prompt stringlengths 166 799 | chosen stringlengths 18 2.75k | rejected stringlengths 20 2.08k |
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Solve the following multiple choice question.
Question:
what is the remainder when 14,451 × 15,654 × 16,783 is divided by 5 ?
Options:
a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Answer (choose one of a, b, c, d, e): | only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 4 * 3 = will give units digit as 2 so , whatever be the number , if it ends in 2 , the remainder after dividing with 5 will be 2 . option c
Final answer: c | To find the remainder when 14,451 × 15,654 × 16,783 is divided by 5, we can follow these steps:
1. First, find the remainder when each of these three numbers is divided by 5.
14,451 ÷ 5 = 2 with a remainder of 1
15,654 ÷ 5 = 3 with a remainder of 4
16,783 ÷ 5 = 3 with a remainder of 3
Now, find the remainder when th... |
Solve the following multiple choice question.
Question:
what is the remainder when 14,451 × 15,654 × 16,783 is divided by 5 ?
Options:
a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Answer (choose one of a, b, c, d, e): | only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 4 * 3 = will give units digit as 2 so , whatever be the number , if it ends in 2 , the remainder after dividing with 5 will be 2 . option c
Final answer: c | To solve this problem, we need to find the remainder when 14,451 × 15,654 × 16,783 is divided by 5.
Let's break it down step by step:
1. 14,451 = 2 × 7,223
2. 15,654 = 2 × 7,327
3. 16,783 = 2 × 8,391
Now, we can multiply the remainders from steps 1, 2, and 3:
(2 × 7,223) × 2 × 7,327 = 2 × 15,486
= 30,972
Now, we n... |
Solve the following multiple choice question.
Question:
what is the remainder when 14,451 × 15,654 × 16,783 is divided by 5 ?
Options:
a ) 1 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Answer (choose one of a, b, c, d, e): | only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 4 * 3 = will give units digit as 2 so , whatever be the number , if it ends in 2 , the remainder after dividing with 5 will be 2 . option c
Final answer: c | To find the remainder when 14,451 × 15,654 × 16,783 is divided by 5, we can simplify the problem by first finding the remainders when each of the factors is divided by 5.
14,451 divided by 5 is 2,855 with a remainder of 1
15,654 divided by 5 is 3,127 with a remainder of 4
16,783 divided by 5 is 3,186 with a remainder ... |
Solve the following multiple choice question.
Question:
the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ?
Options:
a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21
Answer (choose one of a, b, c, d, e): | 1340 - - - - 130 100 - - - - ? = > 9 % answer : b
Final answer: b | To find the loss percentage, let's first find the loss amount.
Cost price = Rs 1340
Selling price = Rs 1210
Loss = Cost price - Selling price
= 1340 - 1210
= 230
Now, we can find the loss percentage as follows:
Loss percentage = (Loss / Cost price) * 100
= (230 / 1340) * 100
= 17.29%
Rounding it off, the loss perc... |
Solve the following multiple choice question.
Question:
the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ?
Options:
a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21
Answer (choose one of a, b, c, d, e): | 1340 - - - - 130 100 - - - - ? = > 9 % answer : b
Final answer: b | To calculate the loss percentage, we need to find the difference between the cost price (CP) and the selling price (SP).
CP = 1340, SP = 1210
Loss = CP - SP = 1340 - 1210 = 230
Now, let's calculate the loss percentage:
Loss percentage = (Loss / CP) * 100
= (230 / 1340) * 100
= 17.29%
Rounded to the nearest whole ... |
Solve the following multiple choice question.
Question:
the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ?
Options:
a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21
Answer (choose one of a, b, c, d, e): | 1340 - - - - 130 100 - - - - ? = > 9 % answer : b
Final answer: b | To find the loss percentage, we first calculate the loss amount and then find the percentage.
Cost price (CP) = Rs. 1340
Sold price (SP) = Rs. 1210
Loss = Cost price - Sold price
Loss = 1340 - 1210 = Rs. 230
Loss percentage = (Loss / Cost price) * 100
= (230 / 1340) * 100
= 17.65%
Rounding to the nearest whole numb... |
Solve the following multiple choice question.
Question:
a sum fetched a total simple interest of rs . 4016.25 at the rate of 3 % p . a . in 5 years . what is the sum ?
Options:
a ) 26775 , b ) 28772 , c ) 28821 , d ) 89255 , e ) 28871
Answer (choose one of a, b, c, d, e): | principal = ( 100 * 4016.25 ) / ( 3 * 5 ) = rs . 26775 . answer : a
Final answer: a | To find the principal amount, we can use the simple interest formula:
Simple Interest (SI) = (Principal * Rate * Time) / 100
Given:
SI = Rs. 4016.25
Rate (R) = 3%
Time (T) = 5 years
We need to find Principal (P):
R = SI / (P * R) = 4016.25 / (P * 3)
R = 4016.25 / P * 100
4016.25 / P = 401.625
P = 401.625 * 100 / 40... |
Solve the following multiple choice question.
Question:
if the simple interest on a sum of money for 3 years at 7 % per annum is rs . 570 , what is the compound interest on the same sum at the rate and for the same time ?
Options:
a ) rs . 610.83 , b ) rs . 810.83 , c ) rs . 617 , d ) rs . 618 , e ) rs . 610.83
Answ... | sum = ( 570 * 100 ) / ( 7 * 3 ) = rs . 2 , 714.29 amount = [ 2 , 714.29 * ( 1 + 7 / 100 ) 3 ] = rs . 3 , 325.12 c . i . = ( 3 , 325.12 - 2 , 714.29 ) = rs . 610.83 . answer : e
Final answer: e | To find the compound interest, we can use the formula:
Compound Interest (CI) = P * (1 + R/100)^n - P
Given values:
Principal (P) = Rs. 570
Rate (R) = 7%
Time (n) = 3 years
First, we need to find the Amount (A) first, which can be calculated using the simple interest formula:
Simple Interest (SI) = (P * R * T) / 10... |
Solve the following multiple choice question.
Question:
if the simple interest on a sum of money for 3 years at 7 % per annum is rs . 570 , what is the compound interest on the same sum at the rate and for the same time ?
Options:
a ) rs . 610.83 , b ) rs . 810.83 , c ) rs . 617 , d ) rs . 618 , e ) rs . 610.83
Answ... | sum = ( 570 * 100 ) / ( 7 * 3 ) = rs . 2 , 714.29 amount = [ 2 , 714.29 * ( 1 + 7 / 100 ) 3 ] = rs . 3 , 325.12 c . i . = ( 3 , 325.12 - 2 , 714.29 ) = rs . 610.83 . answer : e
Final answer: e | To find the compound interest on the same sum, we can use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A = the amount after t years
P = principal amount (initial sum)
r = rate of interest per year
n = number of times interest is compounded per year
t = time in years
Given data:
Principal (P) = Rs. ... |
Solve the following multiple choice question.
Question:
if the simple interest on a sum of money for 3 years at 7 % per annum is rs . 570 , what is the compound interest on the same sum at the rate and for the same time ?
Options:
a ) rs . 610.83 , b ) rs . 810.83 , c ) rs . 617 , d ) rs . 618 , e ) rs . 610.83
Answ... | sum = ( 570 * 100 ) / ( 7 * 3 ) = rs . 2 , 714.29 amount = [ 2 , 714.29 * ( 1 + 7 / 100 ) 3 ] = rs . 3 , 325.12 c . i . = ( 3 , 325.12 - 2 , 714.29 ) = rs . 610.83 . answer : e
Final answer: e | To find the compound interest on a sum of money, we use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = principal amount
r = rate of interest per annum
n = number of times interest is compounded per year
t = time in years
Given:
Principal (P) = ?
Rate (r) = 7%
Time (t) = 3 years
S... |
Solve the following multiple choice question.
Question:
simplify : 99 ^ 48 / 49 * 245 .
Options:
a ) 23345 , b ) 26695 , c ) 24495 , d ) 25575 , e ) none of them
Answer (choose one of a, b, c, d, e): | given expression = ( 100 - 1 / 49 ) * 245 = ( 4899 / 49 ) * 245 = 4899 * 5 = 24495 . answer is c .
Final answer: c | To simplify the expression, we need to follow the order of operations (PEMDAS):
1. Evaluate the exponents:
99 ^ 48 = 99^48 (since 48 is an even power, the result is positive)
2. Divide the fractions:
(99^48 * 245) / 49
3. Simplify the fraction:
99^48 = 99 * 99 * ... 48 times 49 times 245
= 9789700111 (this... |
Solve the following multiple choice question.
Question:
simplify : 99 ^ 48 / 49 * 245 .
Options:
a ) 23345 , b ) 26695 , c ) 24495 , d ) 25575 , e ) none of them
Answer (choose one of a, b, c, d, e): | given expression = ( 100 - 1 / 49 ) * 245 = ( 4899 / 49 ) * 245 = 4899 * 5 = 24495 . answer is c .
Final answer: c | To simplify the expression 99^48 / 49 * 245, we need to evaluate it step by step.
First, let's simplify 99^48.
Since 99 is equal to 81 + 18,
We can rewrite 99^48 as (81 + 18)^48
Using the Binomial Theorem,
(81 + 18)^48 = (81^48 + 48 * 81^47 * 18 + 24 * 81^46 * 18^2 + ...)
However, since 81 is a 3rd degree power, ... |
Solve the following multiple choice question.
Question:
simplify : 99 ^ 48 / 49 * 245 .
Options:
a ) 23345 , b ) 26695 , c ) 24495 , d ) 25575 , e ) none of them
Answer (choose one of a, b, c, d, e): | given expression = ( 100 - 1 / 49 ) * 245 = ( 4899 / 49 ) * 245 = 4899 * 5 = 24495 . answer is c .
Final answer: c | To simplify the given expression 99^48 / 49 * 245, we can start by simplifying the numerator and then looking for any common factors between the numerator and denominator.
First, we can simplify 99:
99 = 7 * 9^2
Then, we can rewrite the expression:
(7 * 9^2)^48 / 49 * 245
Next, we can simplify the denominator and ... |
Solve the following multiple choice question.
Question:
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... | 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 = k , leaving 1 m of empty space . thus , i believe the answer is b ) 1
Fin... | To maximize the number of desks and bookcases along the wall, we need to divide the total length of the wall (15 meters) by the sum of the lengths of a desk and a bookcase.
The length of a desk is 2 meters, and the length of a bookcase is 1.5 meters.
To maximize the number of desks and bookcases, we need to find the ... |
Solve the following multiple choice question.
Question:
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... | 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 = k , leaving 1 m of empty space . thus , i believe the answer is b ) 1
Fin... | To solve this problem, let's consider the lengths of the desk and bookcase and their positions.
Let's assume that there are 'x' number of desks and 'x' number of bookcases on the wall.
The total length of the desk or bookcase will be (2x + 1.5x) = 3.5x.
The length of the wall is 15 meters.
The number of desks or bo... |
Solve the following multiple choice question.
Question:
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... | 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 = k , leaving 1 m of empty space . thus , i believe the answer is b ) 1
Fin... | To find the maximum number of desks and bookcases that can be placed along the wall without any leftovers, we need to minimize the sum of the total length of the desk and the bookcase they occupy.
Let's assume we have a line of n desks and n bookcases. Each desk is 2 meters long and each bookcase is 1.5 meters long.
... |
Solve the following multiple choice question.
Question:
the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 55 sq . cm . find the length of the rectangle .
Options:
a ) 16 cm , b ) 18 cm , c ) 15 cm , d ) 20 c... | explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 55 = > 5 x - 25 = 55 = > x = 16 . length of the rectangle = 16 cm . answer : option a
Final answer: a | To solve this problem, let's first identify the variables and the relationship between the original and new dimensions of the rectangle.
Let's say the original length of the rectangle is L cm and the original breadth is B cm.
Given that the length is decreased by 5 cm and breadth is increased by 5 cm, the new length ... |
Solve the following multiple choice question.
Question:
the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 55 sq . cm . find the length of the rectangle .
Options:
a ) 16 cm , b ) 18 cm , c ) 15 cm , d ) 20 c... | explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 55 = > 5 x - 25 = 55 = > x = 16 . length of the rectangle = 16 cm . answer : option a
Final answer: a | Let's solve the problem step by step.
Let the length of the rectangle be L cm and the breadth be B cm.
According to the given options:
a) L = 16 cm and B = 5
b) L = 18 cm and B = 10
c) L = 15 cm and B = 15
d) L = 20 cm and B = 12
e) L = 23 cm and B = 8
The area of the rectangle is A = L × B.
Given that,
Area = ... |
Solve the following multiple choice question.
Question:
the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 55 sq . cm . find the length of the rectangle .
Options:
a ) 16 cm , b ) 18 cm , c ) 15 cm , d ) 20 c... | explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 55 = > 5 x - 25 = 55 = > x = 16 . length of the rectangle = 16 cm . answer : option a
Final answer: a | Let the breadth of the rectangle be x cm.
Since the length of the rectangle is twice its breadth (b1 = 2x).
Given that,
(new length - 5) + (breadth + 5) = Area
(2x - 5) + (x + 5) = Area
Area = 2x*x + x*x
Area = 3x^2
Initial Area = 2x * x
Initial Area = 2x^2
Difference = 3x^2 - 2x^2
Difference = x^2
Diff = 5... |
Solve the following multiple choice question.
Question:
jill has 42 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options:
a ) 3 , b ) 6 , c ) 9 , d ) 72 , e ) 14
Answer (choose one ... | let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 42 1 3 / 4 w = 42 w = 24 the total number of jars = 3 w = 72 answer : d
Final answer: d | To solve this problem, we need to determine how many quarts Jill has in each size jar. Since she has an equal number of each type of jar, let's say she has x jars of each size.
First, let's find the amount of water in each type of jar:
- 1 gallon jar holds 4 quarts
- Half-gallon jar holds 2 quarts
- Quart jar holds 1... |
Solve the following multiple choice question.
Question:
jill has 42 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options:
a ) 3 , b ) 6 , c ) 9 , d ) 72 , e ) 14
Answer (choose one ... | let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 42 1 3 / 4 w = 42 w = 24 the total number of jars = 3 w = 72 answer : d
Final answer: d | To find the total number of jars, we need to first convert the given quantities to a common denominator. 1 quart = 4 ounces and 1 half-gallon = 8 ounces.
42 gallons is equal to:
= (42 * 128) / (4 * 8)
= 5368 / 32
= 169 ounces
So the total number of jars = 168
Since the number of jars of each s... |
Solve the following multiple choice question.
Question:
jill has 42 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options:
a ) 3 , b ) 6 , c ) 9 , d ) 72 , e ) 14
Answer (choose one ... | let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 42 1 3 / 4 w = 42 w = 24 the total number of jars = 3 w = 72 answer : d
Final answer: d | To find the total number of jars, we need to divide the total gallons of water by the volume of each type of jar and round up to the nearest whole number since we can't use fractions of a jar.
So let's calculate the number of each type of jar first:
- Quart jars: 42 gallons / 1 quart = 42 jars
- Half-gallon jars: 42 ... |
Solve the following multiple choice question.
Question:
two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of rev... | same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 /... | To solve this problem, we need to calculate the circumference of both gears and then find their ratio.
The circumference of a circle is given by the formula: Circumference = π * diameter
Gear A: diameter = 10 cm
Circumference of Gear A = π * 10 cm = 10π cm
Gear B: diameter = 50 cm
Circumference of Gear B = π * 50 cm... |
Solve the following multiple choice question.
Question:
two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of rev... | same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 /... | To find the ratio of the number of revolutions that gear A makes per minute to the number of revolutions that gear B makes per minute, we first need to calculate the number of revolutions per minute for each gear.
The circumference of gear A is 10 cm, and gear B is 50 cm. Since they are connected, we need to find the ... |
Solve the following multiple choice question.
Question:
two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of rev... | same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 /... | To solve this problem, we need to find the relationship between the number of revolutions per minute for gear A and gear B.
Since both gears are interconnected, we can use the concept of circumferential velocity. The ratio of the circumferential velocity of the two gears is equal to the ratio of their diameters.
Let'... |
Solve the following multiple choice question.
Question:
the least number which when increased by 3 each divisible by each one of 24 , 32 , 36 and 54 is :
Options:
a ) 427 , b ) 859 , c ) 869 , d ) 861 , e ) none of these
Answer (choose one of a, b, c, d, e): | solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 3 = 864 - 3 = 861 . answer d
Final answer: d | To solve this question, we need to find the least common multiple (LCM) of 24, 32, 36, and 54, then add 3 to it.
To find the LCM of these numbers:
- First, let's break down the numbers into their prime factors:
24 = 2^3 * 3
32 = 2^5
36 = 2^2 * 3^2
54 = 2 * 3^3
Now, we take the highest power of each prime num... |
Solve the following multiple choice question.
Question:
the least number which when increased by 3 each divisible by each one of 24 , 32 , 36 and 54 is :
Options:
a ) 427 , b ) 859 , c ) 869 , d ) 861 , e ) none of these
Answer (choose one of a, b, c, d, e): | solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 3 = 864 - 3 = 861 . answer d
Final answer: d | To solve this problem, we need to find the least number that when increased by 3 each is divisible by 24, 32, 36, and 54.
First, we can factorize each number:
24 = 2^3 * 3
32 = 2^5
36 = 2^2 * 3^2
54 = 2 * 3^3
Let's find the Least Common Multiple (LCM) of these numbers, which is the smallest number that is divisible ... |
Solve the following multiple choice question.
Question:
the least number which when increased by 3 each divisible by each one of 24 , 32 , 36 and 54 is :
Options:
a ) 427 , b ) 859 , c ) 869 , d ) 861 , e ) none of these
Answer (choose one of a, b, c, d, e): | solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 3 = 864 - 3 = 861 . answer d
Final answer: d | To find the least number that is divisible by each of 24, 32, 36, and 54, let's first find the least common multiple (LCM) of these numbers.
The prime factorization of the given numbers are:
- 24 = 2^3 * 3
- 32 = 2^5
- 36 = 2^2 * 3^2
- 54 = 2 * 3^3
To find the LCM, we need to take the highest power of each prime fact... |
Solve the following multiple choice question.
Question:
1 / 0.06 is equal to
Options:
a ) 25.5 , b ) 16.7 , c ) 25 , d ) . 25 , e ) none of these
Answer (choose one of a, b, c, d, e): | explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b
Final answer: b | To solve this question, we need to divide 1 by 0.06.
1 / 0.06 = 1.1666667 ≈ 1.167
Rounding this down, we have 1.
Therefore, the correct answer is a) 25.5. |
Solve the following multiple choice question.
Question:
1 / 0.06 is equal to
Options:
a ) 25.5 , b ) 16.7 , c ) 25 , d ) . 25 , e ) none of these
Answer (choose one of a, b, c, d, e): | explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b
Final answer: b | To solve 1 / 0.06, we need to convert the divisor into a decimal, since the divisor is already in decimal form.
1/0.06 = 1 / (0.06)
To divide a fraction by a decimal, we can multiply the fraction by the reciprocal of the decimal.
1 / (0.06) = 1 * (1/0.06)
= (1 * 0.06) / 6
= 0.06 / 6
= 0.01
= 1/100
= 0.1
= 10 / 100
= ... |
Solve the following multiple choice question.
Question:
1 / 0.06 is equal to
Options:
a ) 25.5 , b ) 16.7 , c ) 25 , d ) . 25 , e ) none of these
Answer (choose one of a, b, c, d, e): | explanation : 1 / 0.06 = ( 1 * 100 ) / 6 = 100 / 6 = 16.7 option b
Final answer: b | To solve the given problem, let's convert 1/0.06 into decimal form.
First, we convert 0.06 to fraction form.
0.06 is the same as 6/100, which can be simplified to 3/50.
Now, we need to divide 1 by 3/50.
To divide by a fraction, we multiply by its reciprocal.
1 = 1 * (3/50)
1 * 50/3 = 50/3 = 16.67
Since 16.67 is ... |
Solve the following multiple choice question.
Question:
after giving a discount of rs . 100 the shopkeeper still gets a profit of 30 % , if the cost price is rs . 1000 . find the markup % ?
Options:
a ) . 50 , b ) . 45 , c ) . 40 , d ) . 48 , e ) . 52
Answer (choose one of a, b, c, d, e): | cost price = 1000 s . p = 1000 * 130 / 100 = 1300 disc = 100 so . . . mark price = 1300 + 100 = 1400 . . . . . . mark up % = 1400 - 1000 / 1000 = 400 / 1000 = . 40 ( or ) 40 % answer : c
Final answer: c | To find the markup percentage, let's break it down step by step.
Given:
Cost price (CP) = Rs. 1000
Discount = Rs. 100
Profit % = 30%
First, we calculate the selling price (SP) after the discount:
SP = CP - Discount
= 1000 - 100
= Rs. 900
The shopkeeper gets a profit of 30%, which means the profit is Rs. 100, and the... |
Solve the following multiple choice question.
Question:
after giving a discount of rs . 100 the shopkeeper still gets a profit of 30 % , if the cost price is rs . 1000 . find the markup % ?
Options:
a ) . 50 , b ) . 45 , c ) . 40 , d ) . 48 , e ) . 52
Answer (choose one of a, b, c, d, e): | cost price = 1000 s . p = 1000 * 130 / 100 = 1300 disc = 100 so . . . mark price = 1300 + 100 = 1400 . . . . . . mark up % = 1400 - 1000 / 1000 = 400 / 1000 = . 40 ( or ) 40 % answer : c
Final answer: c | To find the markup % , we first calculate the selling price (SP) after discount , and then the markup % .
Original price (CP) : Rs 1000
Discount : Rs 100
Discount Percentage : 30% of 1000 = 0.3 * 1000 = Rs 300
So, the selling price (SP) after discount = 1000 - 300 = Rs 700
Markup = Selling Price - Cost Price
... |
Solve the following multiple choice question.
Question:
after giving a discount of rs . 100 the shopkeeper still gets a profit of 30 % , if the cost price is rs . 1000 . find the markup % ?
Options:
a ) . 50 , b ) . 45 , c ) . 40 , d ) . 48 , e ) . 52
Answer (choose one of a, b, c, d, e): | cost price = 1000 s . p = 1000 * 130 / 100 = 1300 disc = 100 so . . . mark price = 1300 + 100 = 1400 . . . . . . mark up % = 1400 - 1000 / 1000 = 400 / 1000 = . 40 ( or ) 40 % answer : c
Final answer: c | To solve this problem, we can use the formula for finding the selling price (SP) and cost price (CP) after a discount. Given that:
- Cost Price (CP) = 1000
- Discount (D) = 100
Selling Price after discount (SP) = CP + D = 1000 + 100 = 1100
Profit percentage = (SP - CP) / CP * 100
= (1100 - 1000) / 1000 * 100
= 100 /... |
Solve the following multiple choice question.
Question:
from the sale of sleeping bags , a retailer made a gross profit of 14 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options:
a ) 3.0 , b ) 3.36 , c ) 24.56 , d ) 25.0 , e ) 31.36
Answer (choose one of a... | cost price * 1.14 = selling price - - > cost price * 1.14 = $ 28 - - > cost price = $ 24.56 . answer : c .
Final answer: c | To find the wholesale cost per bag, we need to set up an equation.
Let's say the wholesale cost is x. The revenue from the sale is 28 dollars. Since the retailer made a 14% profit, the profit is 14% of the wholesale cost.
Profit = Revenue - Wholesale Cost
Profit = 0.14x
28 = 0.14x
x = 28 / 0.14
x = 200
So, the who... |
Solve the following multiple choice question.
Question:
from the sale of sleeping bags , a retailer made a gross profit of 14 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options:
a ) 3.0 , b ) 3.36 , c ) 24.56 , d ) 25.0 , e ) 31.36
Answer (choose one of a... | cost price * 1.14 = selling price - - > cost price * 1.14 = $ 28 - - > cost price = $ 24.56 . answer : c .
Final answer: c | To find the wholesale cost per sleeping bag, we need to calculate the profit made on each bag and then divide it by the selling price.
Let's assume the wholesale cost per sleeping bag is W. The selling price is $28.
The profit percentage is 14%, so the profit made on each bag is 14% of W.
The formula for profit is:
... |
Solve the following multiple choice question.
Question:
from the sale of sleeping bags , a retailer made a gross profit of 14 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options:
a ) 3.0 , b ) 3.36 , c ) 24.56 , d ) 25.0 , e ) 31.36
Answer (choose one of a... | cost price * 1.14 = selling price - - > cost price * 1.14 = $ 28 - - > cost price = $ 24.56 . answer : c .
Final answer: c | To find the wholesale cost per sleeping bag, we need to reverse the 14% profit.
Let's assume the wholesale cost per sleeping bag is x.
The selling price is $28 and the profit is 14% of the wholesale cost, so we can set up the equation:
Selling price = Wholesale cost + Profit
28 = x + 0.14x
28 = 1.14x
Now, we can di... |
Solve the following multiple choice question.
Question:
a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options:
a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 %
Answer ... | the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e .
Final answer: e | To solve the problem, let's break it down step by step:
Initial solution volume: 90 liters
Initial jasmine concentration: 5%
Initial jasmine volume: 5% of 90 liters = 0.05 x 90 = 4.5 liters
After adding 6.5 liters of jasmine, total jasmine volume: 4.5 + 6.5 = 11 liters
Total solution volume after adding jasmine: 90 ... |
Solve the following multiple choice question.
Question:
a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options:
a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 %
Answer ... | the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e .
Final answer: e | To find the percentage of jasmine in the solution after adding 6.5 liters of jasmine and 13.5 liters of water, we need to calculate the total amount of jasmine and the total volume of the solution after the addition.
Initial jasmine = 90 liters
Initial volume = 90 liters
6.5 liters of jasmine is added, so we need to ... |
Solve the following multiple choice question.
Question:
a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options:
a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 %
Answer ... | the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e .
Final answer: e | Let's calculate the total volume of the solution after adding jasmine and water:
- Initial solution: 90 liters
- Jasmine water added: 6.5 liters
- Total solution after adding jasmine and water: 90 + 6.5 = 96.5 liters
Now, let's calculate the percentage of jasmine in the solution:
Percentage of jasmine = (amount of j... |
Solve the following multiple choice question.
Question:
denominator of a number is 4 less than the numerator . if 6 is added to the numerator , it becomes 3 times the denominator . find the denominator .
Options:
a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Answer (choose one of a, b, c, d, e): | let the numerator be x and denominator be y . then = > x = y + 4 and 6 + x = 3 * y = > 6 + y + 4 = 3 * y = > 2 y = 10 = > y = 5 option c
Final answer: c | To solve this problem, let's call the numerator 'x' and the denominator 'y'. We are given that the denominator is 4 less than the numerator, so we can write:
y = x - 4
We are also given that if 6 is added to the numerator, it becomes 3 times the denominator:
x + 6 = 3y
We can substitute the value of y from the firs... |
Solve the following multiple choice question.
Question:
denominator of a number is 4 less than the numerator . if 6 is added to the numerator , it becomes 3 times the denominator . find the denominator .
Options:
a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Answer (choose one of a, b, c, d, e): | let the numerator be x and denominator be y . then = > x = y + 4 and 6 + x = 3 * y = > 6 + y + 4 = 3 * y = > 2 y = 10 = > y = 5 option c
Final answer: c | To solve this problem, let's represent the numerator as N and the denominator as D.
1) N = D + 4 ... (Equation 1)
2) N + 6 = 3(D) ... (Equation 2)
From Equation 1, we can rewrite N as N = D + 4.
Substitute N in Equation 2:
D + 4 + 6 = 3D
3D + 10 = 3D
Subtract 3D from both sides:
10 = 2D
D = 10/2
D = 5
Therefore, ... |
Solve the following multiple choice question.
Question:
denominator of a number is 4 less than the numerator . if 6 is added to the numerator , it becomes 3 times the denominator . find the denominator .
Options:
a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Answer (choose one of a, b, c, d, e): | let the numerator be x and denominator be y . then = > x = y + 4 and 6 + x = 3 * y = > 6 + y + 4 = 3 * y = > 2 y = 10 = > y = 5 option c
Final answer: c | To solve this problem, let's denote the numerator as x. According to the information given:
- The denominator is 4 less than the numerator, so the denominator can be written as x - 4.
- Adding 6 to the numerator gives 3 times the denominator, so we have: x + 6 = 3(x - 4).
We can now solve for x:
x + 6 = 3x - 12
x - 3... |
Solve the following multiple choice question.
Question:
if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ?
Options:
a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d... | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Final answer: b | To solve this problem, we need to first calculate the probability of getting tails on the first 2 flips and not on the last 3 flips.
The probability of getting tails on a single coin flip is 1/2, so the probability of getting tails on the first 2 flips is (1/2) × (1/2) = 1/4.
The probability of not getting tails on a... |
Solve the following multiple choice question.
Question:
if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ?
Options:
a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d... | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Final answer: b | To solve this, we need to use the concept of complementary probability.
The probability that the coin will land tails on the first two flips is (1/2) x (1/2) = 1/4.
For the last three flips, we are considering a sequence of three flips, out of 5 total flips. We need to find the probability of the sequence TFSS. The... |
Solve the following multiple choice question.
Question:
if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ?
Options:
a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d... | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Final answer: b | To solve this problem, we need to calculate the probability of getting tails up on the first 2 flips and not on the last 3 flips.
The probability of getting tails on a single flip is 1/2. Since we want to calculate the probability of getting tails on 2 out of 5 flips, we can use the binomial probability formula:
P(2 ... |
Solve the following multiple choice question.
Question:
how many digits are in ( 8 × 10 ^ 14 ) ( 10 × 10 ^ 10 ) ?
Options:
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Answer (choose one of a, b, c, d, e): | he question simplifies to ( 8 × 10 ^ 14 ) ( 10 ^ 11 ) = > 8 * 10 ^ 25 = > will contain 25 zeros + 1 digit 8 = > 26 ans c
Final answer: c | To solve this problem, we need to first simplify the given expression.
( 8 × 10 ^ 14 ) ( 10 × 10 ^ 10 ) = ( 8 × ( 10 ^ 14 ) ) × ( 10 ^ 10 )
First, multiply the numbers, 8 and 10 (which are the same).
8 × 10 = 80
Now multiply 80 by the remaining exponent (14) and 10^10.
The multiplication gives us:
80 × ( 10 ^ 14 ) ... |
Solve the following multiple choice question.
Question:
how many digits are in ( 8 × 10 ^ 14 ) ( 10 × 10 ^ 10 ) ?
Options:
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Answer (choose one of a, b, c, d, e): | he question simplifies to ( 8 × 10 ^ 14 ) ( 10 ^ 11 ) = > 8 * 10 ^ 25 = > will contain 25 zeros + 1 digit 8 = > 26 ans c
Final answer: c | To solve this, let's break it down step by step:
First, calculate the value of 10^14.
10^14 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
= 10^15
Now, multiply the two values:
8 × 10^14 × 10 × 10^10
= 8 × (10 × 10^14)
= 80 × 10^14
= 80000000000
This is a 19-digit number.
However, mu... |
Solve the following multiple choice question.
Question:
how many digits are in ( 8 × 10 ^ 14 ) ( 10 × 10 ^ 10 ) ?
Options:
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Answer (choose one of a, b, c, d, e): | he question simplifies to ( 8 × 10 ^ 14 ) ( 10 ^ 11 ) = > 8 * 10 ^ 25 = > will contain 25 zeros + 1 digit 8 = > 26 ans c
Final answer: c | To solve this, we will multiply the numbers 8 and 10^14 and 10 times 10^10, then count the digits.
Step 1:
Multiplying 8 and 10^14
First, convert 10^14 into a number (a number made of 1 followed by 14 zeroes)
10^14 = 1 followed by 14 zeroes
8 * 1 = 8
8 * 0 = 0
Step 2:
Next, multiply 10 and 10^10
10 * 1 = 10
10 * ... |
Solve the following multiple choice question.
Question:
on the xy - coordinate plane , point a lies on the y - axis and point b lies on the x - axis . points a , b , and c form a right triangle with a 90 - degree angle at point c and the triangle has an area of 20 . if ac is parallel to the x - axis , and bc is parall... | the area of the triangle formed will be : 1 / 2 * base * height = 1 / 2 * | ( x - coordinate of point c ) | * | ( y - coordinate of point c ) | = 20 thus | product of coordinates of point c | = 40 the answer is d .
Final answer: d | To find the coordinates of point C, we can use the formula for the area of a right triangle:
Area = (1/2) × base × height
In this case, we're given that the base is AC (which is parallel to the x-axis) and the height is BC. The area of the triangle is given as 20.
We know that BC is parallel to the y-axis, so the h... |
Solve the following multiple choice question.
Question:
on the xy - coordinate plane , point a lies on the y - axis and point b lies on the x - axis . points a , b , and c form a right triangle with a 90 - degree angle at point c and the triangle has an area of 20 . if ac is parallel to the x - axis , and bc is parall... | the area of the triangle formed will be : 1 / 2 * base * height = 1 / 2 * | ( x - coordinate of point c ) | * | ( y - coordinate of point c ) | = 20 thus | product of coordinates of point c | = 40 the answer is d .
Final answer: d | To solve this problem, we need to find the possible coordinates of point C, given that the area of triangle ABC is 20. Let's break it down step by step:
Given information:
- Point A lies on the y-axis (0,0).
- Point B lies on the x-axis (x,0).
- Point C forms a right triangle with points A and B, and the right angle i... |
Solve the following multiple choice question.
Question:
on the xy - coordinate plane , point a lies on the y - axis and point b lies on the x - axis . points a , b , and c form a right triangle with a 90 - degree angle at point c and the triangle has an area of 20 . if ac is parallel to the x - axis , and bc is parall... | the area of the triangle formed will be : 1 / 2 * base * height = 1 / 2 * | ( x - coordinate of point c ) | * | ( y - coordinate of point c ) | = 20 thus | product of coordinates of point c | = 40 the answer is d .
Final answer: d | To solve this problem, let's analyze the information given:
- Point A lies on the y-axis.
- Point B lies on the x-axis.
- Points A, B, and C form a right triangle with a 90-degree angle at point C.
- AC is parallel to the x-axis, meaning AC is horizontal.
- BC is parallel to the y-axis, meaning BC is vertical.
From t... |
Solve the following multiple choice question.
Question:
when 242 is divided by a certain divisor the remainder obtained is 4 . when 698 is divided by the same divisor the remainder obtained is 8 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 7 . what is th... | let that divisor be x since remainder is 4 or 8 it means divisor is greater than 8 . now 242 - 4 = 238 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 8 = 690 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 238 + 690 ) + 4 + 8 = x ( k + l ) + 12 when we divide this numbe... | To solve this problem, let's first list the given information in the form of equations:
1. 242 / x + 4 = 1
2. 698 / x + 8 = 1
3. 242 + 698 / x = 7
From equation 1, 242 = x + 4
From equation 2, 698 = x + 8
Subtract 698 from both sides of both equations and get
242 - 698 = x - 4
-456 = x - 4
452 = x
Add 4 to bo... |
Solve the following multiple choice question.
Question:
when 242 is divided by a certain divisor the remainder obtained is 4 . when 698 is divided by the same divisor the remainder obtained is 8 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 7 . what is th... | let that divisor be x since remainder is 4 or 8 it means divisor is greater than 8 . now 242 - 4 = 238 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 8 = 690 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 238 + 690 ) + 4 + 8 = x ( k + l ) + 12 when we divide this numbe... | To solve this, we'll use the approach of subtracting the remainders.
Given:
- When 242 is divided by x, the remainder is 4, so 242 = q1x + 4.
- When 698 is divided by x, the remainder is 8, so 698 = q2x + 8.
- When the sum of 242 and 698 is divided by x, the remainder is 7, so 1210 = q3x + 7.
Now, we'll subtract 242 ... |
Solve the following multiple choice question.
Question:
when 242 is divided by a certain divisor the remainder obtained is 4 . when 698 is divided by the same divisor the remainder obtained is 8 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 7 . what is th... | let that divisor be x since remainder is 4 or 8 it means divisor is greater than 8 . now 242 - 4 = 238 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 8 = 690 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 238 + 690 ) + 4 + 8 = x ( k + l ) + 12 when we divide this numbe... | Let's analyze the situation:
1. When 242 is divided by the divisor, the remainder is 4. This implies that 242 = aD + 4, where D is the divisor.
2. When 698 is divided by the divisor, the remainder is 8. This implies that 698 = aE + 8, where E is the divisor.
3. The sum of the two numbers 242 and 698 is 940. When 940 i... |
Solve the following multiple choice question.
Question:
a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ?
Options:
a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500
Answer (choose one of a, b, c, d, e): | 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b
Final answer: b | To solve this problem, we first need to calculate the total votes cast.
We know that the candidate got 35% of the votes and lost by 1800 votes.
35% of total votes = 1800
Now, we need to find the total votes cast.
Let the total votes be T. So,
35% of T = 1800
To solve for T, we convert 35% to a decimal:
35/100 ... |
Solve the following multiple choice question.
Question:
a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ?
Options:
a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500
Answer (choose one of a, b, c, d, e): | 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b
Final answer: b | To solve this problem, we need to find out the total votes cast. We know that a candidate got 35% of the votes and lost by 1800 votes to the rival.
Let's assume that total votes = x.
Since the candidate got 35% of the votes, the opponent got 65% of the votes (since a defeated by 1800 votes).
0.35x = 65% of x - 1800... |
Solve the following multiple choice question.
Question:
a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ?
Options:
a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500
Answer (choose one of a, b, c, d, e): | 35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b
Final answer: b | To solve this problem, we need to set up an equation based on the given information. Let's say the total number of voters is V.
Since the candidate got 35% of the votes, the candidate's votes = 0.35V.
The candidate lost by 1800 votes to the rival, so the number of votes the rival received is 0.35V + 1800.
Since the ... |
Solve the following multiple choice question.
Question:
a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 40 % more recliners . what is the percentage increase of the gross ?
Options:
a ) 10 % , b ) 15 % , c ) 11.2 % , d ) 7 % , e ) 13 %
... | say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 40 % more ie . , 140 recliners hence her sales tields 140 * 80 = $ 11200 increase in sales = 11200 - 10000 = $ 1120 so % increase = 1120 * 100 / 10000 = 11.... | To solve this problem, let's first calculate the price of the original recliner and then determine the new price after a 20% drop and an additional 40% increase.
1. The original price of a recliner is 100%.
2. If the price drops by 20%, the new price becomes:
New price = Original price - (20% of Original price)
= 100 ... |
Solve the following multiple choice question.
Question:
a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 40 % more recliners . what is the percentage increase of the gross ?
Options:
a ) 10 % , b ) 15 % , c ) 11.2 % , d ) 7 % , e ) 13 %
... | say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 40 % more ie . , 140 recliners hence her sales tields 140 * 80 = $ 11200 increase in sales = 11200 - 10000 = $ 1120 so % increase = 1120 * 100 / 10000 = 11.... | To solve this problem, we need to first calculate the decrease in price and then find the percentage increase in sales.
Initially, the store owner sold 40% fewer recliners, so let's assume she sold x number of recliners. The decreased number of recliners is 0.6x (40% fewer).
We are also given that the store owner dro... |
Solve the following multiple choice question.
Question:
a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 40 % more recliners . what is the percentage increase of the gross ?
Options:
a ) 10 % , b ) 15 % , c ) 11.2 % , d ) 7 % , e ) 13 %
... | say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 40 % more ie . , 140 recliners hence her sales tields 140 * 80 = $ 11200 increase in sales = 11200 - 10000 = $ 1120 so % increase = 1120 * 100 / 10000 = 11.... | To solve this problem, let's assume the original price of the recliner was $100.
The price was dropped by 20%, so the new price is:
$100 - 20% of $100 = $100 - $20 = $80
By the end of the week, 40% more recliners were sold. 40% of 40 recliners is:
40% of $40 = 0.4 x $40 = $16
The new revenue from the sales is:
$100 ... |
Solve the following multiple choice question.
Question:
what is the minimum percentage increase in the mean of set s { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?
Options:
a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %
Answer (choose one of a, b, c, d, e): | mean of s is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of s , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( ... | To find the minimum percentage increase in the mean of the set, we need to first calculate the mean of the original set.
The original set is: -4, -1, 0, 6, 9
Mean = (−4 + −1 + 0 + 6 + 9)/5
Mean = 10/5
Mean = 2
Now, if the two smallest elements (-4 and -1) are replaced with different primes:
Two smallest elements w... |
Solve the following multiple choice question.
Question:
what is the minimum percentage increase in the mean of set s { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?
Options:
a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %
Answer (choose one of a, b, c, d, e): | mean of s is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of s , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( ... | To find the minimum percentage increase in the mean, we first need to find the original mean and the new set of numbers with the two smallest elements replaced.
The original set is { - 4 , - 1 , 0 , 6 , 9 }
1. Replace -1 with the smallest prime number which is 2
The set becomes { - 4 , 2 , 0 , 6 , 9 }
2. Replace ... |
Solve the following multiple choice question.
Question:
what is the minimum percentage increase in the mean of set s { - 4 , - 1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes ?
Options:
a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 200 %
Answer (choose one of a, b, c, d, e): | mean of s is ( - 4 - 1 + 0 + 6 + 9 ) / 5 = 2 ; in order the increase to be minimal we should replace two smallest elements of s , which are - 4 and - 1 , with two smallest primes , which are 2 and 3 . hence our new set will be { 2 , 3 , 0 , 6 , 9 } - - > new mean is ( 2 + 3 + 0 + 6 + 9 ) / 5 = 4 . percent increase = ( ... | To find the minimum percentage increase in the mean of the set { -4 , -1 , 0 , 6 , 9 } if its two smallest elements are replaced with two different primes, we first need to find the mean of the original set.
The mean of the original set is ( -4 + -1 + 0 + 6 + 9 ) / 5 = 10 / 5 = 2
Next, we need to replace the two smal... |
Solve the following multiple choice question.
Question:
if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 2 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in nove... | n = 2 d / 5 j = n / 2 = d / 5 the average of november and january is ( n + j ) / 2 = 3 d / 5 / 2 = 3 d / 10 d is 10 / 3 times the average of november and january . the answer is c .
Final answer: c | To find the average revenue of November and January, we need to find the product of their revenues and divide it by 2.
Let's say the revenue in November is 'x'. Then the revenue in January is 2x/5 and the revenue in December is 2/5x.
Now, the average revenue of November and January:
(x + 2x/5 + 2/5x) / 2 = (1 + 3x/5... |
Solve the following multiple choice question.
Question:
if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 2 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in nove... | n = 2 d / 5 j = n / 2 = d / 5 the average of november and january is ( n + j ) / 2 = 3 d / 5 / 2 = 3 d / 10 d is 10 / 3 times the average of november and january . the answer is c .
Final answer: c | To find the average of revenues in November and January, first find the revenues for both months.
In November, revenue is 2/5 of December revenue.
Let's call the revenue in December 'D'.
We can set up the equation:
D / 5 = 2D / 5
D = 2D
D = 2D / 1
D = 2D / 2
D = D / 1
D - D = 0
0 = D
This means the store didn't s... |
Solve the following multiple choice question.
Question:
a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options:
a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 %
Answer (choose one of a, b, c, d, e): | number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e
Final answer: e | To find the percentage of runs scored by running between the wickets, we first need to subtract the runs scored by boundaries and sixes from the total runs.
Runs scored by boundaries = 3 * 6 = 18
Runs scored by sixes = 8 * 6 = 48
Total runs scored = 110
Runs scored by running = 110 - 18 - 48 = 44
Now, we can calcula... |
Solve the following multiple choice question.
Question:
a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options:
a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 %
Answer (choose one of a, b, c, d, e): | number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e
Final answer: e | To find the percent of the runs scored by running, we need to divide the runs scored by running by the total runs, then multiply by 100.
Runs scored by running: 110 - (3 boundaries + 8 sixes) = 110 - 11 = 99 runs.
Percent of runs scored by running: (99 / 110) * 100 = 89.09%
Among the given options, the closest to th... |
Solve the following multiple choice question.
Question:
a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options:
a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 %
Answer (choose one of a, b, c, d, e): | number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e
Final answer: e | To find the percentage of runs scored by running, we need to calculate the runs scored by running and then divide it by the total runs scored.
Assuming 1 run = 4 balls
- 3 boundaries scored = 3 * 4 = 12 runs
- 8 sixes scored = 8 * 6 = 48 runs
Total runs scored by running = 12 + 48 = 60 runs
Total runs scored by bats... |
Solve the following multiple choice question.
Question:
if the sales tax be reduced from 3 ( 1 / 5 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 6400 ?
Options:
a ) rs . 150.40 , b ) rs . 44.80 , c ) rs . 140.40 , d ) rs . 50.48 , e ) none of these
... | explanation : required difference = ( 3 ( 1 / 5 ) of rs . 6400 ) - ( 2 ( 1 / 2 ) of rs . 6400 ) = ( 16 / 5 – 5 / 2 ) % of rs . 6400 = ( 7 / 10 ) x ( 1 / 100 ) x 6400 = rs . 44.80 answer b
Final answer: b | To find the difference, we first find the original amount and the new amount after the discount.
1. Original amount: 6400
2. Discount amount:
- When 3 ( 1 / 5 ) % of 6400 is calculated: 1.2071
- When 2 ( 1 / 2 ) % is applied, we can find it in two ways:
- First, find the total discount as a fraction of th... |
Solve the following multiple choice question.
Question:
if the sales tax be reduced from 3 ( 1 / 5 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 6400 ?
Options:
a ) rs . 150.40 , b ) rs . 44.80 , c ) rs . 140.40 , d ) rs . 50.48 , e ) none of these
... | explanation : required difference = ( 3 ( 1 / 5 ) of rs . 6400 ) - ( 2 ( 1 / 2 ) of rs . 6400 ) = ( 16 / 5 – 5 / 2 ) % of rs . 6400 = ( 7 / 10 ) x ( 1 / 100 ) x 6400 = rs . 44.80 answer b
Final answer: b | To find the difference, let's calculate the amount of sales tax and the final amount.
Initial price = Rs. 6400
Tax rate = 3 (1/5) % = 0.6%
Tax amount = 0.6% of 6400 = (0.6 / 100) * 6400 = Rs. 384
Now, new tax rate = 2 (1/2) % = 1% = 0.01
Tax amount = 0.01 of 6400 = (0.01 / 100) * 6400 = Rs. 64
Final amount = Initial... |
Solve the following multiple choice question.
Question:
if the sales tax be reduced from 3 ( 1 / 5 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 6400 ?
Options:
a ) rs . 150.40 , b ) rs . 44.80 , c ) rs . 140.40 , d ) rs . 50.48 , e ) none of these
... | explanation : required difference = ( 3 ( 1 / 5 ) of rs . 6400 ) - ( 2 ( 1 / 2 ) of rs . 6400 ) = ( 16 / 5 – 5 / 2 ) % of rs . 6400 = ( 7 / 10 ) x ( 1 / 100 ) x 6400 = rs . 44.80 answer b
Final answer: b | To calculate the difference, we need to find the amount of tax at the old and new rates and subtract the two amounts.
Old tax rate = 3 (1/5) = 3 * 0.2 = 0.6
New tax rate = 2 (1/2) = 1.5
Original amount = Marked price = Rs 6400
Tax at old rate = 0.6 * 6400 = Rs 3840
Tax at new rate = 1.5 * 6400 = Rs 9600
Difference = ... |
Solve the following multiple choice question.
Question:
there are 6 people in the elevator . their average weight is 156 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options:
a ) 121 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Answer (ch... | solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 156 ) = 1057 - 936 = 121 . answer a
Final answer: a | To find the weight of the 7th person, let's first calculate the total weight of the 6 people:
6 * 156 = 936 lbs
After the 7th person enters, the total number of people becomes 7.
The average weight of the 7 people is given as 151 lbs. Let's set up an equation:
Total weight of 7 people = 7 * 151
Multiply the averag... |
Solve the following multiple choice question.
Question:
two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling... | a 54 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 54 miles
Final answer: a | To solve this problem, let's calculate the distance the friends travel towards each other before the pigeon joins in, and the total distance traveled by the pigeon.
Let's call the speed of the friends' bikes 'F', the speed of the pigeon's 'P', and the distance between them 'D'. They are traveling towards each other at... |
Solve the following multiple choice question.
Question:
two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling... | a 54 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 18 mph = 54 miles
Final answer: a | To solve this problem, let's break it down step by step:
1. The friends travel a total of 36 miles apart. Since they are traveling towards each other, the total distance they cover together is the sum of the distances traveled by both of them. Let's call the distance covered by one friend x. We have the equation x + 6... |
Solve the following multiple choice question.
Question:
a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options:
a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59
Answer (choose one of a, b, c, d, e): | let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c
Final answer: c | To solve this problem, we need to first calculate the total runs scored by the batsman up to 16 innings, and then calculate his average after 17 innings.
Total runs scored by the batsman up to 16 innings = 16 * 83 = 1332
New average after 17 innings = (Total runs + 1332) / 17 = (1332 + 17) / 17 = 1359 / 17 = 79.47
S... |
Solve the following multiple choice question.
Question:
a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options:
a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59
Answer (choose one of a, b, c, d, e): | let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c
Final answer: c | To find the average after the 17th inning, let's first find the total score before the 17th inning. Let's denote the runs scored in the first 16 innings as 'x'. So, the total runs scored before the 17th inning is x + 83.
The average before the 17th inning is x/16.
We know that the average is the total score divided b... |
Solve the following multiple choice question.
Question:
a batsman makes a score of 83 runs in the 17 th inning and thus increases his averages by 3 . find his average after 17 th inning ?
Options:
a ) 19 , b ) 29 , c ) 35 , d ) 49 , e ) 59
Answer (choose one of a, b, c, d, e): | let the average after 17 th inning = x then average after 16 th inning = ( x - 3 ) therefore 16 ( x - 3 ) + 83 = 17 x therefore x = 35 answer : c
Final answer: c | To solve this question, let's first calculate the total runs before the 17th inning.
Let's assume the total runs before the 17th inning is x.
The total runs after 16 innings is x + 83.
The average increase is 3, so the total runs after 17 innings is the average increase + the initial total runs:
x + 83 = 3(x + 16)... |
Solve the following multiple choice question.
Question:
calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days ,
Options:
a ) 6 days , b ) 3 days , c ) 4 days , d ) 2 days , e ) 5 days
Answer (choose one of a, b, c, d, e): | the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c
Final answer: c | To find the number of days required for 7 boys to wash a 35 m long wall, we can follow these steps:
1. Calculate the rate at which the boys work together.
2. Use the rate to calculate how long it will take to complete the wall.
Rate at which 5 boys can wash a 25 m long wall = 1/4 days (since 5 boys can complete a 25 ... |
Solve the following multiple choice question.
Question:
calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days ,
Options:
a ) 6 days , b ) 3 days , c ) 4 days , d ) 2 days , e ) 5 days
Answer (choose one of a, b, c, d, e): | the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c
Final answer: c | To calculate the number of days it will take for 7 boys to wash a 35 m long wall, we need to determine how many boys can be washed in one day.
We know that 5 boys can wash a 25 m long wall in 4 days.
First, let's calculate how many boys can wash 1 m in a day:
5 boys / 25 m = 0.2 boys per minute
0.2 boys per minute *... |
Solve the following multiple choice question.
Question:
calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days ,
Options:
a ) 6 days , b ) 3 days , c ) 4 days , d ) 2 days , e ) 5 days
Answer (choose one of a, b, c, d, e): | the length of wall painted by one boy in one day = 25 / 5 * 1 / 4 = 1.25 m no . of days required to paint 50 m cloth by 8 boys = 35 / 7 * 1 / 1.25 = 4 days . c
Final answer: c | To find the number of days needed to wash a 35m long wall, we can use the ratio of work done by each boy to the length of the wall.
First, let's find the work rate of each boy.
We know that 5 boys can wash a 25m long wall in 4 days, so the work rate is:
5 boys / 4 days = 1.25 boys per day
Now, we want to find the nu... |
Solve the following multiple choice question.
Question:
because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 2 times as much as mork did , what was their combined tax rate ?
Options:
a ) 32.5 % , b ) 34 % , c ) 22.5 % , d... | say morks income is - 100 so tax paid will be 40 say mindys income is 2 * 100 = 200 so tax paid is 30 % * 200 = 60 total tax paid = 40 + 60 = 100 . combined tax % will be 100 / 100 + 200 = 33.3 %
Final answer: d | To solve this problem, let's assume Mork's income as 'M' and Mindy's income as '2M'.
Mork's tax rate is 40%, so the amount of tax he paid = 40% of Mork's income = 0.4M
Mindy's tax rate is 30%, so the amount of tax she paid = 30% of 2M = 0.6M
Combined income = 2M (Mork's) + 2M (Mindy's) = 4M
Combined tax paid = 0.4M ... |
Solve the following multiple choice question.
Question:
because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 2 times as much as mork did , what was their combined tax rate ?
Options:
a ) 32.5 % , b ) 34 % , c ) 22.5 % , d... | say morks income is - 100 so tax paid will be 40 say mindys income is 2 * 100 = 200 so tax paid is 30 % * 200 = 60 total tax paid = 40 + 60 = 100 . combined tax % will be 100 / 100 + 200 = 33.3 %
Final answer: d | To solve this problem, let's assume Mork's income is M and Mindy's income is 2M.
Mork pays a tax rate of 40% on his income, which means he pays 0.4M.
Mindy pays a tax rate of 30% on her income, which means she pays 0.3M.
The combined tax paid by Mindy is 0.3M + 0.3(2M) = 0.6M
To find the combined tax rate, divide th... |
Solve the following multiple choice question.
Question:
because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 2 times as much as mork did , what was their combined tax rate ?
Options:
a ) 32.5 % , b ) 34 % , c ) 22.5 % , d... | say morks income is - 100 so tax paid will be 40 say mindys income is 2 * 100 = 200 so tax paid is 30 % * 200 = 60 total tax paid = 40 + 60 = 100 . combined tax % will be 100 / 100 + 200 = 33.3 %
Final answer: d | To find the combined tax rate, we need to calculate the income of both individuals and their respective tax rates.
Let's assume Mork's income is x. Since Mindy earned 2 times as much as Mork, Mindy's income is 2x.
Tax paid by Mork = 0.4x
Tax paid by Mindy = 0.3(2x) = 0.6x
Combined tax paid = Tax paid by Mork + Tax p... |
Solve the following multiple choice question.
Question:
the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ?
Options:
a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ... | let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b
Final answer: b | To solve this problem, we need to find the area of the floor. We can start by using the given information to find the area in terms of the breadth.
Let's denote the breadth as x. Since the length is 200% more than the breadth, it can be represented as 1.2x.
The area of the floor (A) can be calculated using the formul... |
Solve the following multiple choice question.
Question:
the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ?
Options:
a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ... | let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b
Final answer: b | To solve this problem, we need to find the length of the floor first.
Let the breadth of the floor be x m.
Given that the length is 200% more than the breadth, we can write:
Length = x + 200% of x
Length = x + 2x
Length = 3x
Also, the cost of painting is given as Rs. 624 at the rate of Rs. 4 per sq m.
Area of the ... |
Solve the following multiple choice question.
Question:
the length of a rectangular floor is more than its breadth by 200 % . if rs . 624 is required to paint the floor at the rate of rs . 4 per sq m , then what would be the length of the floor ?
Options:
a ) 22.8 m . , b ) 21.6 m . , c ) 21.1 m . , d ) 20.6 m . , e ... | let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 624 / 4 = 156 sq m l b = 156 i . e . , l * l / 3 = 156 l 2 = 468 = > l = 21.6 m . answer : b
Final answer: b | To solve this question, let's use the formula for the area of a rectangle:
Area = Length x Breadth
Since the length is more than the breadth by 200%, we can write:
Length = Breadth + 200% of Breadth
= Breadth + (200/100) x Breadth
= Breadth + 0.2x Breadth
= 1.2x Breadth
The cost of painting the floor is Rs. 624, an... |
Solve the following multiple choice question.
Question:
in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , - 8 ) . what is the least possible value of the slope of line l ?
Options:
a ) - 6.5 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 10
Answer (choose one of a, b, c, d, e)... | we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 8 ) should satisfy the equation . hence x = t and y = - 8 . - 7 = - t 2 + 9 t = + or -... | To find the slope of line L, we need to use the coordinates of the intersection points (p, 5) and (t, -8). The slope formula is (y2 - y1)/(x2 - x1).
Given that the coordinates of these two points are (p, 5) and (t, -8).
Using the coordinates of these two points, the slope is:
(-8 - 5)/(t - p)
Since we need the least... |
Solve the following multiple choice question.
Question:
in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , - 8 ) . what is the least possible value of the slope of line l ?
Options:
a ) - 6.5 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 10
Answer (choose one of a, b, c, d, e)... | we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 8 ) should satisfy the equation . hence x = t and y = - 8 . - 7 = - t 2 + 9 t = + or -... | To find the least possible slope of the line l, we need to use the coordinates of the two intersection points.
The slope of the line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).
So, the slope of the line l at points (p, 5) and (t, -8) is:
( -8 - 5 ) / ( t - p )
= - 3 / ( t - p... |
Solve the following multiple choice question.
Question:
in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , 5 ) and ( t , - 8 ) . what is the least possible value of the slope of line l ?
Options:
a ) - 6.5 , b ) 2 , c ) - 2 , d ) - 6 , e ) - 10
Answer (choose one of a, b, c, d, e)... | we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 8 ) should satisfy the equation . hence x = t and y = - 8 . - 7 = - t 2 + 9 t = + or -... | To find the slope of line l, we first need to find the coordinates of the slope.
We have two points: (p, 5) and (t, -8). To find the slope, we use the formula:
m = (y2 - y1) / (x2 - x1)
m = (-8 - 5) / (t - p)
m = -13 / (t - p)
We also know that the line intersects the y-axis at p, so (0, p) is another point on th... |
Solve the following multiple choice question.
Question:
106 x 106 - 94 x 94 = ?
Options:
a ) 2400 , b ) 2000 , c ) 1904 , d ) 1906 , e ) none of them
Answer (choose one of a, b, c, d, e): | = ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a
Final answer: a | To solve the equation, we first calculate:
106 x 106 = 11236
94 x 94 = 8836
Now subtract 8836 from 11236:
11236 - 8836 = 2420
Since 2420 is between 2000 and 2400, and not 1904 or 1906, the answer is:
b) 2000 |
Solve the following multiple choice question.
Question:
106 x 106 - 94 x 94 = ?
Options:
a ) 2400 , b ) 2000 , c ) 1904 , d ) 1906 , e ) none of them
Answer (choose one of a, b, c, d, e): | = ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a
Final answer: a | To solve this problem, we can use the properties of multiplication and subtraction:
(106 x 106) = 11020
(94 x 94) = 8836
Then subtract 8836 from 11020:
11020 - 8836 = 2064
The correct answer is:
c ) 1904 |
Solve the following multiple choice question.
Question:
106 x 106 - 94 x 94 = ?
Options:
a ) 2400 , b ) 2000 , c ) 1904 , d ) 1906 , e ) none of them
Answer (choose one of a, b, c, d, e): | = ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a
Final answer: a | To solve this question, we need to calculate the values of 106 x 106 and 94 x 94, and then subtract the second result from the first.
First, let's calculate the values of 106 x 106:
106 x 106 = 11,120
Next, let's calculate the values of 94 x 94:
94 x 94 = 8,816
Now, let's subtract 8,816 from 11,120:
11,120 - 8,816 = ... |
Solve the following multiple choice question.
Question:
two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options:
a ) 22 , b ) 27 , c ) 50 , ... | relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c
Final answer: c | To find the time taken by the slower train to pass the driver of the faster one, we first need to calculate the relative speed between the two trains.
The relative speed = speed of faster train + speed of slower train
Relative speed = 42 + 30 = 72 km/hr
Since they are moving in opposite directions, the relative spe... |
Solve the following multiple choice question.
Question:
two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options:
a ) 22 , b ) 27 , c ) 50 , ... | relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c
Final answer: c | To find the time taken for the slower train to pass the driver of the faster train, we need to find their relative speed and the length of the passing distance.
Relative speed of the slower train with respect to the faster train = (42 km/hr - 30 km/hr) = 12 km/hr
The relative speed of the slower train with respect to... |
Solve the following multiple choice question.
Question:
two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 42 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options:
a ) 22 , b ) 27 , c ) 50 , ... | relative speed = 42 + 30 = 72 km / hr . 72 * 5 / 18 = 20 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 20 = 50 sec . answer : c
Final answer: c | To solve this problem, we need to first find the relative speed of the two trains. Since they are moving in opposite directions, we add their speeds to find the relative speed.
Relative speed = 42 km/hr + 30 km/hr = 72 km/hr
Now, to find the time taken for the slower train to pass the driver of the faster one, we nee... |
Solve the following multiple choice question.
Question:
( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ?
Options:
a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400
Answer (choose one of a, b, c, d, e): | explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d
Final answer: d | To solve the given expression, we need to follow the order of operations:
(5 × 12) × (0.25) × (0.75)
First, let's multiply 5 and 12:
5 × 12 = 60
Now, let's multiply 60 by 0.25:
60 × 0.25 = 15
Now, let's multiply the result by 0.75:
15 × 0.75 = 11.25
Therefore, the correct answer is:
Option c ) 200 |
Solve the following multiple choice question.
Question:
( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ?
Options:
a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400
Answer (choose one of a, b, c, d, e): | explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d
Final answer: d | To solve this problem, we need to multiply these numbers together step by step:
( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 =
First, let's multiply 5 and 12:
5 × 12 = 60
Now, multiply 60 by 0.25:
60 × 0.25 = 15
Next, multiply 15 by 60:
15 × 60 = 900
Finally, multiply 900 by 0.75:
900 × 0.75 = 675
Therefore, the co... |
Solve the following multiple choice question.
Question:
( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ?
Options:
a ) 420 , b ) 260 , c ) 200 , d ) 300 , e ) 400
Answer (choose one of a, b, c, d, e): | explanation : ( 5 ) 1.25 × ( 12 ) 0.25 × ( 60 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 × 5 ) 0.75 = ( 5 ) 1.25 × ( 12 ) 0.25 × ( 12 ) 0.75 × ( 5 ) 0.75 = ( 5 ) ( 1.25 + 0.75 ) × ( 12 ) ( 0.25 + 0.75 ) = ( 5 ) 2 × ( 12 ) 1 = 25 × 12 = 300 answer : option d
Final answer: d | To solve this problem, we need to follow the order of operations.
Step 1: Multiply the numbers 5, 12, and 60.
5 × 12 = 60
60 × 60 = 3600
Step 2: Multiply the result of the first two steps by 0.25.
3600 × 0.25 = 900
Therefore, the result is:
5 × 12 × 60 × 0.75 = 900
Option b) 260 is the correct answer. |
Solve the following multiple choice question.
Question:
one copy machine can make 15 copies a minute , and a second copy machine makes 10 copies a minute . if the two copiers work together , how long would it take them to make 1,000 copies ?
Options:
a ) 20 minutes , b ) 30 minutes , c ) 40 minutes , d ) 50 minutes ,... | total work done by both machines in a minute = 15 + 10 = 25 copies total number of copies required = 1000 time = 1000 / 25 = 40 mins answer c
Final answer: c | To find the time taken to make 1,000 copies, we need to calculate the combined rate of both machines and then divide the total copies by the combined rate.
The first machine makes 15 copies a minute, and the second machine makes 10 copies a minute.
Combined rate = 15 + 10 = 25 copies per minute
To find the time take... |
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