</output> <gadget id="calculator">80 / 100</gadget> <output>4/5 = around 0.8</output> <gadget id="calculator">(4/5) ** (1/2)</gadget> <output>2*sqrt(5)/5 = around 0.894427</output> <gadget id="calculator">1 - (2*sqrt(5)/5)</gadget> <output>1 - 2*sqrt(5)/5 = around 0.105573</output> <gadget id="calculator">(1 - 2*sqrt(5)/5) * 100</gadget> <output>100 - 40*sqrt(5) = around 10.557281</output> <result>D</result>
D
11
If the area of a circle decreases by 20%, then the radius of a circle decreases by
{ "A": "20 %", "B": "18 %", "C": "36 %", "D": "11 %", "E": "none of these" }
multiply(subtract(const_1, sqrt(divide(subtract(const_100, 20), const_100))), const_100)
subtract(const_100,n0)|divide(#0,const_100)|sqrt(#1)|subtract(const_1,#2)|multiply(#3,const_100)
if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 20 ) % = ( 100 − 10 √ 80 ) % = 100 - 89 = 11 % answer d
geometry
math_qa__03DJfHHdBu1ZlxyV
Two trains 140 m and 180 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose the most appropriate option: A) 11.52 sec B) 10.1 sec C) 10.6 sec D) 10.8 sec E) 10.2 sec
<gadget id="calculator">140 + 180</gadget> <output>320</output> <gadget id="calculator">60 + 40</gadget> <output>100</output> <gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">100 * (5/18)</gadget> <output>250/9 = around 27.777778</output> <gadget id="calculator">320 / (250/9)</gadget> <output>288/25 = around 11.52</output> <result>A</result>
A
11.52
Two trains 140 m and 180 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
{ "A": "11.52 sec", "B": "10.1 sec", "C": "10.6 sec", "D": "10.8 sec", "E": "10.2 sec" }
divide(add(140, 180), multiply(add(60, 40), const_0_2778))
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 180 = 320 m . required time = 320 * 9 / 250 = 11.52 sec . answer : a"
physics
math_qa__Ks0RH2TBH3kFGKTK
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability J that the first ball picked up is odd numbered? Choose the correct choice: A) 0 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 1
<gadget id="calculator">2 / 3</gadget> <output>2/3 = around 0.666667</output> <result>D</result>
D
0.666667
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability J that the first ball picked up is odd numbered?
{ "A": "0", "B": "1 / 3", "C": "1 / 2", "D": "2 / 3", "E": "1" }
divide(const_2, 3)
divide(const_2,n3)|
"answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability j is 2 / 3 . d"
probability
math_qa__Ax40RMk4e05d6ZuJ
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 3 inches long, how wide is Jordan's rectangle, in inches? Choose one. A) 25 B) 43 C) 42 D) 40 E) 18
<gadget id="calculator">5 * 24</gadget> <output>120</output> <gadget id="calculator">120 / 3</gadget> <output>40</output> <result>D</result>
D
40
Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 5 inches by 24 inches and Jordan's rectangle is 3 inches long, how wide is Jordan's rectangle, in inches?
{ "A": "25", "B": "43", "C": "42", "D": "40", "E": "18" }
divide(rectangle_area(5, 24), 3)
rectangle_area(n0,n1)|divide(#0,n2)|
"area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d"
geometry
math_qa__E0p5ZcEo6N7KrQu4
Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Choose the correct option. A) 98 B) 78 C) 76 D) 87 E) 75
<gadget id="calculator">76 + 65</gadget> <output>141</output> <gadget id="calculator">141 + 82</gadget> <output>223</output> <gadget id="calculator">223 + 67</gadget> <output>290</output> <gadget id="calculator">290 + 85</gadget> <output>375</output> <gadget id="calculator">10 / 2</gadget> <output>5</output> <gadget id="calculator">375 / 5</gadget> <output>75</output> <result>E</result>
E
75
Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
{ "A": "98", "B": "78", "C": "76", "D": "87", "E": "75" }
divide(add(add(add(add(76, 65), 82), 67), 85), divide(const_10, const_2))
add(n0,n1)|divide(const_10,const_2)|add(n2,#0)|add(n3,#2)|add(n4,#3)|divide(#4,#1)|
"average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : e"
general
math_qa__Xp6bBF3042YLYjdN
16 ltr of water is added with 24 ltr of a solution containing 90%of alcohol in the water. The %of alcohol in the new mixture is? Choose the correct option: A) 48 % B) 52 % C) 54 % D) 60 % E) 70 %
<gadget id="calculator">90 / 100</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">(9/10) * 24</gadget> <output>108/5 = around 21.6</output> <gadget id="calculator">16 + 24</gadget> <output>40</output> <gadget id="calculator">(108/5) / 40</gadget> <output>27/50 = around 0.54</output> <gadget id="calculator">100 * (27/50)</gadget> <output>54</output> <result>C</result>
C
54
16 ltr of water is added with 24 ltr of a solution containing 90%of alcohol in the water. The %of alcohol in the new mixture is?
{ "A": "48 %", "B": "52 %", "C": "54 %", "D": "60 %", "E": "70 %" }
multiply(const_100, divide(multiply(divide(90, const_100), 24), add(16, 24)))
add(n0,n1)|divide(n2,const_100)|multiply(n1,#1)|divide(#2,#0)|multiply(#3,const_100)|
"we have a 24 litre solution containing 90 % of alcohol in the water . = > quantity of alcohol in the solution = 24 ã — 90 / 100 now 16 litre of water is added to the solution . = > total quantity of the new solution = 24 + 16 = 40 percentage of alcohol in the new solution = 24 ã — 90 / 100 40 ã — 100 = 24 ã — 9010040 ã — 100 = 24 ã — 2.25 / 100 = 54 % c"
general
math_qa__Ko9HRWeMrBt3XV2N
A bag contains 3 white marbles and 3 black marbles. If each of 3 girls and 3 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble? Choose the correct choice from the following choices: A) 1 / 35 B) 1 / 10 C) 1 / 15 D) 1 / 20 E) 1 / 25
<gadget id="calculator">3 + 3</gadget> <output>6</output> <gadget id="calculator">binomial(6, 3)</gadget> <output>20</output> <gadget id="calculator">2 / 20</gadget> <output>1/10 = around 0.1</output> <result>B</result>
B
0.1
A bag contains 3 white marbles and 3 black marbles. If each of 3 girls and 3 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
{ "A": "1 / 35", "B": "1 / 10", "C": "1 / 15", "D": "1 / 20", "E": "1 / 25" }
divide(const_2, choose(add(3, 3), 3))
add(n0,n0)|choose(#0,n0)|divide(const_2,#1)
first , total ways to select for all boys and girls , i . e 6 ! / ( 3 ! * 3 ! ) = 6 * 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 3 * 2 * 1 = 20 then there are one two way girls can have all same colors , either white or black . the number of ways in which 3 girls can select 3 white balls = 3 c 3 = 1 the number of ways in which 3 girls can select 3 black balls = 3 c 3 = 1 therefore , total favorable outcomes / total outcomes = 2 / 20 = 1 / 10 b
probability
math_qa__NR6GX0inQrFSTzCN
If 4 and 8 are factors of 60n, what is the minimum value of n? Choose the correct answer. A) 2 B) 3 C) 8 D) 14 E) 56
<gadget id="calculator">lcm(4, 8)</gadget> <output>8</output> <result>C</result>
C
8
If 4 and 8 are factors of 60n, what is the minimum value of n?
{ "A": "2", "B": "3", "C": "8", "D": "14", "E": "56" }
lcm(4, 8)
lcm(n0,n1)
60 n / 4 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 2 * 2 * 2 * 2 = 3 * 5 * n / 8 must be an integer for this to be true n must multiple of 8 , thus min of n = 8 hence c
other
math_qa__t9tD6sREvYZfhyO5
If 3^8 x 3^7 = 3^n what is the value of n? Pick one A) 20 B) 18 C) 17 D) 16 E) 15
<gadget id="calculator">3 ** 7</gadget> <output>2_187</output> <gadget id="calculator">3 ** 8</gadget> <output>6_561</output> <gadget id="calculator">2_187 * 6_561</gadget> <output>14_348_907</output> <gadget id="calculator">log(14_348_907)</gadget> <output>log(14348907) = around 16.479184</output> <gadget id="calculator">log(3)</gadget> <output>log(3) = around 1.098612</output> <gadget id="calculator">log(14348907) / log(3)</gadget> <output>log(14348907)/log(3) = around 15</output> <result>E</result>
E
15
If 3^8 x 3^7 = 3^n what is the value of n?
{ "A": "20", "B": "18", "C": "17", "D": "16", "E": "15" }
divide(log(multiply(power(3, 7), power(3, 8))), log(3))
log(n4)|power(n2,n3)|power(n0,n1)|multiply(#1,#2)|log(#3)|divide(#4,#0)|
"3 ^ 8 * 3 ^ 7 = 3 ^ n or 3 ^ 8 + 7 = 3 ^ n n = 15 e"
general
math_qa__XvbPIelJctg5XNHs
In Karthik's opinion, his weight is greater than 55 Kg but less than 62 Kg. His brother does not agree with Karthik and he thinks that Karthik's weight is greater than 50 Kg but less than 60 Kg. His father's view is that his weight cannot be greater than 58 Kg. If all of them are correct in their estimation, what is the average of different probable weights of Karthik? Choose the most appropriate option. A) 54.5 B) 56.5 C) 59.2 D) 61 E) 62
<gadget id="calculator">55 + 58</gadget> <output>113</output> <gadget id="calculator">113 / 2</gadget> <output>113/2 = around 56.5</output> <result>B</result>
B
56.5
In Karthik's opinion, his weight is greater than 55 Kg but less than 62 Kg. His brother does not agree with Karthik and he thinks that Karthik's weight is greater than 50 Kg but less than 60 Kg. His father's view is that his weight cannot be greater than 58 Kg. If all of them are correct in their estimation, what is the average of different probable weights of Karthik?
{ "A": "54.5", "B": "56.5", "C": "59.2", "D": "61", "E": "62" }
divide(add(55, 58), const_2)
add(n0,n4)|divide(#0,const_2)
explanation : solution : assume karthik ' s weight be x kg . according to karthik , 55 < x < 62 according to karthik ; s brother , 50 < x < 60 . according to karthik ' s mother , x < 58 . the values satisfying all the above conditions are 56 and 57 . . ' . required average = ( 56 + 57 ) / 2 = 56.5 . answer : b
general
math_qa__O0Z3PqA0Y1dR2H0d
If 20 men can build a wall 66 metres long in 8 days, what length of a similar can be built by 86 men in 8 days? Choose the correct choice from the following options. A) 283.8 mtrs B) 378.4 mtrs C) 478.4 mtrs D) 488.4 mtrs E) 578.4 mtrs
<gadget id="calculator">86 * 8</gadget> <output>688</output> <gadget id="calculator">20 * 8</gadget> <output>160</output> <gadget id="calculator">688 / 160</gadget> <output>43/10 = around 4.3</output> <gadget id="calculator">66 * (43/10)</gadget> <output>1_419/5 = around 283.8</output> <result>A</result>
A
283.8
If 20 men can build a wall 66 metres long in 8 days, what length of a similar can be built by 86 men in 8 days?
{ "A": "283.8 mtrs", "B": "378.4 mtrs", "C": "478.4 mtrs", "D": "488.4 mtrs", "E": "578.4 mtrs" }
multiply(66, divide(multiply(86, 8), multiply(20, 8)))
multiply(n3,n4)|multiply(n0,n2)|divide(#0,#1)|multiply(n1,#2)|
"if 20 men can build a wall 66 metres long in 8 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 8 * 20 ) = 283.8 mtrs answer : a"
physics
math_qa__kG0Jdj3pSpR1MUuP
The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 770 the Other is Choose the correct choice from the following answers. A) 330 B) 90 C) 270 D) 250 E) 350
<gadget id="calculator">30 * 2_310</gadget> <output>69_300</output> <gadget id="calculator">69_300 / 770</gadget> <output>90</output> <result>B</result>
B
90
The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 770 the Other is
{ "A": "330", "B": "90", "C": "270", "D": "250", "E": "350" }
divide(multiply(30, 2310), 770)
multiply(n0,n1)|divide(#0,n2)|
"the other number = l . c . m * h . c . f / given number = 2310 * 30 / 770 = 90 answer is b ."
physics
math_qa__TLa1cl3ypnXUoEeT
A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.20 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy? Choose one A) $ 94.03 B) $ 96.75 C) $ 98.68 D) $ 102.07 E) $ 105.3
<gadget id="calculator">2 * 32.2</gadget> <output>64.4</output> <gadget id="calculator">1 * 20.43</gadget> <output>20.43</output> <gadget id="calculator">64.4 + 20.43</gadget> <output>84.83</output> <gadget id="calculator">1 * 13.85</gadget> <output>13.85</output> <gadget id="calculator">84.83 + 13.85</gadget> <output>98.68</output> <result>C</result>
C
98.68
A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.43 per bag, and 25-pound bags $32.20 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?
{ "A": "$ 94.03", "B": "$ 96.75", "C": "$ 98.68", "D": "$ 102.07", "E": "$ 105.3" }
add(add(multiply(const_2, 32.20), multiply(const_1, 20.43)), multiply(const_1, 13.85))
multiply(n5,const_2)|multiply(n3,const_1)|multiply(n1,const_1)|add(#0,#1)|add(#3,#2)|
"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.68 or 2 ) 25 + 25 + 25 = $ 96.60 c"
general
math_qa__nxbMqjj0T9wDwIJc
A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 10:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke? Choose the most appropriate option. A) 42 B) 36 C) 46 D) 38 E) 40
<gadget id="calculator">10 - 1</gadget> <output>9</output> <gadget id="calculator">9 + 10</gadget> <output>19</output> <gadget id="calculator">6 - 1</gadget> <output>5</output> <gadget id="calculator">5 + 6</gadget> <output>11</output> <gadget id="calculator">22 / 11</gadget> <output>2</output> <gadget id="calculator">19 * 2</gadget> <output>38</output> <result>D</result>
D
38
A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 10:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
{ "A": "42", "B": "36", "C": "46", "D": "38", "E": "40" }
multiply(add(subtract(10, const_1), 10), divide(22, add(subtract(6, const_1), 6)))
subtract(n3,const_1)|subtract(n0,const_1)|add(n3,#0)|add(n0,#1)|divide(n2,#3)|multiply(#2,#4)|
"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 10 strikes , there would be 9 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 10 strikes and 9 intervals will take 2 * ( 10 + 9 ) = 38 secs d d"
general
math_qa__jxYl5lKmeY3a6VEF
Two trains, each 100 m long, moving in opposite directions, cross other in 20 sec. If one is moving twice as fast the other, then the speed of the faster train is? Choose the correct answer: A) 22 B) 98 C) 60 D) 88 E) 24
<gadget id="calculator">100 + 100</gadget> <output>200</output> <gadget id="calculator">1 + 2</gadget> <output>3</output> <gadget id="calculator">20 * 3</gadget> <output>60</output> <gadget id="calculator">200 / 60</gadget> <output>10/3 = around 3.333333</output> <gadget id="calculator">(10/3) * 2</gadget> <output>20/3 = around 6.666667</output> <gadget id="calculator">(20/3) * 3_600</gadget> <output>24_000</output> <gadget id="calculator">24_000 / 1_000</gadget> <output>24</output> <result>E</result>
E
24
Two trains, each 100 m long, moving in opposite directions, cross other in 20 sec. If one is moving twice as fast the other, then the speed of the faster train is?
{ "A": "22", "B": "98", "C": "60", "D": "88", "E": "24" }
divide(multiply(multiply(divide(add(100, 100), multiply(20, add(const_1, const_2))), const_2), const_3600), const_1000)
add(n0,n0)|add(const_1,const_2)|multiply(n1,#1)|divide(#0,#2)|multiply(#3,const_2)|multiply(#4,const_3600)|divide(#5,const_1000)|
"let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 20 = 3 x = > x = 10 / 3 . so , speed of the faster train = 20 / 3 = 20 / 3 * 18 / 5 = 24 km / hr . answer : e"
physics
math_qa__sBRW31MhtB8jxpG8
On dividing 171 by a number, the quotient is 8 and the remainder is 3. Find the divisor. Select: A) 18 B) 19 C) 20 D) 21 E) 22
<gadget id="calculator">171 / 8</gadget> <output>171/8 = around 21.375</output> <gadget id="calculator">floor(171/8)</gadget> <output>21</output> <result>D</result>
D
21
On dividing 171 by a number, the quotient is 8 and the remainder is 3. Find the divisor.
{ "A": "18", "B": "19", "C": "20", "D": "21", "E": "22" }
floor(divide(171, 8))
divide(n0,n1)|floor(#0)|
"d = ( d - r ) / q = ( 171 - 3 ) / 8 = 168 / 8 = 21 d"
general
math_qa__wa0MFw3gpPUz3Ryo
40 men shake hands with each other. Maximum no of handshakes without cyclic handshakes. Choose the correct option: A) 780 B) 200 C) 210 D) 220 E) 230
<gadget id="calculator">40 - 1</gadget> <output>39</output> <gadget id="calculator">40 / 2</gadget> <output>20</output> <gadget id="calculator">39 * 20</gadget> <output>780</output> <result>A</result>
A
780
40 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.
{ "A": "780", "B": "200", "C": "210", "D": "220", "E": "230" }
multiply(subtract(40, const_1), divide(40, const_2))
divide(n0,const_2)|subtract(n0,const_1)|multiply(#0,#1)|
"or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a"
general
math_qa__VujdoyH0ax6XoH7G
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is? Choose the correct choice from the following answers: A) 2999 B) 2778 C) 7000 D) 2889 E) 6612
<gadget id="calculator">1 * 12</gadget> <output>12</output> <gadget id="calculator">12 - 6</gadget> <output>6</output> <gadget id="calculator">6 * 2</gadget> <output>12</output> <gadget id="calculator">12 + 12</gadget> <output>24</output> <gadget id="calculator">12 - 8</gadget> <output>4</output> <gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">24 + 12</gadget> <output>36</output> <gadget id="calculator">21_000 / 36</gadget> <output>1_750/3 = around 583.333333</output> <gadget id="calculator">12 * (1_750/3)</gadget> <output>7_000</output> <result>C</result>
C
7,000
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.21000. A's share is?
{ "A": "2999", "B": "2778", "C": "7000", "D": "2889", "E": "6612" }
multiply(multiply(const_1, const_12), divide(21000, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3))))
multiply(const_1,const_12)|subtract(const_12,n0)|subtract(const_12,n1)|multiply(#1,const_2)|multiply(#2,const_3)|add(#0,#3)|add(#5,#4)|divide(n2,#6)|multiply(#7,#0)|
"x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 21000 = 7000 answer : c"
gain
math_qa__nSjNVfmgnUBo3d1G
How long does a train 150 m long traveling at 36 kmph takes to cross a signal post? Choose the correct choice: A) 8 sec B) 15 sec C) 20 sec D) 10 sec E) 22 sec
<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">36 * (5/18)</gadget> <output>10</output> <gadget id="calculator">150 / 10</gadget> <output>15</output> <result>B</result>
B
15
How long does a train 150 m long traveling at 36 kmph takes to cross a signal post?
{ "A": "8 sec", "B": "15 sec", "C": "20 sec", "D": "10 sec", "E": "22 sec" }
divide(150, multiply(36, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)
d = 150 m s = 36 * 5 / 18 = 10 t = 150 * 1 / 10 = 15 sec answer : b
physics
math_qa__2LAmWnDXJksB1HVh
A car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 50% of which are not silver, what percentage of total number of cars are silver? Choose the correct option A) 30 % B) 35 % C) 40 % D) 45 % E) 50 %
<gadget id="calculator">20 / 100</gadget> <output>1/5 = around 0.2</output> <gadget id="calculator">40 * (1/5)</gadget> <output>8</output> <gadget id="calculator">50 / 100</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">80 * (1/2)</gadget> <output>40</output> <gadget id="calculator">8 + 40</gadget> <output>48</output> <gadget id="calculator">40 + 80</gadget> <output>120</output> <gadget id="calculator">48 / 120</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">(2/5) * 100</gadget> <output>40</output> <result>C</result>
C
40
A car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 50% of which are not silver, what percentage of total number of cars are silver?
{ "A": "30 %", "B": "35 %", "C": "40 %", "D": "45 %", "E": "50 %" }
multiply(divide(add(multiply(40, divide(20, const_100)), multiply(80, divide(50, const_100))), add(40, 80)), const_100)
add(n0,n2)|divide(n1,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n2,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)|
"the number of silver cars is 0.2 * 40 + 0.5 * 80 = 48 the percentage of cars which are silver is 48 / 120 = 40 % the answer is c ."
gain
math_qa__QKbFA5CS2XacJzfx
The two lines y=x and x=-7 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis? Choose the correct answer: A) 18.5 B) 21.5 C) 24.5 D) 27.5 E) 30.5
<gadget id="calculator">7 * 7</gadget> <output>49</output> <gadget id="calculator">49 / 2</gadget> <output>49/2 = around 24.5</output> <result>C</result>
C
24.5
The two lines y=x and x=-7 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
{ "A": "18.5", "B": "21.5", "C": "24.5", "D": "27.5", "E": "30.5" }
divide(multiply(7, 7), const_2)
multiply(n0,n0)|divide(#0,const_2)|
"the point of intersection is ( - 7 , - 7 ) . the triangle has a base of length 7 and a height of 7 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 7 * 7 = 24.5 the answer is c ."
general
math_qa__9B2xXkw9dqplxkq7
If 16^y = 4^14, what is y? Choose the correct answer A) 2 B) 3 C) 4 D) 6 E) 7
<gadget id="calculator">14 / 2</gadget> <output>7</output> <result>E</result>
E
7
If 16^y = 4^14, what is y?
{ "A": "2", "B": "3", "C": "4", "D": "6", "E": "7" }
divide(14, const_2)
divide(n2,const_2)
16 ^ y = 4 ^ 2 y = 4 ^ 14 2 y = 14 y = 7 the answer is e .
general
math_qa__NTnb4dCQkxxucaGw
If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 105 games will be played during the tournament. Find the number of participants. Choose the correct option: A) 15 B) 16 C) 17 D) 18 E) 19
<gadget id="calculator">105 * 2</gadget> <output>210</output> <gadget id="calculator">210 * 4</gadget> <output>840</output> <gadget id="calculator">840 + 1</gadget> <output>841</output> <gadget id="calculator">841 ** (1/2)</gadget> <output>29</output> <gadget id="calculator">29 + 1</gadget> <output>30</output> <gadget id="calculator">30 / 2</gadget> <output>15</output> <result>A</result>
A
15
If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 105 games will be played during the tournament. Find the number of participants.
{ "A": "15", "B": "16", "C": "17", "D": "18", "E": "19" }
divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2)
multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2)|
"let p be the number of participants . pc 2 = 105 ( p ) ( p - 1 ) = 210 = 15 * 14 p = 15 the answer is a ."
general
math_qa__oWx1VOHGkOUT1bN7
A train running at the speed of 90 km/hr crosses a pole in 6 seconds. Find the length of the train. Choose the correct choice from the following answers A) 150 meter B) 100 meter C) 105 meter D) 120 meter E) 130 meter
<gadget id="calculator">90 * 1_000</gadget> <output>90_000</output> <gadget id="calculator">90_000 / 3_600</gadget> <output>25</output> <gadget id="calculator">25 * 6</gadget> <output>150</output> <result>A</result>
A
150
A train running at the speed of 90 km/hr crosses a pole in 6 seconds. Find the length of the train.
{ "A": "150 meter", "B": "100 meter", "C": "105 meter", "D": "120 meter", "E": "130 meter" }
multiply(divide(multiply(90, const_1000), const_3600), 6)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
"speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 6 = 150 meter answer : a"
physics
math_qa__t4JLA6Oj7rIX0Tki
Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner? Choose the most appropriate option: A) 2 / 7 B) 3 / 7 C) 4 / 7 D) 9 / 14 E) 11 / 14
<gadget id="calculator">7 - 3</gadget> <output>4</output> <gadget id="calculator">4 / 7</gadget> <output>4/7 = around 0.571429</output> <result>C</result>
C
0.571429
Jen has a jar of jam, and she ate 1/3 of the jam for lunch. If Jen ate 1/7 of the remaining jam for dinner, what fraction of the jam was left after dinner?
{ "A": "2 / 7", "B": "3 / 7", "C": "4 / 7", "D": "9 / 14", "E": "11 / 14" }
divide(subtract(7, 3), 7)
subtract(n3,n1)|divide(#0,n3)
let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c .
general
math_qa__dsOsmZzBLAaDJSr6
A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.42 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy? Choose the correct option: A) $ 94.03 B) $ 96.75 C) $ 98.78 D) $ 98.77 E) $ 105.3
<gadget id="calculator">2 * 32.25</gadget> <output>64.5</output> <gadget id="calculator">1 * 20.42</gadget> <output>20.42</output> <gadget id="calculator">64.5 + 20.42</gadget> <output>84.92</output> <gadget id="calculator">1 * 13.85</gadget> <output>13.85</output> <gadget id="calculator">84.92 + 13.85</gadget> <output>98.77</output> <result>D</result>
D
98.77
A garden center sells a certain grass seed in 5-pound bags at $13.85 per bag, 10-pound bags at $20.42 per bag, and 25-pound bags $32.25 per bag. If a customer is to buy at least 65 pounds of the grass seed, but no more than 80 pounds, what is the least possible cost of the grass seed that the customer will buy?
{ "A": "$ 94.03", "B": "$ 96.75", "C": "$ 98.78", "D": "$ 98.77", "E": "$ 105.3" }
add(add(multiply(const_2, 32.25), multiply(const_1, 20.42)), multiply(const_1, 13.85))
multiply(n5,const_2)|multiply(n3,const_1)|multiply(n1,const_1)|add(#0,#1)|add(#3,#2)|
"there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.77 or 2 ) 25 + 25 + 25 = $ 96.75 d"
general
math_qa__300hId5RKQE6WDhv
The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town? Select the correct option. A) 3 . B) 7 . C) 10 . D) 16 . E) 15 .
<gadget id="calculator">4 * 4</gadget> <output>16</output> <result>D</result>
D
16
The distance between West-Town to East-Town is 20 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 4 kilometers per minute and the second bird, leaving from East-Town, at a speed of 1 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town?
{ "A": "3 .", "B": "7 .", "C": "10 .", "D": "16 .", "E": "15 ." }
multiply(4, const_4)
multiply(n1,const_4)
time taken by the birds to meet = 20 / ( 4 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : d
physics
math_qa__Ti4YTSi2lnQTLwuR
If p^2 – 13p + 40 = s, and p is a positive integer between 1 and 10, inclusive, what is the probability that s < 0? Choose the correct answer: A) 1 / 10 B) 1 / 5 C) 2 / 5 D) 3 / 5 E) 3 / 10
<gadget id="calculator">13 ** 2</gadget> <output>169</output> <gadget id="calculator">4 * 40</gadget> <output>160</output> <gadget id="calculator">169 - 160</gadget> <output>9</output> <gadget id="calculator">9 ** (1/2)</gadget> <output>3</output> <gadget id="calculator">13 + 3</gadget> <output>16</output> <gadget id="calculator">16 / 2</gadget> <output>8</output> <gadget id="calculator">13 - 8</gadget> <output>5</output> <gadget id="calculator">8 - 5</gadget> <output>3</output> <gadget id="calculator">3 - 1</gadget> <output>2</output> <gadget id="calculator">2 / 10</gadget> <output>1/5 = around 0.2</output> <result>B</result>
B
0.2
If p^2 – 13p + 40 = s, and p is a positive integer between 1 and 10, inclusive, what is the probability that s < 0?
{ "A": "1 / 10", "B": "1 / 5", "C": "2 / 5", "D": "3 / 5", "E": "3 / 10" }
divide(subtract(subtract(divide(add(13, sqrt(subtract(power(13, const_2), multiply(const_4, 40)))), const_2), subtract(13, divide(add(13, sqrt(subtract(power(13, const_2), multiply(const_4, 40)))), const_2))), const_1), 10)
multiply(n2,const_4)|power(n1,const_2)|subtract(#1,#0)|sqrt(#2)|add(n1,#3)|divide(#4,const_2)|subtract(n1,#5)|subtract(#5,#6)|subtract(#7,const_1)|divide(#8,n4)
p 2 – 13 p + 40 = s so ( p – 8 ) ( p – 5 ) = s for q to be negative , the expressions ( p – 8 ) and ( p – 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p – 8 ) and ( p – 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b .
general
math_qa__Gua0KHlwIyUBhqh1
A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days? Choose the correct choice. A) 3.75 days B) 3.78 days C) 3.25 days D) 3.15 days E) 2.75 days
<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/6) + (1/10)</gadget> <output>4/15 = around 0.266667</output> <gadget id="calculator">1 / (4/15)</gadget> <output>15/4 = around 3.75</output> <result>A</result>
A
3.75
A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
{ "A": "3.75 days", "B": "3.78 days", "C": "3.25 days", "D": "3.15 days", "E": "2.75 days" }
inverse(add(inverse(6), inverse(10)))
inverse(n0)|inverse(n1)|add(#0,#1)|inverse(#2)|
"1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer : a"
physics
math_qa__kAbsCY1IsjtQOaTP
5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is Answers A) 0 B) 2 C) 5 D) 7 E) 9
<gadget id="calculator">5 * 100</gadget> <output>500</output> <gadget id="calculator">500 + 2</gadget> <output>502</output> <gadget id="calculator">1 * 10</gadget> <output>10</output> <gadget id="calculator">502 + 10</gadget> <output>512</output> <gadget id="calculator">512 + 10</gadget> <output>522</output> <gadget id="calculator">522 - 502</gadget> <output>20</output> <gadget id="calculator">20 / 10</gadget> <output>2</output> <result>B</result>
B
2
5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is
{ "A": "0", "B": "2", "C": "5", "D": "7", "E": "9" }
divide(subtract(add(add(add(multiply(5, const_100), 2), multiply(const_1, const_10)), multiply(const_1, const_10)), add(multiply(5, const_100), 2)), multiply(const_1, const_10))
multiply(n0,const_100)|multiply(const_1,const_10)|add(n1,#0)|add(#2,#1)|add(#3,#1)|subtract(#4,#2)|divide(#5,#1)
sol . let the number be 5 x 2 . clearly , it is divisible by 2 . now , 5 + x + 2 = ( 7 + x ) must be divisible by 3 . so , x = 2 . answer b
general
math_qa__ukkO61VcahfrvouA
How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 38 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb? Choose the most appropriate option: A) 2 B) 5 C) 8 D) 15 E) 25
<gadget id="calculator">48 * 40</gadget> <output>1_920</output> <gadget id="calculator">100 + 20</gadget> <output>120</output> <gadget id="calculator">120 / 100</gadget> <output>6/5 = around 1.2</output> <gadget id="calculator">38 * 40</gadget> <output>1_520</output> <gadget id="calculator">(6/5) * 1_520</gadget> <output>1_824</output> <gadget id="calculator">1_920 - 1_824</gadget> <output>96</output> <gadget id="calculator">50 * (6/5)</gadget> <output>60</output> <gadget id="calculator">60 - 48</gadget> <output>12</output> <gadget id="calculator">96 / 12</gadget> <output>8</output> <result>C</result>
C
8
How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 38 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
{ "A": "2", "B": "5", "C": "8", "D": "15", "E": "25" }
divide(subtract(multiply(48, 40), multiply(divide(add(const_100, 20), const_100), multiply(38, 40))), subtract(multiply(50, divide(add(const_100, 20), const_100)), 48))
add(n3,const_100)|multiply(n1,n4)|multiply(n1,n2)|divide(#0,const_100)|multiply(#3,#2)|multiply(n0,#3)|subtract(#1,#4)|subtract(#5,n4)|divide(#6,#7)
selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 38 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 38 ) = 5 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 8 lbs . answer ( c )
gain
math_qa__rJklnBsPufPyImKW
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 600 newborn members of the population, approximately how many would be expected to survive the first 3 months of life? Pick. A) 438 B) 446 C) 452 D) 462 E) 470
<gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">1 - (1/10)</gadget> <output>9/10 = around 0.9</output> <gadget id="calculator">600 * (9/10)</gadget> <output>540</output> <gadget id="calculator">540 * (9/10)</gadget> <output>486</output> <gadget id="calculator">486 * (9/10)</gadget> <output>2_187/5 = around 437.4</output> <result>A</result>
A
438
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 600 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
{ "A": "438", "B": "446", "C": "452", "D": "462", "E": "470" }
multiply(multiply(multiply(600, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10)))
divide(n1,n2)|subtract(n1,#0)|multiply(n3,#1)|multiply(#2,#1)|multiply(#3,#1)|
"number of newborns that can die in first month = 1 / 10 * 600 = 60 survived = 540 number of newborns that can die in second month = 1 / 10 * 540 = 54 survived = 486 number of newborns that can die in third month = 1 / 10 * 486 = 48 survived = 438 answer : a"
probability
math_qa__A4fuPCVRAWrWZzrJ
the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ? Answers: A) 120 B) 240 C) 360 D) 720 E) 1440
<gadget id="calculator">4 * 3</gadget> <output>12</output> <gadget id="calculator">4 + 1</gadget> <output>5</output> <gadget id="calculator">factorial(5)</gadget> <output>120</output> <gadget id="calculator">factorial(3)</gadget> <output>6</output> <gadget id="calculator">120 / 6</gadget> <output>20</output> <gadget id="calculator">12 * 20</gadget> <output>240</output> <result>B</result>
B
240
the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ?
{ "A": "120", "B": "240", "C": "360", "D": "720", "E": "1440" }
multiply(multiply(4, const_3), divide(factorial(add(4, const_1)), factorial(const_3)))
add(n0,const_1)|factorial(const_3)|multiply(n0,const_3)|factorial(#0)|divide(#3,#1)|multiply(#4,#2)
x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 4 - x - x - 3 . other x ' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b .
general
math_qa__ULJL9558hdO0fiW4
In the new budget the price of milk rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase? Choose one. A) 7.5 % B) 9.1 % C) 10.9 % D) 16.67 % E) 15 %
<gadget id="calculator">20 + 100</gadget> <output>120</output> <gadget id="calculator">20 / 120</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/6) * 100</gadget> <output>50/3 = around 16.666667</output> <result>D</result>
D
16.67
In the new budget the price of milk rose by 20%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
{ "A": "7.5 %", "B": "9.1 %", "C": "10.9 %", "D": "16.67 %", "E": "15 %" }
multiply(divide(20, add(20, const_100)), const_100)
add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100)
reduce in consumption = r / ( 100 + r ) * 100 % = 20 / 120 * 100 = 16.67 % answer is d
general
math_qa__g48qqaJGCmicYgff
Evaluate 64 / .08 Pick one A) 800 B) 500 C) 505 D) none of these E) 506
<gadget id="calculator">8 / 64</gadget> <output>1/8 = around 0.125</output> <gadget id="calculator">100 / (1/8)</gadget> <output>800</output> <result>A</result>
A
800
Evaluate 64 / .08
{ "A": "800", "B": "500", "C": "505", "D": "none of these", "E": "506" }
divide(const_100.0, divide(08, 64))
divide(n1,const_100)|divide(n0,#0)|
"explanation : 64 / . 08 = 6400 / 8 = 800 option a"
general
math_qa__M7HxZDVd2MxGcrfy
A man goes downstream at 14 kmph, and upstream8 kmph. The speed of the stream is Choose the correct choice A) 0 kmph B) 4 kmph C) 16 kmph D) 2.5 kmph E) 3 kmph
<gadget id="calculator">14 - 8</gadget> <output>6</output> <gadget id="calculator">6 / 2</gadget> <output>3</output> <result>E</result>
E
3
A man goes downstream at 14 kmph, and upstream8 kmph. The speed of the stream is
{ "A": "0 kmph", "B": "4 kmph", "C": "16 kmph", "D": "2.5 kmph", "E": "3 kmph" }
divide(subtract(14, 8), const_2)
subtract(n0,n1)|divide(#0,const_2)
speed of the stream = 1 / 2 ( 14 - 8 ) kmph = 3 kmph . correct option : e
physics
math_qa__WjMgNoIVmcspee87
The ratio of radius of a circle and the side of a square is 2 : 11. Find the ratio of their areas: Pick one: A) 2 : 1 B) 4 : 7 C) 8 : 77 D) 4 : 121 E) none
<gadget id="calculator">2 / 11</gadget> <output>2/11 = around 0.181818</output> <gadget id="calculator">(2/11) ** 2</gadget> <output>4/121 = around 0.033058</output> <result>D</result>
D
0.033058
The ratio of radius of a circle and the side of a square is 2 : 11. Find the ratio of their areas:
{ "A": "2 : 1", "B": "4 : 7", "C": "8 : 77", "D": "4 : 121", "E": "none" }
power(divide(2, 11), 2)
divide(n0,n1)|power(#0,n0)|
"radius / side = 2 / 11 ⇒ area of circle / area of square = 4 / 121 answer : d"
geometry
math_qa__0Frmusd6aPmSQJWH
A train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is: Pick: A) 45 m B) 50 m C) 54 m D) 72 m E) none of these
<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">4 * (5/18)</gadget> <output>10/9 = around 1.111111</output> <gadget id="calculator">(10/9) * 10</gadget> <output>100/9 = around 11.111111</output> <gadget id="calculator">2 * (5/18)</gadget> <output>5/9 = around 0.555556</output> <gadget id="calculator">9 * (5/9)</gadget> <output>5</output> <gadget id="calculator">(100/9) - 5</gadget> <output>55/9 = around 6.111111</output> <gadget id="calculator">(55/9) - (5/9)</gadget> <output>50/9 = around 5.555556</output> <gadget id="calculator">9 * (50/9)</gadget> <output>50</output> <result>B</result>
B
50
A train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
{ "A": "45 m", "B": "50 m", "C": "54 m", "D": "72 m", "E": "none of these" }
multiply(9, subtract(subtract(multiply(multiply(4, const_0_2778), 10), multiply(9, multiply(2, const_0_2778))), multiply(2, const_0_2778)))
multiply(n1,const_0_2778)|multiply(n0,const_0_2778)|multiply(n3,#0)|multiply(n2,#1)|subtract(#2,#3)|subtract(#4,#1)|multiply(n2,#5)
let actual speed of train = s m / sec and length of train = l m . then , s - 2 × 5 / 18 = l 9 ⇒ 9 s = l + 5 . . . … ( i ) and s - 4 × 5 ⁄ 18 = l ⁄ 10 ⇒ 90 s = 9 l + 100 . . . . . ( ii ) by ( i ) & ( ii ) , we get l = 50 m . answer b
physics
math_qa__3fFE2ZUdE80HWltw
If the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is? Choose the correct answer. A) 11 B) 14 C) 16 D) 12 E) 19
<gadget id="calculator">3 * 100</gadget> <output>300</output> <gadget id="calculator">1 * 10</gadget> <output>10</output> <gadget id="calculator">300 + 10</gadget> <output>310</output> <gadget id="calculator">310 + 4</gadget> <output>314</output> <gadget id="calculator">314 / 100</gadget> <output>157/50 = around 3.14</output> <gadget id="calculator">2 * (157/50)</gadget> <output>157/25 = around 6.28</output> <gadget id="calculator">(157/25) * 12</gadget> <output>1_884/25 = around 75.36</output> <gadget id="calculator">1_240 / (1_884/25)</gadget> <output>7_750/471 = around 16.454352</output> <result>C</result>
C
16
If the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is?
{ "A": "11", "B": "14", "C": "16", "D": "12", "E": "19" }
divide(1240, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 12))
multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)|
"2 * 22 / 7 * 12 * x = 1240 = > x = 16 answer : c"
physics
math_qa__hzsUWb0CeGNVadv5
(ab)x−2=(ba)x−7. What is the value of x ? Choices: A) 1.5 B) 4.5 C) 7.5 D) 9.5 E) 8.7
<gadget id="calculator">2 + 7</gadget> <output>9</output> <gadget id="calculator">9 / 2</gadget> <output>9/2 = around 4.5</output> <result>B</result>
B
4.5
(ab)x−2=(ba)x−7. What is the value of x ?
{ "A": "1.5", "B": "4.5", "C": "7.5", "D": "9.5", "E": "8.7" }
divide(add(2, 7), 2)
add(n0,n1)|divide(#0,n0)
explanation : ( a / b ) x − 2 = ( b / a ) x − 7 ⇒ ( a / b ) x − 2 = ( a / b ) − ( x − 7 ) ⇒ x − 2 = − ( x − 7 ) ⇒ x − 2 = − x + 7 ⇒ x − 2 = − x + 7 ⇒ 2 x = 9 ⇒ x = 92 = 4.5 option b
general
math_qa__gwhvnixvrv6i9m50
A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it? Choose one: A) 12 days B) 18 days C) 15 days D) 21 days E) 22 days
<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">1 / 10</gadget> <output>1/10 = around 0.1</output> <gadget id="calculator">(1/6) - (1/10)</gadget> <output>1/15 = around 0.066667</output> <gadget id="calculator">1 / (1/15)</gadget> <output>15</output> <result>C</result>
C
15
A and B together can do a piece of work in 6 days and A alone can do it in 10 days. In how many days can B alone can do it?
{ "A": "12 days", "B": "18 days", "C": "15 days", "D": "21 days", "E": "22 days" }
inverse(subtract(inverse(6), inverse(10)))
inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)|
"explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 10 work in 1 day b alone can do ( 1 / 6 - 1 / 10 ) = 1 / 15 work in 1 day = > complete work can be done in 15 days by b answer : option c"
physics
math_qa__76OHxgAFNbexh69n
Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 94. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test? Choose the correct choice from the following choices. A) 87 B) 89 C) 90 D) 93 E) 102
<gadget id="calculator">94 + 2</gadget> <output>96</output> <gadget id="calculator">4 * 96</gadget> <output>384</output> <gadget id="calculator">94 * 3</gadget> <output>282</output> <gadget id="calculator">384 - 282</gadget> <output>102</output> <result>E</result>
E
102
Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 94. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
{ "A": "87", "B": "89", "C": "90", "D": "93", "E": "102" }
subtract(multiply(4, add(94, 2)), multiply(94, 3))
add(n2,n3)|multiply(n0,n2)|multiply(n1,#0)|subtract(#2,#1)
total score on 3 tests = 94 * 3 = 282 jerry wants the average to be = 96 hence total score on 4 tests should be = 96 * 4 = 384 score required on the fourth test = 384 - 282 = 102 option e
general
math_qa__LIJP3OlLVilPL1Kw
In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 18000*10^(-3) Petri dishes. How many germs live happily in a single dish? Answers. A) 100 B) 200 C) 300 D) 400 E) 500
<gadget id="calculator">1_000 * 100</gadget> <output>100_000</output> <gadget id="calculator">100_000 * 0.036</gadget> <output>3_600</output> <gadget id="calculator">18_000 / 1_000</gadget> <output>18</output> <gadget id="calculator">3_600 / 18</gadget> <output>200</output> <result>B</result>
B
200
In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 18000*10^(-3) Petri dishes. How many germs live happily in a single dish?
{ "A": "100", "B": "200", "C": "300", "D": "400", "E": "500" }
divide(multiply(multiply(const_1000, const_100), 0.036), divide(18000, const_1000))
divide(n3,const_1000)|multiply(const_100,const_1000)|multiply(n0,#1)|divide(#2,#0)|
"0.036 * 10 ^ 5 can be written as 3600 18000 * 10 ^ ( - 3 ) can be written as 18 required = 3600 / 18 = 200 answer : b"
general
math_qa__ot4M9q0kJkkyK3CE
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4400, what will be the difference between Q and R's share? Choose the correct choice from the following options: A) 2788 B) 5500 C) 7282 D) 2782 E) 2729
<gadget id="calculator">12 - 7</gadget> <output>5</output> <gadget id="calculator">7 - 3</gadget> <output>4</output> <gadget id="calculator">4_400 / 4</gadget> <output>1_100</output> <gadget id="calculator">5 * 1_100</gadget> <output>5_500</output> <result>B</result>
B
5,500
An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4400, what will be the difference between Q and R's share?
{ "A": "2788", "B": "5500", "C": "7282", "D": "2782", "E": "2729" }
multiply(subtract(12, 7), divide(4400, subtract(7, 3)))
subtract(n1,n0)|subtract(n2,n1)|divide(n3,#0)|multiply(#2,#1)
4 - - - 4400 5 - - - ? = > 5500 answer : b
general
math_qa__YwwngIj6pBU6KtlE
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own? Choose the correct answer: A) 25 minutes . B) 30 minutes . C) 40 minutes . D) 55 minutes E) 1 hour and 20 minutes
<gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">1 / 2.5</gadget> <output>0.4</output> <gadget id="calculator">(1/3) + 0.4</gadget> <output>0.733333</output> <gadget id="calculator">1 - 0.733333</gadget> <output>0.266667</output> <gadget id="calculator">0.266667 / 0.4</gadget> <output>0.666667</output> <gadget id="calculator">0.666667 * 60</gadget> <output>40.00002</output> <result>C</result>
C
40
It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
{ "A": "25 minutes .", "B": "30 minutes .", "C": "40 minutes .", "D": "55 minutes", "E": "1 hour and 20 minutes" }
multiply(divide(subtract(const_1, add(divide(const_1, 3), divide(const_1, 2.5))), divide(const_1, 2.5)), const_60)
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|subtract(const_1,#2)|divide(#3,#1)|multiply(#4,const_60)|
"avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 2.5 = 40 % they worked together for 1 hour and finished 73 % of the job remaining = 27 % tom will complete 40 % in 60 minutes , 20 % in 30 minutes and , 7 % in 60 * 7 / 40 minutes = 10.5 minutes time taken by tom to finish the remaining on his own = 30 + 10.5 = 40.5 minutes ( adjusting for the 0.333 ) ~ 40 minutes answer : c"
physics
math_qa__GtpdkgzBt93edQAM
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is? Select the correct option: A) 127 B) 688 C) 200 D) 121 E) 123
<gadget id="calculator">350 - 340</gadget> <output>10</output> <gadget id="calculator">5 / 100</gadget> <output>1/20 = around 0.05</output> <gadget id="calculator">10 / (1/20)</gadget> <output>200</output> <result>C</result>
C
200
If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is?
{ "A": "127", "B": "688", "C": "200", "D": "121", "E": "123" }
divide(subtract(350, 340), divide(5, const_100))
divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)|
"let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c"
gain
math_qa__b3inG4bvH0nxvuzH
an article with cost price of 180 is sold at 15% profit. what is the selling price? Pick: A) 198 B) 200 C) 204 D) 207 E) 210
<gadget id="calculator">15 / 100</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">180 * (3/20)</gadget> <output>27</output> <gadget id="calculator">180 + 27</gadget> <output>207</output> <result>D</result>
D
207
an article with cost price of 180 is sold at 15% profit. what is the selling price?
{ "A": "198", "B": "200", "C": "204", "D": "207", "E": "210" }
add(180, multiply(180, divide(15, const_100)))
divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|
"sp = 1.15 * 180 = 207 answer : d"
gain
math_qa__3R69NQHzaLye75Ce
The average monthly salary of 15 employees in an organisation is Rs. 1800. If the manager's salary is added, then the average salary increases by Rs. 150. What is the manager's monthly salary? Choose the correct choice: A) rs . 3601 B) rs . 3618 C) rs . 4200 D) rs . 3619 E) rs . 3610
<gadget id="calculator">1_800 + 150</gadget> <output>1_950</output> <gadget id="calculator">15 + 1</gadget> <output>16</output> <gadget id="calculator">1_950 * 16</gadget> <output>31_200</output> <gadget id="calculator">1_800 * 15</gadget> <output>27_000</output> <gadget id="calculator">31_200 - 27_000</gadget> <output>4_200</output> <result>C</result>
C
4,200
The average monthly salary of 15 employees in an organisation is Rs. 1800. If the manager's salary is added, then the average salary increases by Rs. 150. What is the manager's monthly salary?
{ "A": "rs . 3601", "B": "rs . 3618", "C": "rs . 4200", "D": "rs . 3619", "E": "rs . 3610" }
subtract(multiply(add(1800, 150), add(15, const_1)), multiply(1800, 15))
add(n1,n2)|add(n0,const_1)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
"manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c"
general
math_qa__EvCo7x6SbsuIaz7w
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X? Choose the correct choice. A) 10 % B) 33 1 / 3 % C) 40 % D) 50 % E) 66 2 / 3 %
<gadget id="calculator">30 - 25</gadget> <output>5</output> <gadget id="calculator">40 / 100</gadget> <output>2/5 = around 0.4</output> <gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">(2/5) - (1/4)</gadget> <output>3/20 = around 0.15</output> <gadget id="calculator">5 / (3/20)</gadget> <output>100/3 = around 33.333333</output> <result>B</result>
B
33
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 % fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?
{ "A": "10 %", "B": "33 1 / 3 %", "C": "40 %", "D": "50 %", "E": "66 2 / 3 %" }
divide(subtract(30, 25), subtract(divide(40, const_100), divide(25, const_100)))
divide(n0,const_100)|divide(n2,const_100)|subtract(n4,n2)|subtract(#0,#1)|divide(#2,#3)|
"assuming the weight of the mixture to be 100 g * * , then the weight of ryegrass in the mixture would be 30 g . also , assume the weight mixture x used in the mixture is xg , then the weight of mixture y used in the mixture would be ( 100 - x ) g . so we can now equate the parts of the ryegrass in the mixture as : 0.4 x + 0.25 ( 100 - x ) = 30 0.4 x + 25 - 0.25 x = 30 0.15 x = 5 x = 5 / 0.15 = 500 / 15 = 100 / 3 so the weight of mixture x as a percentage of the weight of the mixture = ( weight of x / weight of mixture ) * 100 % = ( 100 / 3 ) / 100 * 100 % = 33 % answer : b"
gain
math_qa__S3TMR80cVWRzLbPJ
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water in ? Choose the correct option. A) 10 hr B) 14 hr C) 12 hr D) 9 hr E) 15 hr
<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">2 * 3</gadget> <output>6</output> <gadget id="calculator">6 + 1</gadget> <output>7</output> <gadget id="calculator">7 / 3</gadget> <output>7/3 = around 2.333333</output> <gadget id="calculator">1 / (7/3)</gadget> <output>3/7 = around 0.428571</output> <gadget id="calculator">(1/2) - (3/7)</gadget> <output>1/14 = around 0.071429</output> <gadget id="calculator">1 / (1/14)</gadget> <output>14</output> <result>B</result>
B
14
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water in ?
{ "A": "10 hr", "B": "14 hr", "C": "12 hr", "D": "9 hr", "E": "15 hr" }
inverse(subtract(divide(1, 2), inverse(divide(add(multiply(2, 3), 1), 3))))
divide(n2,n0)|multiply(n0,n3)|add(n2,#1)|divide(#2,n3)|inverse(#3)|subtract(#0,#4)|inverse(#5)|
"work done by the leak in 1 hour = 1 / 2 - 3 / 7 = 1 / 14 leak will empty the tank in 14 hrs answer is b"
physics
math_qa__vDsRV085oMcu00XQ
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 55 minutes? Pick: A) 80 B) 100 C) 150 D) 180 E) 220
<gadget id="calculator">60 / 15</gadget> <output>4</output> <gadget id="calculator">4 * 55</gadget> <output>220</output> <result>E</result>
E
220
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 55 minutes?
{ "A": "80", "B": "100", "C": "150", "D": "180", "E": "220" }
multiply(divide(const_60, 15), 55)
divide(const_60,n0)|multiply(n1,#0)|
"since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 55 minutes the population increases by 55 x 4 = 220 people . answer . e ."
physics
math_qa__2kcxbEUFyF87xd0p
Five 6 faced dice are thrown together. The probability that all the three show the same number on them is? Choose one: A) 1 / 32 B) 1 / 1296 C) 1 / 33 D) 1 / 38 E) 1 / 34
<gadget id="calculator">1 / 6</gadget> <output>1/6 = around 0.166667</output> <gadget id="calculator">(1/6) * (1/6)</gadget> <output>1/36 = around 0.027778</output> <gadget id="calculator">(1/36) * (1/6)</gadget> <output>1/216 = around 0.00463</output> <gadget id="calculator">(1/216) * (1/6)</gadget> <output>1/1_296 = around 0.000772</output> <result>B</result>
B
0.000772
Five 6 faced dice are thrown together. The probability that all the three show the same number on them is?
{ "A": "1 / 32", "B": "1 / 1296", "C": "1 / 33", "D": "1 / 38", "E": "1 / 34" }
multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6))
divide(const_1,n0)|multiply(#0,#0)|multiply(#0,#1)|multiply(#0,#2)
the three dice can fall in 6 * 6 * 6 * 6 * 6 = 7776 ways . hence the probability is 6 / 7776 = 1 / 1296 answer : b
probability
math_qa__XedBiuKVMAzLzs2n
If P is a prime number greater than 3, find the remainder when P^2 + 15 is divided by 12. Choose the correct choice from the following answers: A) 6 B) 4 C) 0 D) 8 E) 7
<gadget id="calculator">1 + 4</gadget> <output>5</output> <gadget id="calculator">5 ** 2</gadget> <output>25</output> <gadget id="calculator">15 + 25</gadget> <output>40</output> <gadget id="calculator">12 * 3</gadget> <output>36</output> <gadget id="calculator">40 - 36</gadget> <output>4</output> <result>B</result>
B
4
If P is a prime number greater than 3, find the remainder when P^2 + 15 is divided by 12.
{ "A": "6", "B": "4", "C": "0", "D": "8", "E": "7" }
subtract(add(15, power(add(const_1, const_4), 2)), multiply(12, 3))
add(const_1,const_4)|multiply(n0,n3)|power(#0,n1)|add(n2,#2)|subtract(#3,#1)|
"every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 15 = 36 n ^ 2 + 12 n + 1 + 15 = 36 n ^ 2 + 12 n + 12 + 4 if p = 6 n - 1 , then p ^ 2 + 15 = 36 n ^ 2 - 12 n + 1 + 15 = 36 n ^ 2 - 12 n + 12 + 4 when divided by 12 , it must leave a remainder of 4 . the answer is b ."
general
math_qa__fp4hQbEFExM2usz9
A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount? Select the correct option: A) 8 % B) 14 % C) 26 % D) 15 % E) 17 %
<gadget id="calculator">40 + 100</gadget> <output>140</output> <gadget id="calculator">140 * 10</gadget> <output>1_400</output> <gadget id="calculator">1_400 / 100</gadget> <output>14</output> <gadget id="calculator">140 - 14</gadget> <output>126</output> <gadget id="calculator">126 - 100</gadget> <output>26</output> <result>C</result>
C
26
A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
{ "A": "8 %", "B": "14 %", "C": "26 %", "D": "15 %", "E": "17 %" }
subtract(subtract(add(40, const_100), divide(multiply(add(40, const_100), 10), const_100)), const_100)
add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|subtract(#0,#2)|subtract(#3,const_100)|
"let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 10 % on 126 . profit = 126 - 100 26 % answer c"
gain
math_qa__TM2Vx168mPTHqc5g
The average age of 18 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is? Select the correct option A) 9 B) 31 C) 56 D) 72 E) 90
<gadget id="calculator">18 * 15</gadget> <output>270</output> <gadget id="calculator">5 * 14</gadget> <output>70</output> <gadget id="calculator">270 - 70</gadget> <output>200</output> <gadget id="calculator">9 * 16</gadget> <output>144</output> <gadget id="calculator">200 - 144</gadget> <output>56</output> <result>C</result>
C
56
The average age of 18 persons in a office is 15 years. Out of these, the average age of 5 of them is 14 years and that of the other 9 persons is 16 years. The age of the 15th person is?
{ "A": "9", "B": "31", "C": "56", "D": "72", "E": "90" }
subtract(subtract(multiply(18, 15), multiply(5, 14)), multiply(9, 16))
multiply(n0,n1)|multiply(n2,n3)|multiply(n4,n5)|subtract(#0,#1)|subtract(#3,#2)
age of the 15 th student = 18 * 15 - ( 14 * 5 + 16 * 9 ) = 270 - 214 = 56 years answer is c
general
math_qa__iUTCBrzsyEkQDLrJ
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1800 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years? Select the correct option: A) $ 16,200 B) $ 5,600 C) $ 8,100 D) $ 15,000 E) $ 22,500
<gadget id="calculator">112 / 8</gadget> <output>14</output> <gadget id="calculator">28 / 14</gadget> <output>2</output> <gadget id="calculator">3 ** 2</gadget> <output>9</output> <gadget id="calculator">1_800 * 9</gadget> <output>16_200</output> <result>A</result>
A
16,200
Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1800 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
{ "A": "$ 16,200", "B": "$ 5,600", "C": "$ 8,100", "D": "$ 15,000", "E": "$ 22,500" }
multiply(1800, power(const_3, divide(28, divide(112, 8))))
divide(n0,n2)|divide(n3,#0)|power(const_3,#1)|multiply(n1,#2)|
"x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1800 triples to $ 5400 , in 28 years , it will again triple to $ 5400 * 3 = $ 16,200 answer a"
gain
math_qa__RCDhD0teJRX6ukrY
A profit of Rs. 700 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ? Choices. A) s . 240 B) s . 140 C) s . 340 D) s . 50 E) s . 90
<gadget id="calculator">1 / 2</gadget> <output>1/2 = around 0.5</output> <gadget id="calculator">1 / 3</gadget> <output>1/3 = around 0.333333</output> <gadget id="calculator">(1/2) + (1/3)</gadget> <output>5/6 = around 0.833333</output> <gadget id="calculator">700 / (5/6)</gadget> <output>840</output> <gadget id="calculator">840 / 2</gadget> <output>420</output> <gadget id="calculator">840 / 3</gadget> <output>280</output> <gadget id="calculator">420 - 280</gadget> <output>140</output> <result>B</result>
B
140
A profit of Rs. 700 is divided between X and Y in the ratio of 1/2:1/3 . What is the difference between their profit shares ?
{ "A": "s . 240", "B": "s . 140", "C": "s . 340", "D": "s . 50", "E": "s . 90" }
subtract(divide(divide(700, add(divide(1, 2), divide(1, 3))), 2), divide(divide(700, add(divide(1, 2), divide(1, 3))), 3))
divide(n1,n2)|divide(n1,n4)|add(#0,#1)|divide(n0,#2)|divide(#3,n2)|divide(#3,n4)|subtract(#4,#5)|
"a profit of rs . 700 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 300 and 200 . difference in profit share = 420 - 280 = 140 answer : b"
general
math_qa__J9Op10GGsLTJOMbN
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount had been offered? Select the correct option. A) 28.5 B) 27.675 C) 30 D) data inadequate E) none of these
<gadget id="calculator">100 + 23.5</gadget> <output>123.5</output> <gadget id="calculator">123.5 * 100</gadget> <output>12_350</output> <gadget id="calculator">100 - 5</gadget> <output>95</output> <gadget id="calculator">12_350 / 95</gadget> <output>130</output> <gadget id="calculator">130 - 100</gadget> <output>30</output> <result>C</result>
C
30
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount had been offered?
{ "A": "28.5", "B": "27.675", "C": "30", "D": "data inadequate", "E": "none of these" }
subtract(divide(multiply(add(const_100, 23.5), const_100), subtract(const_100, 5)), const_100)
add(n1,const_100)|subtract(const_100,n0)|multiply(#0,const_100)|divide(#2,#1)|subtract(#3,const_100)|
"giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 × ( 100 + 23.5 ) / ( 100 − 5 ) = 100 × 247 / 190 = 130 hence , required % profit = 130 – 100 = 30 % answer c"
gain
math_qa__BZ1ktUdjnZPS34Df
P and Q started a business investing Rs 10000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively. Choices: A) 2 : 7 B) 2 : 6 C) 17 : 6 D) 2 : 3 E) 7 : 8
<gadget id="calculator">10_000 / 15_000</gadget> <output>2/3 = around 0.666667</output> <result>D</result>
D
0.666667
P and Q started a business investing Rs 10000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively.
{ "A": "2 : 7", "B": "2 : 6", "C": "17 : 6", "D": "2 : 3", "E": "7 : 8" }
divide(10000, 15000)
divide(n0,n1)|
"explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 10000 : 15000 = 10 : 15 = 2 : 3 option d"
gain
math_qa__6skijdH5xc2RqpMN
The compound ratio of 2/3, 6/7, 1/3 and 3/8 is given by? Select the correct option A) 7 / 98 B) 1 / 48 C) 1 / 98 D) 1 / 96 E) 3 / 42
<gadget id="calculator">2 * 7</gadget> <output>14</output> <gadget id="calculator">1 / 14</gadget> <output>1/14 = around 0.071429</output> <result>E</result>
E
0.071429
The compound ratio of 2/3, 6/7, 1/3 and 3/8 is given by?
{ "A": "7 / 98", "B": "1 / 48", "C": "1 / 98", "D": "1 / 96", "E": "3 / 42" }
inverse(multiply(2, 7))
multiply(n0,n3)|inverse(#0)
2 / 3 * 6 / 7 * 1 / 3 * 3 / 8 = 36 / 504 = 3 / 42 answer : e
other
math_qa__gVm0nYhsW0p5jen4
There are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed. Choose the correct option: A) 5 B) 1 C) 3 D) 6 E) 7
<gadget id="calculator">binomial(3, 2)</gadget> <output>3</output> <gadget id="calculator">3 + 3</gadget> <output>6</output> <result>D</result>
D
6
There are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
{ "A": "5", "B": "1", "C": "3", "D": "6", "E": "7" }
add(choose(3, 2), choose(3, 2))
choose(n0,n1)|add(#0,#0)|
"first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 3 and for second = 2 so total methods = 3 * 2 = 6 answer : d"
probability
math_qa__3sBMECFlgLvD5CPQ
A boy is traveling from his house to school at 10km/hr and reached school 2hours late. Next day he traveled 20km/hr and reached 1hour early. Then find the distance between house and school? Choose the correct choice from the following answers A) 50 km B) 45 km C) 33 km D) 60 km E) 54 km
<gadget id="calculator">2 * 10</gadget> <output>20</output> <gadget id="calculator">20 + 20</gadget> <output>40</output> <gadget id="calculator">20 - 10</gadget> <output>10</output> <gadget id="calculator">40 / 10</gadget> <output>4</output> <gadget id="calculator">4 + 2</gadget> <output>6</output> <gadget id="calculator">6 * 10</gadget> <output>60</output> <result>D</result>
D
60
A boy is traveling from his house to school at 10km/hr and reached school 2hours late. Next day he traveled 20km/hr and reached 1hour early. Then find the distance between house and school?
{ "A": "50 km", "B": "45 km", "C": "33 km", "D": "60 km", "E": "54 km" }
multiply(add(divide(add(multiply(2, 10), 20), subtract(20, 10)), 2), 10)
multiply(n0,n1)|subtract(n2,n0)|add(n2,#0)|divide(#2,#1)|add(n1,#3)|multiply(n0,#4)
let distance be x s 1 = 10 km / hr s 2 = 20 km / hr t 1 = x / 10 hr t 2 = x / 20 hr difference in time = 2 + 1 = 3 hr ( x / 10 ) - ( x / 20 ) = 3 x = 60 km answer is d
physics
math_qa__dxz92H1EtqwXXpIB
The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 285, then the mean profit for the last 15 days would be Pick. A) rs . 200 B) rs . 350 C) rs . 275 D) rs . 415 E) none of these
<gadget id="calculator">30 * 350</gadget> <output>10_500</output> <gadget id="calculator">15 * 285</gadget> <output>4_275</output> <gadget id="calculator">10_500 - 4_275</gadget> <output>6_225</output> <gadget id="calculator">6_225 / 15</gadget> <output>415</output> <result>D</result>
D
415
The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 285, then the mean profit for the last 15 days would be
{ "A": "rs . 200", "B": "rs . 350", "C": "rs . 275", "D": "rs . 415", "E": "none of these" }
divide(subtract(multiply(30, 350), multiply(15, 285)), 15)
multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n3)|
"average would be : 350 = ( 285 + x ) / 2 on solving , x = 415 . answer : d"
gain
math_qa__eOI6dtdkunrshJqx
In the first 7 overs of a cricket game, the run rate was only 4.2. What should be the rate in the remaining 30 overs to reach the target of 282 runs? Answers A) 6.25 B) 8.42 C) 8.3 D) 8.1 E) 6.21
<gadget id="calculator">7 * 4.2</gadget> <output>29.4</output> <gadget id="calculator">282 - 29.4</gadget> <output>252.6</output> <gadget id="calculator">252.6 / 30</gadget> <output>8.42</output> <result>B</result>
B
8.42
In the first 7 overs of a cricket game, the run rate was only 4.2. What should be the rate in the remaining 30 overs to reach the target of 282 runs?
{ "A": "6.25", "B": "8.42", "C": "8.3", "D": "8.1", "E": "6.21" }
divide(subtract(282, multiply(7, 4.2)), 30)
multiply(n0,n1)|subtract(n3,#0)|divide(#1,n2)|
"required run rate = [ 282 - ( 4.2 * 7 ) ] / 30 = 252.60 / 40 = 8.42 answer : b"
gain
math_qa__pMKJ4I3s1afi4PQm
An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank? Choose the correct choice from the following answers. A) 51.6 B) 51.5 C) 51.7 D) 51.1 E) 51.0
<gadget id="calculator">30 + 35</gadget> <output>65</output> <gadget id="calculator">65 + 42</gadget> <output>107</output> <gadget id="calculator">107 - 2</gadget> <output>105</output> <gadget id="calculator">105 / 2</gadget> <output>105/2 = around 52.5</output> <result>B</result>
B
51.5
An empty tank be filled with an inlet pipe ‘A’ in 42 minutes. After 12 minutes an outlet pipe ‘B’ is opened which can empty the tank in 30 minutes. After 6 minutes another inlet pipe ‘C’ opened into the same tank, which can fill the tank in 35 minutes and the tank is filled. Find the time taken to fill the tank?
{ "A": "51.6", "B": "51.5", "C": "51.7", "D": "51.1", "E": "51.0" }
divide(subtract(add(add(30, 35), 42), const_2), const_2)
add(n2,n4)|add(n0,#0)|subtract(#1,const_2)|divide(#2,const_2)
assume total tank capacity = 210 liters now capacity of pipe a = 210 / 42 = 5 liters capacity of b = 210 / 30 = - 7 liters capacity of c = 210 / 35 = 6 min assume tank gets filled in x min after the third pipe got opened . so x × 5 + 6 × ( − 2 ) + 4 x = 210 x × 5 + 6 × ( − 2 ) + 4 x = 210 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 ⇒ 48 + 4 x = 210 ⇒ 4 x = 162 ⇒ x = 40.5 total time taken to fill the tank = 40.5 + 12 + 6 = 51.5 answer : b
physics
math_qa__DsdMQ7lUE1ScEApk
In a group of 50 people, 25 have visited Iceland and 23 have visited Norway. If 21 people have visited both Iceland and Norway, how many people have visited neither country? Choose the correct choice from the following answers A) 20 B) 21 C) 22 D) 23 E) 24
<gadget id="calculator">25 + 23</gadget> <output>48</output> <gadget id="calculator">48 - 21</gadget> <output>27</output> <gadget id="calculator">50 - 27</gadget> <output>23</output> <result>D</result>
D
23
In a group of 50 people, 25 have visited Iceland and 23 have visited Norway. If 21 people have visited both Iceland and Norway, how many people have visited neither country?
{ "A": "20", "B": "21", "C": "22", "D": "23", "E": "24" }
subtract(50, subtract(add(25, 23), 21))
add(n1,n2)|subtract(#0,n3)|subtract(n0,#1)|
"this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 50 = 25 + 23 - 21 + ( # in neither group ) = 23 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
other
math_qa__elKWiZYCuClxtmKZ
A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume? Choose the correct choice from the following answers. A) 4 / 3 B) 5 / 3 C) 7 / 3 D) 8 / 3 E) 10 / 3
<gadget id="calculator">3 / 5</gadget> <output>3/5 = around 0.6</output> <gadget id="calculator">4 / (3/5)</gadget> <output>20/3 = around 6.666667</output> <gadget id="calculator">(20/3) - 4</gadget> <output>8/3 = around 2.666667</output> <result>D</result>
D
2.666667
A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?
{ "A": "4 / 3", "B": "5 / 3", "C": "7 / 3", "D": "8 / 3", "E": "10 / 3" }
subtract(divide(4, divide(3, 5)), 4)
divide(n2,n3)|divide(n0,#0)|subtract(#1,n0)
let the number of quarts that should be added to get the required ratio = x so total quarts of water = ( x + 4 ) but the original number of quarts of alcohol remains the same , so we have : 4 / ( x + 4 ) = 3 / 5 cross - multiply : now we have 20 = 3 x + 12 = > 3 x = 20 - 12 = > x = 8 / 3 answer - d
general
math_qa__vkEEoDpjVtomy1Bj
An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters Q long? Choose the correct choice from the following options. A) 0.5 B) 1 C) 1.5 D) 2 E) 3
<gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">4 * 1.5</gadget> <output>6</output> <gadget id="calculator">8 + 6</gadget> <output>14</output> <gadget id="calculator">15 - 14</gadget> <output>1</output> <result>B</result>
B
1
An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many meters Q long?
{ "A": "0.5", "B": "1", "C": "1.5", "D": "2", "E": "3" }
subtract(15, add(multiply(const_4, 2), multiply(const_4, 1.5)))
multiply(n1,const_4)|multiply(n2,const_4)|add(#0,#1)|subtract(n0,#2)|
"let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m = q , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
general
math_qa__dcxL4h7lgbWtOKsi
When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 39, what is the remainder when k is divided by 7? Choose the correct choice from the following. A) 4 B) 5 C) 6 D) 3 E) 7
<gadget id="calculator">12 + 5</gadget> <output>17</output> <gadget id="calculator">17 % 7</gadget> <output>3</output> <result>D</result>
D
3
When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 39, what is the remainder when k is divided by 7?
{ "A": "4", "B": "5", "C": "6", "D": "3", "E": "7" }
reminder(add(const_12, 5), 7)
add(n0,const_12)|reminder(#0,n5)
cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 39 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 39 ) 17 is the only common number in both the sets . hence k = 17 answer : d
general
math_qa__wCC0guBqziDWhi9w
The batting average of a particular batsman is 61 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score. Select: A) 179 B) 202 C) 210 D) 223 E) 229
<gadget id="calculator">61 * 46</gadget> <output>2_806</output> <gadget id="calculator">46 - 2</gadget> <output>44</output> <gadget id="calculator">58 * 44</gadget> <output>2_552</output> <gadget id="calculator">2_806 - 2_552</gadget> <output>254</output> <gadget id="calculator">150 + 254</gadget> <output>404</output> <gadget id="calculator">404 / 2</gadget> <output>202</output> <result>B</result>
B
202
The batting average of a particular batsman is 61 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
{ "A": "179", "B": "202", "C": "210", "D": "223", "E": "229" }
divide(add(150, subtract(multiply(61, 46), multiply(58, subtract(46, const_2)))), const_2)
multiply(n0,n1)|subtract(n1,const_2)|multiply(n3,#1)|subtract(#0,#2)|add(n2,#3)|divide(#4,const_2)|
"explanation : total runs scored by the batsman = 61 * 46 = 2806 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2806 – 2552 = 254 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 254 2 x = 404 x = 202 runs answer b"
general
math_qa__viBMJMYoOFAk3Sgw
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere? Choose the correct choice from the following choices: A) 6 / π B) 9 / π C) 6 D) 9 E) 12
<gadget id="calculator">4 * pi</gadget> <output>4*pi = around 12.566371</output> <gadget id="calculator">3 / pi</gadget> <output>3/pi = around 0.95493</output> <gadget id="calculator">(4*pi) * (3/pi)</gadget> <output>12</output> <gadget id="calculator">12 / 2</gadget> <output>6</output> <gadget id="calculator">pi * (3/pi)</gadget> <output>3</output> <gadget id="calculator">6 + 3</gadget> <output>9</output> <result>D</result>
D
9
The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area T of that hemisphere?
{ "A": "6 / π", "B": "9 / π", "C": "6", "D": "9", "E": "12" }
add(divide(multiply(multiply(4, const_pi), divide(3, const_pi)), 2), multiply(const_pi, divide(3, const_pi)))
divide(n2,const_pi)|multiply(n0,const_pi)|multiply(#0,#1)|multiply(#0,const_pi)|divide(#2,n1)|add(#4,#3)|
"given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
geometry
math_qa__wqzOcni2jgNRMlVT
There are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed. Choose the most appropriate option. A) 26 B) 32 C) 35 D) 30 E) 45
<gadget id="calculator">408 + 216</gadget> <output>624</output> <gadget id="calculator">2 * 2</gadget> <output>4</output> <gadget id="calculator">4 * 2</gadget> <output>8</output> <gadget id="calculator">8 * 3</gadget> <output>24</output> <gadget id="calculator">624 / 24</gadget> <output>26</output> <result>A</result>
A
26
There are 408 boys and 216 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
{ "A": "26", "B": "32", "C": "35", "D": "30", "E": "45" }
divide(add(408, 216), multiply(multiply(multiply(const_2, const_2), const_2), const_3))
add(n0,n1)|multiply(const_2,const_2)|multiply(#1,const_2)|multiply(#2,const_3)|divide(#0,#3)|
"explanation : hcf ( 408 , 216 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 216 / 24 = 17 + 9 = 26 answer : a"
general
math_qa__V2nrzIgtNx1vqMxC
The number 250 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers? Choose the correct option A) 18 B) 22 C) 21 D) 20 E) 19
<gadget id="calculator">250 / 2</gadget> <output>125</output> <gadget id="calculator">125 ** (1/2)</gadget> <output>5*sqrt(5) = around 11.18034</output> <gadget id="calculator">2 * (5*sqrt(5))</gadget> <output>10*sqrt(5) = around 22.36068</output> <result>B</result>
B
22
The number 250 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers?
{ "A": "18", "B": "22", "C": "21", "D": "20", "E": "19" }
multiply(const_2, sqrt(divide(250, const_2)))
divide(n0,const_2)|sqrt(#0)|multiply(#1,const_2)
sum of the squares of 3 different positive integers = 250 15 ^ 2 + 3 ^ 2 + 4 ^ 2 = 250 now , sum of these 3 different integers = 15 + 3 + 4 = 22 ans - b
geometry
math_qa__UHJCOB9ZNb65VNmT
13 ltr of water is added with 11 ltr of a solution containing 16%of alcohol in the water. The %of alcohol in the new mixture is? Choose the correct choice from the following: A) 7.33 % B) 9 % C) 9.67 % D) 11 % E) 11.5 %
<gadget id="calculator">16 / 100</gadget> <output>4/25 = around 0.16</output> <gadget id="calculator">(4/25) * 11</gadget> <output>44/25 = around 1.76</output> <gadget id="calculator">13 + 11</gadget> <output>24</output> <gadget id="calculator">(44/25) / 24</gadget> <output>11/150 = around 0.073333</output> <gadget id="calculator">100 * (11/150)</gadget> <output>22/3 = around 7.333333</output> <result>A</result>
A
7.33
13 ltr of water is added with 11 ltr of a solution containing 16%of alcohol in the water. The %of alcohol in the new mixture is?
{ "A": "7.33 %", "B": "9 %", "C": "9.67 %", "D": "11 %", "E": "11.5 %" }
multiply(const_100, divide(multiply(divide(16, const_100), 11), add(13, 11)))
add(n0,n1)|divide(n2,const_100)|multiply(n1,#1)|divide(#2,#0)|multiply(#3,const_100)|
"we have an 11 litre solution containing 16 % of alcohol in the water . = > quantity of alcohol in the solution = 11 ã — 16 / 100 now 13 litre of water is added to the solution . = > total quantity of the new solution = 11 + 13 = 24 percentage of alcohol in the new solution = 11 ã — 16 / 100 24 ã — 100 = 11 ã — 1610024 ã — 100 = 11 ã — 0.67 / 100 = 7.33 % a"
general
math_qa__2DJuw9PU76FWfqD7
A straight line in the xy- plane has y-intercept of 49 . On this line the x-coordinate of the point is 71 and y-coordinate is 12 then what is the slope of the line? Choose the correct choice from the following: A) 0.5 B) 0.51 C) - 0.52 D) 0.31 E) - 0.49
<gadget id="calculator">12 - 49</gadget> <output>-37</output> <gadget id="calculator">(-37) / 71</gadget> <output>-37/71 = around -0.521127</output> <result>C</result>
C
-0.52
A straight line in the xy- plane has y-intercept of 49 . On this line the x-coordinate of the point is 71 and y-coordinate is 12 then what is the slope of the line?
{ "A": "0.5", "B": "0.51", "C": "- 0.52", "D": "0.31", "E": "- 0.49" }
divide(subtract(12, 49), 71)
subtract(n2,n0)|divide(#0,n1)|
"eq of line = y = mx + c c = 49 x = 71 y = 12 substitute given : m = ( y - c ) / x = ( 12 - 49 ) / 71 = - 37 / 71 = - 0.52 correct option is c"
general
math_qa__F9BpveUt1gw3iPRd
A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1116 in total compensation, how many total hours did he work that week? Choose the most appropriate option A) 36 B) 57 C) 44 D) 48 E) 52
<gadget id="calculator">16 * 40</gadget> <output>640</output> <gadget id="calculator">1_116 - 640</gadget> <output>476</output> <gadget id="calculator">100 + 75</gadget> <output>175</output> <gadget id="calculator">16 * 175</gadget> <output>2_800</output> <gadget id="calculator">2_800 / 100</gadget> <output>28</output> <gadget id="calculator">476 / 28</gadget> <output>17</output> <gadget id="calculator">40 + 17</gadget> <output>57</output> <result>B</result>
B
57
A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1116 in total compensation, how many total hours did he work that week?
{ "A": "36", "B": "57", "C": "44", "D": "48", "E": "52" }
add(40, divide(subtract(1116, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))
add(n3,const_100)|multiply(n0,n1)|multiply(n0,#0)|subtract(n4,#1)|divide(#2,const_100)|divide(#3,#4)|add(n1,#5)|
"for 40 hrs = 40 * 16 = 640 excess = 1116 - 640 = 476 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 476 / 28 = 17 total hrs = 40 + 17 = 57 answer b 57"
general
math_qa__Ka2waiXhDerius32
A train 450 m long running at 126 kmph crosses a platform in 20 sec. What is the length of the platform? Choose the correct option: A) 271 B) 250 C) 350 D) 277 E) 232
<gadget id="calculator">10 / 36</gadget> <output>5/18 = around 0.277778</output> <gadget id="calculator">126 * (5/18)</gadget> <output>35</output> <gadget id="calculator">20 * 35</gadget> <output>700</output> <gadget id="calculator">700 - 450</gadget> <output>250</output> <result>B</result>
B
250
A train 450 m long running at 126 kmph crosses a platform in 20 sec. What is the length of the platform?
{ "A": "271", "B": "250", "C": "350", "D": "277", "E": "232" }
subtract(multiply(20, multiply(126, const_0_2778)), 450)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
"length of the platform = 126 * 5 / 18 * 20 = 700 – 450 = 250 answer : b"
physics
math_qa__rFH0kgzTFhEpoqjk
200 is increased by 25%. Find the final number. Choose the correct choice from the following choices A) 200 B) 210 C) 250 D) 190 E) 220
<gadget id="calculator">25 / 100</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">200 * (1/4)</gadget> <output>50</output> <gadget id="calculator">200 + 50</gadget> <output>250</output> <result>C</result>
C
250
200 is increased by 25%. Find the final number.
{ "A": "200", "B": "210", "C": "250", "D": "190", "E": "220" }
add(200, multiply(200, divide(25, const_100)))
divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|
explanation final number = initial number + 25 % ( original number ) = 200 + 25 % ( 200 ) = 200 + 50 = 250 . answer c
gain
math_qa__LpqrmZW8eMP7jQF4
Given that 268x74= 19332, find the value of 2.68x.74. Choose the correct choice from the following choices: A) 1.9332 B) 1.0025 C) 1.5693 D) 1.0266 E) none
<gadget id="calculator">268 / 100</gadget> <output>67/25 = around 2.68</output> <gadget id="calculator">74 / 100</gadget> <output>37/50 = around 0.74</output> <gadget id="calculator">(67/25) * (37/50)</gadget> <output>2_479/1_250 = around 1.9832</output> <result>A</result>
A
1.9332
Given that 268x74= 19332, find the value of 2.68x.74.
{ "A": "1.9332", "B": "1.0025", "C": "1.5693", "D": "1.0266", "E": "none" }
multiply(divide(268, const_100), divide(74, const_100))
divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|
"solution sum of decimals places = ( 2 + 2 ) = 4 . therefore , = 2.68 × . 74 = 1.9332 answer a"
general
math_qa__npQZF9AjB6kL3VxR
A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 30% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save? Options A) 21 % B) 22.5 % C) 25 % D) 30 % E) 40 %
<gadget id="calculator">100 + 30</gadget> <output>130</output> <gadget id="calculator">130 + 100</gadget> <output>230</output> <gadget id="calculator">2 * 100</gadget> <output>200</output> <gadget id="calculator">230 - 200</gadget> <output>30</output> <gadget id="calculator">30 / 100</gadget> <output>3/10 = around 0.3</output> <gadget id="calculator">(3/10) * 100</gadget> <output>30</output> <result>D</result>
D
30
A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 30% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
{ "A": "21 %", "B": "22.5 %", "C": "25 %", "D": "30 %", "E": "40 %" }
multiply(divide(subtract(add(add(100, 30), 100), multiply(2, 100)), 100), 100)
add(n0,n1)|multiply(n1,n2)|add(n1,#0)|subtract(#2,#1)|divide(#3,n1)|multiply(#4,n1)|
"1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.3 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 30 % income the savings increased by 100 % . or s = . 3 i or s = 30 % of income d is the answer"
general
math_qa__VjLJ9hBj9DBUrlU8
The average age of applicants for a new job is 31, with a standard deviation of 8. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants? Choose the correct option A) 8 B) 14 C) 15 D) 17 E) 30
<gadget id="calculator">8 * 2</gadget> <output>16</output> <gadget id="calculator">16 + 1</gadget> <output>17</output> <result>D</result>
D
17
The average age of applicants for a new job is 31, with a standard deviation of 8. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
{ "A": "8", "B": "14", "C": "15", "D": "17", "E": "30" }
add(multiply(8, const_2), const_1)
multiply(n1,const_2)|add(#0,const_1)|
"within one standard deviation of the average age means 31 + / - 7 23 - - 31 - - 39 number of dif . ages - 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 total = 17 d"
general
math_qa__FWP0kkCfckXr2N80
4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 12 weavers in 12 days? Choose the correct choice: A) 12 B) 18 C) 24 D) 30 E) 36
<gadget id="calculator">4 * 4</gadget> <output>16</output> <gadget id="calculator">4 / 16</gadget> <output>1/4 = around 0.25</output> <gadget id="calculator">12 * (1/4)</gadget> <output>3</output> <gadget id="calculator">12 * 3</gadget> <output>36</output> <result>E</result>
E
36
4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 12 weavers in 12 days?
{ "A": "12", "B": "18", "C": "24", "D": "30", "E": "36" }
multiply(12, multiply(12, divide(4, multiply(4, 4))))
multiply(n0,n0)|divide(n0,#0)|multiply(n3,#1)|multiply(n3,#2)|
"1 weaver can weave 1 mat in 4 days . 12 weavers can weave 12 mats in 4 days . 12 weavers can weave 36 mats in 12 days . the answer is e ."
gain