prompt stringlengths 160 756 | chosen stringlengths 18 2.75k | rejected stringlengths 19 1.83k |
|---|---|---|
Solve the following multiple choice question.
Question:
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 500 newborn members of the population , approximately how many would be expected to survive the first 3 ... | number of newborns that can die in first month = 1 / 10 * 500 = 50 survived = 450 number of newborns that can die in second month = 1 / 10 * 450 = 45 survived = 405 number of newborns that can die in third month = 1 / 10 * 405 = 40 survived = 365 answer : d
Final answer: d | To solve this, let's break it down step by step:
1. In the first month, there's a 1/10 chance that each of the 500 newborns will die. To calculate the number of deaths in the first month, we multiply the number of newborns by the probability of dying each: 500 * (1/10) = 50.
2. In the second month, similarly, 500 * (... |
Solve the following multiple choice question.
Question:
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 500 newborn members of the population , approximately how many would be expected to survive the first 3 ... | number of newborns that can die in first month = 1 / 10 * 500 = 50 survived = 450 number of newborns that can die in second month = 1 / 10 * 450 = 45 survived = 405 number of newborns that can die in third month = 1 / 10 * 405 = 40 survived = 365 answer : d
Final answer: d | To solve this problem, we need to find the probability of an animal surviving each month. Since the probability of dying in the first month is 1/10, the probability of surviving each month is 1 - 1/10 = 9/10.
For the first month, the probability of surviving is 9/10, for the second month it's (9/10)^2, and for the thi... |
Solve the following multiple choice question.
Question:
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 500 newborn members of the population , approximately how many would be expected to survive the first 3 ... | number of newborns that can die in first month = 1 / 10 * 500 = 50 survived = 450 number of newborns that can die in second month = 1 / 10 * 450 = 45 survived = 405 number of newborns that can die in third month = 1 / 10 * 405 = 40 survived = 365 answer : d
Final answer: d | To solve this problem, let's calculate the expected number of animals that would be expected to survive the first 3 months.
For each month, the probability of a newborn animal dying is 1/10, or 0.1.
Let's calculate the expected number of animals that would die each month:
- Month 1: 500 animals x 0.1 = 50 animals
- M... |
Solve the following multiple choice question.
Question:
the duplicate ratio of 6 : 4 is ?
Options:
a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Answer (choose one of a, b, c, d, e): | 36 ^ 2 : 4 ^ 2 = 36 : 16 = 9 : 4 answer : b
Final answer: b | To solve the duplicate ratio, we need to find a number that when multiplied by 6 gives a number that is divisible by 4.
This number is the LCM of 6 and 4, which is 12.
Therefore, we can write 6 as 3 × 2 and 4 as 2 × 2.
Now, when we multiply 3 by 2 and 2, we get 6 × 2 = 12 and 6 × 2 = 12, both of which are divisible ... |
Solve the following multiple choice question.
Question:
the duplicate ratio of 6 : 4 is ?
Options:
a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Answer (choose one of a, b, c, d, e): | 36 ^ 2 : 4 ^ 2 = 36 : 16 = 9 : 4 answer : b
Final answer: b | To find the duplicate ratio, we need to multiply each part of the given ratio by the same number and find the greatest common divisor.
Given ratio: 6 : 4
To find the greatest common divisor (GCD) of 6 and 4, we can list the factors of each number:
Factors of 6: 1, 2, 3, 6
Factors of 4: 1, 2, 4
The greatest common d... |
Solve the following multiple choice question.
Question:
the duplicate ratio of 6 : 4 is ?
Options:
a ) 1 : 2 , b ) 9 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Answer (choose one of a, b, c, d, e): | 36 ^ 2 : 4 ^ 2 = 36 : 16 = 9 : 4 answer : b
Final answer: b | To solve this, let's convert the given ratio into a mixed number:
6 : 4 is equal to 3 : 2.
Then, we need to find a number that when divided by 2 gives us 3. This number is 3 itself.
Therefore, the duplicate ratio of 6 : 4 is 3 : 2. The answer is (a) 1 : 2. |
Solve the following multiple choice question.
Question:
free notebooks were distributed in a class among all the students . each student got notebooks which were 1 / 8 th of the number of student . if number of student been half , then each child would have received 16 notebooks in total . find the total number of boo... | let suppose total number of students in class are x . then from the question we can conclude it that , x ∗ 18 x = x 2 ∗ 16 = > x = 64 total notebooks , = 18 x 2 = ( 18 ∗ 64 ∗ 64 ) = 512 e
Final answer: e | Let's solve it step by step.
Let the total number of students be 'x'.
Each student got 1/8th of the total number of students as notebooks. So, each student got (1/8)x notebooks.
If the number of students were doubled, each student would get 2(x/8) = x/4 notebooks. Since the total number of notebooks remains the sam... |
Solve the following multiple choice question.
Question:
free notebooks were distributed in a class among all the students . each student got notebooks which were 1 / 8 th of the number of student . if number of student been half , then each child would have received 16 notebooks in total . find the total number of boo... | let suppose total number of students in class are x . then from the question we can conclude it that , x ∗ 18 x = x 2 ∗ 16 = > x = 64 total notebooks , = 18 x 2 = ( 18 ∗ 64 ∗ 64 ) = 512 e
Final answer: e | To find the total number of books distributed among students, let's assume the total number of students is x.
Since each student received 1/8x notebooks, the total number of notebooks distributed is x * 1/8x = x/8.
When half the number of students were distributed, each child received 16 notebooks. So the total numb... |
Solve the following multiple choice question.
Question:
free notebooks were distributed in a class among all the students . each student got notebooks which were 1 / 8 th of the number of student . if number of student been half , then each child would have received 16 notebooks in total . find the total number of boo... | let suppose total number of students in class are x . then from the question we can conclude it that , x ∗ 18 x = x 2 ∗ 16 = > x = 64 total notebooks , = 18 x 2 = ( 18 ∗ 64 ∗ 64 ) = 512 e
Final answer: e | Let's break down the problem step by step:
1. Let the number of students be represented as x.
2. Since each student got 1/8th of the number of students, each student got 1/8*x notebooks.
3. If the number of students was halved, then the number of students would be 1/2*x and each student would get 1/2*x notebooks.
4. S... |
Solve the following multiple choice question.
Question:
a ratio between two numbers is 7 : 9 and their l . c . m . is 189 . the second number is
Options:
a ) 35 , b ) 25 , c ) 20 , d ) 27 , e ) none
Answer (choose one of a, b, c, d, e): | sol . let the required numbers be 7 x and 9 x . then , their l . c . m . is 63 x . ∴ 63 x = 189 ⇔ x = 3 . hence , the second number is 27 . answer d
Final answer: d | To solve this question, let's use the fact that the ratio between two numbers is 7 : 9.
Let's assume the two numbers are 7x and 9x, where x is a common factor.
Since the LCM of the two numbers is 189, we know that LCM = 7x * 9x = 63x.
We know that LCM = 189, so 63x = 189.
To solve for x, divide both sides by 63:
... |
Solve the following multiple choice question.
Question:
a ratio between two numbers is 7 : 9 and their l . c . m . is 189 . the second number is
Options:
a ) 35 , b ) 25 , c ) 20 , d ) 27 , e ) none
Answer (choose one of a, b, c, d, e): | sol . let the required numbers be 7 x and 9 x . then , their l . c . m . is 63 x . ∴ 63 x = 189 ⇔ x = 3 . hence , the second number is 27 . answer d
Final answer: d | To solve this problem, let's use the concept of LCM (Least Common Multiple) and the given ratio.
First, let's write the ratio as an equation:
7/9 = x/2
Now, cross multiply to get:
7 × 2 = 9 × x
14 = 9x
Divide both sides by 9:
x = 14/9
Now, multiply both sides by 3 to get rid of the fraction:
3x = 42
x = 14
The se... |
Solve the following multiple choice question.
Question:
a ratio between two numbers is 7 : 9 and their l . c . m . is 189 . the second number is
Options:
a ) 35 , b ) 25 , c ) 20 , d ) 27 , e ) none
Answer (choose one of a, b, c, d, e): | sol . let the required numbers be 7 x and 9 x . then , their l . c . m . is 63 x . ∴ 63 x = 189 ⇔ x = 3 . hence , the second number is 27 . answer d
Final answer: d | To find the second number, we need to use the ratio and the least common multiple (LCM).
Let's break down the ratio to its prime factors:
7:9 = 7^1:3^2
We know that the LCM of 7 and 3 is 63.
We can set up the equation using the ratio and LCM:
7x = 63
x = 63/7
x = 9
Now, let's find the second number using the giv... |
Solve the following multiple choice question.
Question:
what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 449 * 349 ) ^ 2
Options:
a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 24
Answer (choose one of a, b, c, d, e): | ( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 449 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 9,9 ; 5 & 9 are missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 49 * 49 . s... | To find the last two digits of the expression (301 * 402 * 503 * 604 * 646 * 547 * 449 * 349)^2, we can first calculate the product of the given numbers modulo 100, as the last two digits of a number raised to a power is the same as the last two digits of the number raised to that power.
301 * 402 = 120502, which has ... |
Solve the following multiple choice question.
Question:
what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 449 * 349 ) ^ 2
Options:
a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 24
Answer (choose one of a, b, c, d, e): | ( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 449 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 9,9 ; 5 & 9 are missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 49 * 49 . s... | To solve this, we can calculate the product of 301 * 402 * 503 * 604 * 646 * 547 * 449 * 349 first, then find its square root, and finally focus on the last two digits.
Let's calculate it step by step:
301 * 402 = 120202
120202 * 503 = 6037314
6037314 * 604 = 3638474890
3638474890 * 646 = 239239190820
239239190820 * ... |
Solve the following multiple choice question.
Question:
a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 100 more than that by the previous schema ... | [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 100 x = 32000 answer : c
Final answer: c | To solve this problem, let's first calculate the salesman's old and new remuneration.
Let the total sales be denoted by x.
Under the old scheme, his remuneration was Rs. 5% of x = 0.05x
His new remuneration would be Rs. 1000 + 2.5% of x = 1000 + 0.025x.
Equating the old and new remuneration, we have:
0.05x = 1000 +... |
Solve the following multiple choice question.
Question:
a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 100 more than that by the previous schema ... | [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 100 x = 32000 answer : c
Final answer: c | To solve this problem, let's calculate the sales without commission and with commission.
In the previous scheme, the salesman earned a fixed salary of Rs. 1000 plus 5% on sales exceeding Rs. 4000. Let's call the sales before commission 'x'. Then, his salary and commission would be 1000 + 0.05x.
Since his new scheme ... |
Solve the following multiple choice question.
Question:
a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 100 more than that by the previous schema ... | [ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 100 x = 32000 answer : c
Final answer: c | To solve this problem, we need to calculate the difference in remuneration between the two schemes.
Let's denote the salesman's sales as 'x'. In the old scheme, his commission was 5% of the sales, so his remuneration was:
x × 0.05 = 0.05x
In the new scheme, his commission is 2.5% of the sales exceeding 4000, so hi... |
Solve the following multiple choice question.
Question:
for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers q are there between 6 * + 2 and 6 * + 6 , inclusive ?
Options:
a ) none , b ) one , c ) two , d ) three , e ) four
Answer (choose one... | given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so ... | To solve this question, we need to find the range of numbers for which the product of all integers from 1 to n (inclusive) is greater than 6 * + 2 and less than 6 * + 6, i.e., 8.
The product of integers from 1 to 6 is:
1 * 2 * 3 * 4 * 5 * 6 = 720
Given that 720 is between 8 and 84 (since 2 * 6 is 12)
We need to fi... |
Solve the following multiple choice question.
Question:
if x > 0 , x / 50 + x / 25 is what percent of x ?
Options:
a ) 6 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Answer (choose one of a, b, c, d, e): | just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 50 + 100 / 25 = 2 + 4 = 6 6 is 6 % of 100 . answer : a
Final answer: a | To find what percent x / 50 + x / 25 of x is, we first need to add the two fractions first to simplify the equation.
x / 50 + x / 25 = 6/25 x
Now that we have the common denominator of 50, we can rewrite the equation as:
(2x + 2x) / 50
(4x / 50)
Combine like terms to simplify the equation:
4x / 50
Since 4x is pre... |
Solve the following multiple choice question.
Question:
in a weight - lifting competition , the total weight of joe ' s two lifts was 1500 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options:
a ) 225 , b ... | this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1500 pounds . we sum the two variables to obtain : f +... | To solve this problem, let's assign variables to the weights of the lifts:
Let x be the weight of the first lift.
Let y be the weight of the second lift.
We know the total weight of both lifts is 1500 pounds, so we can write an equation:
x + y = 1500
We also know that twice the weight of the first lift is 300 pounds... |
Solve the following multiple choice question.
Question:
in a weight - lifting competition , the total weight of joe ' s two lifts was 1500 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options:
a ) 225 , b ... | this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1500 pounds . we sum the two variables to obtain : f +... | To find the weight of Joe's first lift, let's call the weight of his first lift 'x'.
According to the question, the weight of his second lift was twice the weight of his first lift, so it's 2x.
We also know that the total weight of both lifts is 1500 pounds. Therefore, we can set up the equation:
x + 2x = 1500
Com... |
Solve the following multiple choice question.
Question:
in a weight - lifting competition , the total weight of joe ' s two lifts was 1500 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options:
a ) 225 , b ... | this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1500 pounds . we sum the two variables to obtain : f +... | Let's denote the weight of Joe's first lift as x and the weight of his second lift as y.
We are given two pieces of information:
1. The total weight of both lifts is 1500 pounds: x + y = 1500.
2. Twice the weight of his first lift is 300 pounds more than the weight of his second lift: 2x = y + 300.
We can solve thes... |
Solve the following multiple choice question.
Question:
how many different ways can 2 students be seated in a row of 6 desks , so that there is always at least one empty desk between the students ?
Options:
a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12
Answer (choose one of a, b, c, d, e): | 10 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 10 x 2 = 20 d
Final answer: d | To determine the number of ways to seat 2 students in a row of 6 desks so that there is always at least one empty desk between the students, we need to consider the seating arrangements without any constraints (including seated arrangement) first.
Since we have 6 desks, we can arrange 2 students in the 4 spaces betwee... |
Solve the following multiple choice question.
Question:
how many different ways can 2 students be seated in a row of 6 desks , so that there is always at least one empty desk between the students ?
Options:
a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12
Answer (choose one of a, b, c, d, e): | 10 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 10 x 2 = 20 d
Final answer: d | To solve this problem, we need to find the number of ways to seat the students so that there's always at least one empty desk between the students. We will use the concept of permutations.
First, we'll find the total number of ways to seat the 2 students without any restriction. This is a permutation of 6 items taken ... |
Solve the following multiple choice question.
Question:
how many different ways can 2 students be seated in a row of 6 desks , so that there is always at least one empty desk between the students ?
Options:
a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12
Answer (choose one of a, b, c, d, e): | 10 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 10 x 2 = 20 d
Final answer: d | To solve this problem, we can use a combinatorial approach. We can think of the 2 students as two distinct items that need to be placed into 6 slots with restrictions.
One possible way to place the students is to imagine a row of 6 dots or counters. We can place the two students at any of the 7 possible positions, bu... |
Solve the following multiple choice question.
Question:
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 . ... | for 40 hrs = 40 * 16 = 640 excess = 920 - 640 = 280 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 280 / 28 = 70 / 7 = 10 total hrs = 40 + 10 = 50 answer d 50
Final answer: d | To solve the problem, we first need to understand the bus driver's compensation system:
1. He is paid $16 per hour for the first 40 hours.
2. For the hours worked beyond 40, he is paid 75% more than his regular rate, which is $16 + (75% of $16) = $16 + $12 = $28.
Let's denote the number of overtime hours worked as 'x... |
Solve the following multiple choice question.
Question:
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 . ... | for 40 hrs = 40 * 16 = 640 excess = 920 - 640 = 280 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 280 / 28 = 70 / 7 = 10 total hrs = 40 + 10 = 50 answer d 50
Final answer: d | To solve this problem, we need to break down the payment into parts.
Let's denote the number of regular hours worked as 'x'.
The regular pay for x hours is $16x
The overtime pay is 75% of the regular pay, which is $16x * 0.75 = $12x
The total payment is the sum of the regular pay and overtime pay:
$16x + $12x = $2... |
Solve the following multiple choice question.
Question:
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 . ... | for 40 hrs = 40 * 16 = 640 excess = 920 - 640 = 280 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 280 / 28 = 70 / 7 = 10 total hrs = 40 + 10 = 50 answer d 50
Final answer: d | Let's break down the problem step by step:
1. The bus driver is paid 80% of the regular rate for 40 hours, which is $16 x 40 = $640.
2. The bus driver worked 60 hours (40 regular + 20 overtime) at 75% of the regular rate for overtime hours. The overtime rate is $16 + 0.75 x 16 = $24 per hour.
3. The total overtime pay... |
Solve the following multiple choice question.
Question:
what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?
Options:
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Answer (choose one of a, b, c, d, e): | ( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d
Final answer: d | To solve this, we need to find the remainder when 1056 is divided by 27, and then determine what number needs to be added to 1056 to make it completely divisible by 27.
First, we divide 1056 by 27:
1056 ÷ 27 = 38 with a remainder of 8.
So, 1056 = 38 * 27 + 8.
To make the sum divisible by 27, we need to find the nex... |
Solve the following multiple choice question.
Question:
what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?
Options:
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Answer (choose one of a, b, c, d, e): | ( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d
Final answer: d | To find the least number that should be added to 1056 so the sum is completely divisible by 27, we need to divide 1056 by 27.
1056 ÷ 27 = 38.74
The least number that would make 1056 divisible by 27 would be to add 1.
Therefore, the correct option is:
a) 21 |
Solve the following multiple choice question.
Question:
what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?
Options:
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Answer (choose one of a, b, c, d, e): | ( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d
Final answer: d | To find the least number that needs to be added to 1056 so that the sum is completely divisible by 27, we can use the concept of finding the remainder when 1056 is divided by 27 and then finding the number that makes the remainder 0.
1056 / 27 = 38 with a remainder of 20.
So, to make the total sum divisible by 27, we... |
Solve the following multiple choice question.
Question:
one fourth of a solution that was 13 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options:
a ) 25 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8... | consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.13 + 25 * x = 100 * 0.16 - - > x = 0.25 . answer : a .
Final answer: a | Let's solve the problem step by step.
Initially, the solution is 13% salt by weight.
One fourth of this solution is replaced with a second solution. The result is 16% salt by weight.
This means 3/4 of the initial solution is left and the remaining part of the solution is 16%.
So, the amount of salt in the initial ... |
Solve the following multiple choice question.
Question:
one fourth of a solution that was 13 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options:
a ) 25 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8... | consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.13 + 25 * x = 100 * 0.16 - - > x = 0.25 . answer : a .
Final answer: a | To find the percentage of salt in the second solution, let's follow these steps:
1. We know that 1/4 of the original solution was replaced, so the amount of salt in the original solution is 3/4 (1 - 1/4 = 3/4).
Let's denote the percent of salt in the second solution as 'x'. Since the resulting solution is 16% by weig... |
Solve the following multiple choice question.
Question:
one fourth of a solution that was 13 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options:
a ) 25 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8... | consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.13 + 25 * x = 100 * 0.16 - - > x = 0.25 . answer : a .
Final answer: a | To solve this problem, let's denote the amount of solution that was replaced as \(x\) kilograms.
The original solution had 13% salt by weight.
So, the amount of salt in the original solution = 0.13x kg.
The second solution was 16% salt by weight. Therefore, the amount of salt in the second solution = 0.16(x + x) =... |
Solve the following multiple choice question.
Question:
the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
Options:
a ) 32 , b ) 37 , c ) 84 , d ) 29 , e ) 21
Answer (choose one of a, b, c, d, e): | explanation : let the numbers be x and 4 x . then , \ inline \ fn _ jvn x \ times 4 x = 84 \ times 21 \ : \ : \ leftrightarrow \ : \ : x ^ { 2 } = \ frac { 84 \ times 21 } { 4 } \ : \ : \ leftrightarrow \ : \ : x = 21 hence larger number = 4 x = 84 answer : c ) 84
Final answer: c | To solve this problem, we need to find the numbers.
We know the HCF (Highest Common Factor) and LCM (Least Common Multiple) of two numbers, and the ratio of these numbers.
The ratio of the two numbers is 1 : 4. Let's denote the two numbers as a and b. Then we can write:
LCM(a, b) / HCF(a, b) = 1 / 4
Since LCM is a ... |
Solve the following multiple choice question.
Question:
the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
Options:
a ) 32 , b ) 37 , c ) 84 , d ) 29 , e ) 21
Answer (choose one of a, b, c, d, e): | explanation : let the numbers be x and 4 x . then , \ inline \ fn _ jvn x \ times 4 x = 84 \ times 21 \ : \ : \ leftrightarrow \ : \ : x ^ { 2 } = \ frac { 84 \ times 21 } { 4 } \ : \ : \ leftrightarrow \ : \ : x = 21 hence larger number = 4 x = 84 answer : c ) 84
Final answer: c | To solve this, let's first find the actual numbers using the least common multiple (LCM) of 84 and 21.
The prime factorization of 84 is 2^2 * 3^1 * 7^1
The prime factorization of 21 is 3^1 * 7^1
To get LCM, take the highest power of each prime factor from both numbers:
LCM = 2^2 * 3^1 * 7^1 = 252
Since the ratio of... |
Solve the following multiple choice question.
Question:
the h . c . f and l . c . m of two numbers are 84 and 21 respectively . if the ratio of the two numbers is 1 : 4 , then the larger of the two numbers is
Options:
a ) 32 , b ) 37 , c ) 84 , d ) 29 , e ) 21
Answer (choose one of a, b, c, d, e): | explanation : let the numbers be x and 4 x . then , \ inline \ fn _ jvn x \ times 4 x = 84 \ times 21 \ : \ : \ leftrightarrow \ : \ : x ^ { 2 } = \ frac { 84 \ times 21 } { 4 } \ : \ : \ leftrightarrow \ : \ : x = 21 hence larger number = 4 x = 84 answer : c ) 84
Final answer: c | To solve this problem, we need to find the two numbers.
Given that the ratio of the two numbers is 1:4, we can let the numbers be x and 4x.
The HCF of the two numbers is given as 84, so it should divide both numbers. Let's say the HCF is the number d. So, d = 84.
x * 4x = 84
x^2 = 84
x = sqrt(84)
x = 2*sqrt(21)
... |
Solve the following multiple choice question.
Question:
water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 144 grams of water ?
Options:
a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 142
Answer (choose one of... | see h / o = 2 / 16 add 1 to both sides : h / o + 1 = 2 / 16 + 1 take lcm ( h + o ) / o = ( 2 + 16 ) / 16 water / o = 18 / 16 now that we have the water to oxygen ratio , put in the amount of water i . e . 144 gm = > o = 144 * 16 / 18 = 128 answer : d
Final answer: d | To find the mass of oxygen in 144 grams of water, we need to set up a ratio and then use it to calculate the mass of oxygen.
Given ratio:
Hydrogen: Oxygen = 2 : 16
Mass of water = 144 grams
Let's break it down:
Hydrogen = 2/16 * 144
= 18 grams
Now we know the mass of hydrogen, we can find the mass of oxygen:
Mas... |
Solve the following multiple choice question.
Question:
water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 144 grams of water ?
Options:
a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 142
Answer (choose one of... | see h / o = 2 / 16 add 1 to both sides : h / o + 1 = 2 / 16 + 1 take lcm ( h + o ) / o = ( 2 + 16 ) / 16 water / o = 18 / 16 now that we have the water to oxygen ratio , put in the amount of water i . e . 144 gm = > o = 144 * 16 / 18 = 128 answer : d
Final answer: d | To solve this problem, let's use the given ratio of hydrogen to oxygen in water. We are given that the ratio is 2:16, meaning for every 2 units of hydrogen, there are 16 units of oxygen.
Let's use this ratio to find the mass of oxygen in 144 grams of water.
We can set up a proportion to solve for the mass of oxygen:
... |
Solve the following multiple choice question.
Question:
water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 144 grams of water ?
Options:
a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 142
Answer (choose one of... | see h / o = 2 / 16 add 1 to both sides : h / o + 1 = 2 / 16 + 1 take lcm ( h + o ) / o = ( 2 + 16 ) / 16 water / o = 18 / 16 now that we have the water to oxygen ratio , put in the amount of water i . e . 144 gm = > o = 144 * 16 / 18 = 128 answer : d
Final answer: d | To solve this problem, we can use the ratio given, which is 2:16. This means that for every 2 parts of hydrogen, there are 16 parts of oxygen. We have 144 grams of water, which is essentially 2.75% water.
Let's set up a proportion to find out how many grams of oxygen there are:
2/16 = 144/x, where x is the amount of ... |
Solve the following multiple choice question.
Question:
a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 555 in all . for how many days was he absent ?
Options:
a ) 8 , b ) 10 , c ) 15 , d ) 6 , e ) 19
Answer... | 30 * 25 = 750 455 - - - - - - - - - - - 195 25 + 7.50 = 32.5 195 / 32.5 = 6 d
Final answer: d | Let's break this problem down step by step:
Let's denote the number of days the contractor worked as 'x' and the number of days he was absent as 'y'.
The total income is 25x + 7.50y = 555
Since the contractor was engaged for 30 days, we have the equation:
x + y = 30
We can solve the system of equations. Let's isol... |
Solve the following multiple choice question.
Question:
a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 555 in all . for how many days was he absent ?
Options:
a ) 8 , b ) 10 , c ) 15 , d ) 6 , e ) 19
Answer... | 30 * 25 = 750 455 - - - - - - - - - - - 195 25 + 7.50 = 32.5 195 / 32.5 = 6 d
Final answer: d | To solve this problem, let's first denote the number of days the contractor worked by 'x' and the number of days he was absent by 'y'.
Given:
- Contractor's daily wage = Rs. 25
- Daily fine for absence = Rs. 7.50
- Total income ( worked + absent) = Rs. 555
We can set up the equation based on the given information:
... |
Solve the following multiple choice question.
Question:
a contractor is engaged for 30 days on the condition thathe receives rs . 25 for each day he works & is fined rs . 7.50 for each day is absent . he gets rs . 555 in all . for how many days was he absent ?
Options:
a ) 8 , b ) 10 , c ) 15 , d ) 6 , e ) 19
Answer... | 30 * 25 = 750 455 - - - - - - - - - - - 195 25 + 7.50 = 32.5 195 / 32.5 = 6 d
Final answer: d | To solve this, we need to calculate the difference between the amount received and the amount earned to determine the number of days worked.
Let's use the formula:
Earned amount = Total amount received - (Time * Fine per day * Number of days worked)
Given:
Earned amount = Rs. 555
Fine per day * Number of days worked... |
Solve the following multiple choice question.
Question:
a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 140 . find the unknown rate of two blankets ?
O... | 10 * 140 = 15 = 1400 3 * 100 + 5 * 150 = 1050 1400 – 1050 = 350 answer : a
Final answer: a | To find the unknown rate of two blankets, we need to first calculate the total cost of all the blankets.
Total cost of 3 blankets = 3 * 100 = 300
Total cost of 5 blankets = 5 * 150 = 750
Total cost of 8 blankets = 300 + 750 = 1050
The total number of blankets = 3 + 5 + 2 = 10
We know that the average price of all 1... |
Solve the following multiple choice question.
Question:
a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 140 . find the unknown rate of two blankets ?
O... | 10 * 140 = 15 = 1400 3 * 100 + 5 * 150 = 1050 1400 – 1050 = 350 answer : a
Final answer: a | To solve this problem, let's use the formula for average price:
Average price = (Total price of all blankets) / (Total number of blankets)
We know the average price is 140, and the number of blankets is 3 + 5 + 2 = 10. We also know the price of the first 3 blankets and the 5th blankets (2).
Price of first 3 blanket... |
Solve the following multiple choice question.
Question:
a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 140 . find the unknown rate of two blankets ?
O... | 10 * 140 = 15 = 1400 3 * 100 + 5 * 150 = 1050 1400 – 1050 = 350 answer : a
Final answer: a | To find the unknown rate of the two blankets, we first need to calculate the total cost of the blankets.
Total cost of 3 blankets at Rs. 100 each = 3 x 100 = Rs. 300
Total cost of 5 blankets at Rs. 150 each = 5 x 150 = Rs. 750
The total cost of all blankets is the sum of the costs of the first 5 blankets and the unk... |
Solve the following multiple choice question.
Question:
what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ?
Options:
a ) 6893 , b ) 6993 , c ) 6093 , d ) 693 , e ) none
Answer (choose one of a, b, c, d, e): | 7770 7077 - - - - - - - - - - - - - 693 answer : d
Final answer: d | To solve this problem, let's analyze the given numbers: 7, 7, 0, and 7.
The number 7 is a single digit, so its value remains the same regardless of its placement.
- 1000 * 7 = 7000
To find the largest number possible using these digits, we arrange them in descending order, starting with the largest possible number, ... |
Solve the following multiple choice question.
Question:
what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ?
Options:
a ) 6893 , b ) 6993 , c ) 6093 , d ) 693 , e ) none
Answer (choose one of a, b, c, d, e): | 7770 7077 - - - - - - - - - - - - - 693 answer : d
Final answer: d | To solve this question, let's analyze the numbers and see how they can be formed:
- The number "7" is already a single-digit number, and "0" can be appended or placed in the front of a number to make it a two-digit number.
1. 707
- If the digit "7" is in the front of the number, the other digit is "07", we get 707. ... |
Solve the following multiple choice question.
Question:
what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ?
Options:
a ) 6893 , b ) 6993 , c ) 6093 , d ) 693 , e ) none
Answer (choose one of a, b, c, d, e): | 7770 7077 - - - - - - - - - - - - - 693 answer : d
Final answer: d | To find the difference between the largest and smallest number written with 7, 7, 0, 7, let's analyze the possible combinations:
Options for the largest number:
1. 7777:
- 1. The sequence pattern is 7, 7, 7, 7.
- Since the digit is the same, it doesn't make sense as we're replacing each digit with 0 and 7
... |
Solve the following multiple choice question.
Question:
if the sides of a square are multiplied by 5 , the area of the original square is how many times as large as the area of the resultant square ?
Options:
a ) 4 % , b ) 25 % , c ) 50 % , d ) 200 % , e ) 400 %
Answer (choose one of a, b, c, d, e): | let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 5 x , so the area is 25 x ^ 2 . the area of the original square is 1 / 25 = 4 % times the area of the new square . the answer is a .
Final answer: a | To solve this problem, let's consider the original square with side length 's'. The area of the original square is s^2.
When the side length is multiplied by 5, the side length becomes 5s. The area of the resultant square is (5s)^2 = 25s^2.
Now, we can calculate the ratio of the area of the resultant square to the or... |
Solve the following multiple choice question.
Question:
if the sides of a square are multiplied by 5 , the area of the original square is how many times as large as the area of the resultant square ?
Options:
a ) 4 % , b ) 25 % , c ) 50 % , d ) 200 % , e ) 400 %
Answer (choose one of a, b, c, d, e): | let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 5 x , so the area is 25 x ^ 2 . the area of the original square is 1 / 25 = 4 % times the area of the new square . the answer is a .
Final answer: a | To solve this problem, we need to find the ratio of the areas of the squares.
Let's say the side length of the original square is 'x'. Then, the area of the original square is x^2.
When the sides of the square are multiplied by 5, the new side length becomes 5x. The area of the resultant square is (5x)^2 = 25x^2.
Th... |
Solve the following multiple choice question.
Question:
a man can row downstream at 18 kmph and upstream at 16 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options:
a ) 13 , 3 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) 17 , 1
Answer (choose one of a, b, c, d, e): | explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 16 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 1 . answer : option e
Final answer: e | To find the speed of the man in still water and the speed of the stream, we use the following formulas:
Speed of the man in still water = (Speed downstream + Speed upstream) / 2
Speed of the stream = (Speed upstream - Speed downstream) / 2
Given, Speed downstream = 18 kmph
Speed upstream = 16 kmph
Using the first fo... |
Solve the following multiple choice question.
Question:
a man can row downstream at 18 kmph and upstream at 16 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options:
a ) 13 , 3 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) 17 , 1
Answer (choose one of a, b, c, d, e): | explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 16 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 1 . answer : option e
Final answer: e | To solve this question, let's use the formula:
Speed downstream (DS) = Speed of boat + Speed of stream
Speed upstream (US) = Speed of boat - Speed of stream
Given:
DS = 18 kmph, US = 16 kmph
First, we need to find the speed of the boat in still water.
Speed downstream (DS) = Speed of boat + Speed of stream
18 = S... |
Solve the following multiple choice question.
Question:
a man can row downstream at 18 kmph and upstream at 16 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options:
a ) 13 , 3 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) 17 , 1
Answer (choose one of a, b, c, d, e): | explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 16 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 1 . answer : option e
Final answer: e | To solve this problem, we need to consider the concept of velocity. When a boat moves downstream (in the direction of the flow of the stream), its speed is the sum of the speed of the boat in still water and the speed of the stream.
Let the speed of the man in still water be 'v' and the speed of the stream be 's'.
Do... |
Solve the following multiple choice question.
Question:
by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?
Options:
a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Answer (choose one of a, b, c, d, e): | for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .
Final answer: e | To find the larger root of the equation 2q^2 + 5q = 12, we can use the quadratic formula:
q = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 5, and c = -12.
q = (-(5) ± √((5)^2 - 4(2)(-12)) / 2(2)
q = (-5 ± √(25 + 96) / 4
q = (-5 ± √121 / 4
q = (-5 ± 11/4)
The two roots are:
q = (-5 + 11/4) = 1/4
q = (-5 - 11/4)... |
Solve the following multiple choice question.
Question:
by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?
Options:
a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Answer (choose one of a, b, c, d, e): | for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .
Final answer: e | To find the roots of the equation 2x^2 + 5x - 12 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 5, and c = -12.
Plugging these values into the formula, we get:
x = (-(5) ± √((5)^2 - 4(2)(-12)) / 2(2))
x = (-5 ± √(25 + 96) / 4)
x = (-5 ± √121 / 4)
x = (-5 ± 11 / 4)
This... |
Solve the following multiple choice question.
Question:
by how much does the larger root of the equation 2 q ^ 2 + 5 q = 12 exceed the smaller root ?
Options:
a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Answer (choose one of a, b, c, d, e): | for 2 q ^ 2 + 5 q = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) .
Final answer: e | To solve the equation 2q^2 + 5q = 12, we need to find the roots of the equation.
First, let's isolate q by moving the 2 to the other side of the equation:
2q^2 + 5q = 12
Subtract 5q from both sides:
2q^2 = 12 - 5q
Now, add 5q to both sides:
2q^2 + 5q = 12
Divide both sides by 2:
q^2 + 5q/2 = 6
Now, multiply bo... |
Solve the following multiple choice question.
Question:
a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of bein... | the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d .
Final answer: d | To find the probability of selling 3 bottles of apple juice among 6 bottles in a random selection, we can use the combination formula:
Total number of ways to select 6 bottles out of 10 = 10C6
Total number of favorable outcomes (selling 3 bottles of apple juice) = 6C3
6C3 = 20
Probability = Favorable outcomes / Tot... |
Solve the following multiple choice question.
Question:
a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of bein... | the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d .
Final answer: d | To find the probability of selling 3 bottles of apple juice among 6 bottles of juice sold, we need to first calculate the total number of possible combinations of 6 bottles that can be sold.
Total number of ways to choose 3 apples (and thus 3 non-apples) from 10 bottles:
(6C3) × (4C3) = 20 × 4 = 80
The number of w... |
Solve the following multiple choice question.
Question:
a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of bein... | the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 3 bottles of apple juice is 6 c 3 * 4 c 3 = 20 * 4 = 80 p ( selling 3 bottles of apple juice ) = 80 / 210 = 8 / 21 the answer is d .
Final answer: d | To solve this problem, we first need to find the total number of ways to choose 6 bottles out of 10, and then find the number of ways to choose 3 apple juice bottles.
The total number of ways to choose 6 bottles out of 10 is given by the combination formula: C(10, 6) = 10! / (6! * (10 - 6)!) = 210
The number of ways ... |
Solve the following multiple choice question.
Question:
x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?
Options:
a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24
Answer (choose one of a, b, c, d, e): | for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know tha... | To find the number of possible values for 's', we need to find the discriminant (b² - 4ac) of the quadratic equation x² + sx + 72 = 0 and find the factors of 72.
1. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The square root of the discriminant (s² - 4ac) = √((s² - 4 * 1 * 72) = √(s² - 288) = √(s² - 4 * 9 ... |
Solve the following multiple choice question.
Question:
x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?
Options:
a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24
Answer (choose one of a, b, c, d, e): | for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know tha... | To solve the given quadratic equation \( x^2 + sx + 72 = 0 \), let's recall the property that for a quadratic equation of the form \( ax^2 + bx + c = 0 \), the sum of the roots (\( r_1 \) and \( r_2 \)) is equal to \(-\frac{b}{a}\) and the product of the roots is equal to \( \frac{c}{a} \).
In this case, \( a = 1 \), ... |
Solve the following multiple choice question.
Question:
x ^ 2 + sx + 72 = 0 has two distinct integer roots ; how many values are possible for s ?
Options:
a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 24
Answer (choose one of a, b, c, d, e): | for a quadratic equation ax ^ 2 + sx + c = 0 , we know that - s / a is sum of roots and c / a is product of roots . the quadratic equation here is x ^ 2 + sx + 72 = 0 , where product of roots is 72 . if we find all the factors of 72 , we have the answer . by prime factorization , we get 72 = 2 ^ 3 * 3 ^ 2 . we know tha... | To solve this problem, we can use the quadratic formula to find the possible values of the roots. The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a
In this case, the coefficients of the quadratic equation are a = 1, b = s, and c = 72.
Plugging these values into the quadratic formula, we get:
x = (-s ± √(s² - 4(... |
Solve the following multiple choice question.
Question:
a candidate who gets 30 % of the marks fails by 30 marks . but another candidate who gets 45 % marks gets 15 marks more than necessary for passing . find the number of marks for passing ?
Options:
a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 371 marks , e... | 30 % - - - - - - - - - - - - 30 45 % - - - - - - - - - - - - 15 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 45 30 % - - - - - - - - - - - - - - ? 90 + 30 = 120 marks answer : e
Final answer: e | Let's calculate the marks for the passing percentage and options given.
First, let's find the passing marks for both candidates.
Candidate A (Passing Marks) = (100 + 30) = 130
Candidate B (Passing Marks) = 45% of 150 = 0.45 * 150 = 67.5
Now, let's use the difference between the candidate's marks and the passing mar... |
Solve the following multiple choice question.
Question:
a candidate who gets 30 % of the marks fails by 30 marks . but another candidate who gets 45 % marks gets 15 marks more than necessary for passing . find the number of marks for passing ?
Options:
a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 371 marks , e... | 30 % - - - - - - - - - - - - 30 45 % - - - - - - - - - - - - 15 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 45 30 % - - - - - - - - - - - - - - ? 90 + 30 = 120 marks answer : e
Final answer: e | To find the passing marks, let's analyze the information given:
- Candidate A fails by 30 marks, and the candidate B fails by 30% of the total marks. This means for the same total marks, the passing marks would be 70% of the total marks.
However, option 'a') 100 marks, is not possible because it would imply B would g... |
Solve the following multiple choice question.
Question:
a candidate who gets 30 % of the marks fails by 30 marks . but another candidate who gets 45 % marks gets 15 marks more than necessary for passing . find the number of marks for passing ?
Options:
a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 371 marks , e... | 30 % - - - - - - - - - - - - 30 45 % - - - - - - - - - - - - 15 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 45 30 % - - - - - - - - - - - - - - ? 90 + 30 = 120 marks answer : e
Final answer: e | To solve this, let's analyze the information given:
The candidate who gets 30% of the marks fails by 30 marks. This means that the passing marks can be calculated by adding 30 marks to the marks that the candidate fails by.
Let's call the passing marks 'x'. The marks that the candidate fails by is 30. Therefore, the ... |
Solve the following multiple choice question.
Question:
find the probability that a non leap year selected at random will have 53 sundays
Options:
a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Answer (choose one of a, b, c, d, e): | there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e .
Final answer: e | To find the probability of a non-leap year having 53 Sundays, we need to calculate the probability that it is a leap year (which has 366 days) and the probability that it is not a leap year (which has 365 days).
The probability of a non-leap year being a leap year is 1/7.
Since there are 4 extra days in a leap year (... |
Solve the following multiple choice question.
Question:
find the probability that a non leap year selected at random will have 53 sundays
Options:
a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Answer (choose one of a, b, c, d, e): | there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e .
Final answer: e | To solve this question, we need to calculate the probability that a non-leap year selected at random will have 53 Sundays.
A non-leap year has 365 days. The probability of having at least one Sunday in a year can be found by subtracting the probability of not having a Sunday from 1.
The probability of not having a Su... |
Solve the following multiple choice question.
Question:
find the probability that a non leap year selected at random will have 53 sundays
Options:
a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Answer (choose one of a, b, c, d, e): | there are 365 days in a leap year : 52 weeks and 1 more days . so , 52 sundays and 1 days . this 1 days can be { mon , tue , wed , thu , fri , sat , sun } ( 7 cases ) . in order to have 53 sundays we should have sun case . the probability of that is 1 / 7 . answer : e .
Final answer: e | To find the probability that a non-leap year selected at random will have 53 Sundays, we need to find the probability of a non-leap year having 52 Sundays and then subtract it from 1.
Non-leap years have 365 days in total.
Number of days in a non-leap year = 365
Number of days in a week = 7
Number of days in a non-le... |
Solve the following multiple choice question.
Question:
a candidate who gets 30 % of the marks fails by 60 marks . but another candidate who gets 45 % marks gets 30 marks more than necessary for passing . find the number of marks for passing ?
Options:
a ) 100 marks , b ) 240 marks , c ) 280 marks , d ) 371 marks , e... | 30 % - - - - - - - - - - - - 60 45 % - - - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 90 30 % - - - - - - - - - - - - - - 180 180 + 60 = 240 marks answer : b
Final answer: b | To solve this problem, we need to first find out the marks required for a pass.
Let's assume the total marks for the exam are x.
Candidate 1 (30% of x) is 0.3x. He fails, hence the passing marks for him would be:
0.7x (assuming the rest of the marks, i.e., 100% of x)
Candidate 2 (45% of x) is 0.45x and he gets 30... |
Solve the following multiple choice question.
Question:
a candidate who gets 30 % of the marks fails by 60 marks . but another candidate who gets 45 % marks gets 30 marks more than necessary for passing . find the number of marks for passing ?
Options:
a ) 100 marks , b ) 240 marks , c ) 280 marks , d ) 371 marks , e... | 30 % - - - - - - - - - - - - 60 45 % - - - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 90 30 % - - - - - - - - - - - - - - 180 180 + 60 = 240 marks answer : b
Final answer: b | To find the marks for passing, we need to first find the marks obtained by both candidates.
Given:
- Candidate 1: Marks to fail = 30%
- Candidate 2: Marks to pass = 30% more than Candidate 1
First, find the marks for Candidate 1.
Let the total marks be x.
Candidate 1 fails by 30% (i.e., 0.30x)
Candidate 2 gets 30 mar... |
Solve the following multiple choice question.
Question:
a candidate who gets 30 % of the marks fails by 60 marks . but another candidate who gets 45 % marks gets 30 marks more than necessary for passing . find the number of marks for passing ?
Options:
a ) 100 marks , b ) 240 marks , c ) 280 marks , d ) 371 marks , e... | 30 % - - - - - - - - - - - - 60 45 % - - - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 90 30 % - - - - - - - - - - - - - - 180 180 + 60 = 240 marks answer : b
Final answer: b | To find the marks for passing, let's first assume the total marks for the exam is x.
Given that a candidate who gets 30% of the marks fails by 60 marks, this means the total marks are 60% above the passing mark. So, the passing marks would be x - 60.
For the other candidate, who gets 45% of the marks, it's given that... |
Solve the following multiple choice question.
Question:
there are two positive numbers in the ratio 3 : 11 . if the larger number exceeds the smaller by 32 , then what is the smaller number ?
Options:
a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 17
Answer (choose one of a, b, c, d, e): | let the two positive numbers be 3 x and 11 x respectively . 11 x - 3 x = 32 8 x = 32 = > x = 4 thus , the smaller number = 3 x = 12 . answer : c
Final answer: c | To find the smaller number, let's assume the numbers are x and 3x.
The larger number is x + 32, as it exceeds the smaller number by 32.
The ratio of the larger number to the smaller number is 11:3
Therefore, we can set up an equation based on the ratio:
x + 32 = 11k
3x = 3k
x = k
Substituting this value of x... |
Solve the following multiple choice question.
Question:
there are two positive numbers in the ratio 3 : 11 . if the larger number exceeds the smaller by 32 , then what is the smaller number ?
Options:
a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 17
Answer (choose one of a, b, c, d, e): | let the two positive numbers be 3 x and 11 x respectively . 11 x - 3 x = 32 8 x = 32 = > x = 4 thus , the smaller number = 3 x = 12 . answer : c
Final answer: c | Let's denote the smaller number as x. According to the problem, the larger number is 11x + 32.
The ratio of the two numbers is given as 3:11. This means that the smaller number to the larger number is in the ratio of 3:11.
Since they are in the same ratio, we can set up the following proportion:
x / (11x + 32) = 3 ... |
Solve the following multiple choice question.
Question:
there are two positive numbers in the ratio 3 : 11 . if the larger number exceeds the smaller by 32 , then what is the smaller number ?
Options:
a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 17
Answer (choose one of a, b, c, d, e): | let the two positive numbers be 3 x and 11 x respectively . 11 x - 3 x = 32 8 x = 32 = > x = 4 thus , the smaller number = 3 x = 12 . answer : c
Final answer: c | To solve this problem, let's assume the two numbers are 3x and 11x, where x is a positive number. Since the larger number exceeds the smaller number by 32, we can set up the equation:
11x - 3x = 32
8x = 32
x = 4
So the smaller number is 3x = 3 * 4 = 12.
Therefore, the correct answer is (c) 12. |
Solve the following multiple choice question.
Question:
two stations a and b are 200 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options:
a ) 9... | suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 200 45 x = 225 x = 5 . so , they meet at 12 a . m . answer : option d
Final answer: d | To find the time they will meet, we can first find the distance covered by each train in one hour.
Train A:
Distance = 20 km/h x 60 minutes / 60 = 20 km/min
Speed = 20 km/h
Time = Distance / Speed = 200 km / 20 km/min = 10 minutes
So, the train A travels for 10 minutes before meeting the train B
Train B:
Speed = 25... |
Solve the following multiple choice question.
Question:
two stations a and b are 200 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options:
a ) 9... | suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 200 45 x = 225 x = 5 . so , they meet at 12 a . m . answer : option d
Final answer: d | To find when the two trains will meet, we need to calculate their relative speed and the distance covered.
Relative speed = speed of A - speed of B = 20 - 25 = -5 kmph.
As it is a straight line, they will meet after a certain time, which is the same as their relative speed divided by the distance between them.
Time ... |
Solve the following multiple choice question.
Question:
two stations a and b are 200 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options:
a ) 9... | suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 200 45 x = 225 x = 5 . so , they meet at 12 a . m . answer : option d
Final answer: d | To solve this problem, we need to calculate the combined speed of both trains.
Train from A starts at 7 a.m. with a speed of 20 kmph.
Train from B starts at 8 a.m. with a speed of 25 kmph.
Combined speed = 20 + 25 = 45 kmph
Distance to cover = 200 km
Time taken = Distance / Combined speed = 200 / 45
= 4.44 hours
... |
Solve the following multiple choice question.
Question:
all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 150 liters was now transferred from c to b , then both the containers would... | a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 150 liters was transferred from conta... | Let's break down the problem:
We know that container b has 62.5% less milk than container a, so let's say container a has an initial quantity of 100 (we can assume the initial quantity of milk in a to be 100 for easier calculation).
Container a is filled to its brim, so the total capacity of a is 100.
Container b ha... |
Solve the following multiple choice question.
Question:
if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ?
Options:
a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64
Answer (cho... | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 64 answer : e
Final answer: e | To find the probability of all heads after 6 coin flips, we need to multiply the probabilities of getting heads on each individual flip.
The probability of getting heads on a single flip is 1/2.
The probability of getting heads on each of the 6 flips is (1/2)^6 = 1/64
So the probability of getting all heads is 1/64... |
Solve the following multiple choice question.
Question:
if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ?
Options:
a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64
Answer (cho... | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 64 answer : e
Final answer: e | To find the probability of getting heads on all 6 flips, we need to multiply the probability of getting heads on each individual flip.
Probability of getting heads on a single flip = 1/2 (given in the question)
Probability of getting tails on a single flip = 1 - Probability of getting heads on a single flip = 1 - 1/2 ... |
Solve the following multiple choice question.
Question:
if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ?
Options:
a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64
Answer (cho... | ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 64 answer : e
Final answer: e | To find the probability of getting heads on all 6 flips of a coin, we need to use the concept of probability.
Since the probability of getting heads in a single flip is 1/2, we can multiply this probability by itself 6 times (6 flips) to get the probability of getting heads on all 6 flips.
(1/2) * (1/2) * (1/2) * (1/... |
Solve the following multiple choice question.
Question:
john began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after john ?
Options:
a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Answer (choo... | carla starts 30 minutes later and it takes 3 hr for carla to meet john so john total time travelled = 3 hr + 30 minutes john distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet john in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Final answer: a | To solve this problem, we need to understand that Carla needs to catch up to John in 3 hours, which means she needs to cover the same distance that John covers in those 3 hours.
Since John is driving at 30 miles per hour, the distance he covers in 3 hours is:
Distance = Speed × Time = 30 × 3 = 90 miles
Now, if Carla... |
Solve the following multiple choice question.
Question:
john began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after john ?
Options:
a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Answer (choo... | carla starts 30 minutes later and it takes 3 hr for carla to meet john so john total time travelled = 3 hr + 30 minutes john distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet john in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Final answer: a | To solve this problem, we need to find the distance that John drives before Carla catches up with him.
Let's start by converting 3 hours into minutes. 3 hours is equal to 180 minutes.
Since Carla leaves 30 minutes after John, she will catch up with him in 180 minutes - 30 minutes = 150 minutes.
Now we need to find t... |
Solve the following multiple choice question.
Question:
john began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after john ?
Options:
a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Answer (choo... | carla starts 30 minutes later and it takes 3 hr for carla to meet john so john total time travelled = 3 hr + 30 minutes john distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet john in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Final answer: a | To solve this problem, we need to find Carla's speed to catch up to John.
Since John is driving at 30 miles per hour and Carla leaves 30 minutes after him, that means Carla is driving for 1.5 hours (60 minutes / 40 minutes per hour).
In 1.5 hours, he will cover a distance of (30 + 0.5) * 1.5 (to account for his 30 ... |
Solve the following multiple choice question.
Question:
if 12 men can reap 120 acres of land in 36 days , how many acres of land can 24 men reap in 62 days ?
Options:
a ) 266.5 , b ) 413.3 , c ) 425.8 , d ) 189.3 , e ) 249.6
Answer (choose one of a, b, c, d, e): | 12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b
Final answer: b | To solve this problem, let's use the concept of work done by a unit of work (in this case, man-days).
12 men can reap 120 acres in 36 days, so the total work done is 120 acres * 36 days = 4320 man-days.
Now, we want to know how many acres 24 men can reap in 62 days.
First, let's find the work done by 24 men in 62 ... |
Solve the following multiple choice question.
Question:
if 12 men can reap 120 acres of land in 36 days , how many acres of land can 24 men reap in 62 days ?
Options:
a ) 266.5 , b ) 413.3 , c ) 425.8 , d ) 189.3 , e ) 249.6
Answer (choose one of a, b, c, d, e): | 12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b
Final answer: b | To solve this problem, let's first calculate the rate at which each man can reap acres of land per day.
12 men can reap 120 acres in 36 days, so the rate per man per day is:
120 acres / (12 men * 36 days) = 120 / 432 = 0.2794 acres per man per day
Now, we want to find out how many acres 24 men can reap in 62 days at... |
Solve the following multiple choice question.
Question:
if 12 men can reap 120 acres of land in 36 days , how many acres of land can 24 men reap in 62 days ?
Options:
a ) 266.5 , b ) 413.3 , c ) 425.8 , d ) 189.3 , e ) 249.6
Answer (choose one of a, b, c, d, e): | 12 men 120 acres 36 days 24 men ? 62 days 120 * 24 / 12 * 62 / 36 120 * 2 * 31 / 18 240 * 1.72 = 413.3 answer : b
Final answer: b | To solve this problem, let's first find out how many acres a man can reap per day.
12 men can reap 120 acres in 36 days, so we can calculate the daily amount of land that 12 men can reap:
120 acres / 36 days = 3.33 acres per day.
Now that we know how many acres 12 men can reap per day, we can calculate how many acre... |
Solve the following multiple choice question.
Question:
a person travels equal distances with speeds of 5 km / hr , 10 km / hr , 15 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options:
a ) 1 km , b ) 1500 mts , c ) 1600 mts , d ) 2 km , e ) 1250 mts
Answer (choose one of a, b, c, d, e)... | let the each distance be x km total distance = 3 x then total time , ( x / 5 ) + ( x / 10 ) + ( x / 15 ) = 11 / 60 x = 0.5 total distance = 3 * 0.5 = 1.5 km = 1500 meters correct option is b
Final answer: b | To find the total distance traveled, we need to calculate the time taken for each leg of the journey and add them up.
Let's break it down:
Leg 1: Distance = Speed × Time
= 5 km/hr × 10 minutes
= 5 × 10 / 60 = 0.833 km (or 833 meters, since 1 km = 1000 meters)
= 833 meters
Leg 2: Distance = Speed × Time
= 10 km/hr × ... |
Solve the following multiple choice question.
Question:
a person travels equal distances with speeds of 5 km / hr , 10 km / hr , 15 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options:
a ) 1 km , b ) 1500 mts , c ) 1600 mts , d ) 2 km , e ) 1250 mts
Answer (choose one of a, b, c, d, e)... | let the each distance be x km total distance = 3 x then total time , ( x / 5 ) + ( x / 10 ) + ( x / 15 ) = 11 / 60 x = 0.5 total distance = 3 * 0.5 = 1.5 km = 1500 meters correct option is b
Final answer: b | To solve this problem, let's first convert all the speeds to a common unit. All the speeds are given in kilometers per hour, so we can convert them to meters per minute as follows:
- 5 km/hr = 5000 meters per hour = 5000/60 = 83.33 meters per minute
- 10 km/hr = 10000 meters per hour = 10000/60 = 166.67 meters per min... |
Solve the following multiple choice question.
Question:
a person travels equal distances with speeds of 5 km / hr , 10 km / hr , 15 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options:
a ) 1 km , b ) 1500 mts , c ) 1600 mts , d ) 2 km , e ) 1250 mts
Answer (choose one of a, b, c, d, e)... | let the each distance be x km total distance = 3 x then total time , ( x / 5 ) + ( x / 10 ) + ( x / 15 ) = 11 / 60 x = 0.5 total distance = 3 * 0.5 = 1.5 km = 1500 meters correct option is b
Final answer: b | To find the total distance traveled by the person, we first find the time taken to travel at each speed and then sum up the distances traveled at each speed.
Speeds:
- S1 = 5 km/hr
- S2 = 10 km/hr
- S3 = 15 km/hr
Time taken to travel at each speed:
- T1 = Distance / Speed
- T2 = Distance / Speed
- T3 = Distance / S... |
Solve the following multiple choice question.
Question:
reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 192 as interest at the end of the loan period , what was the rate of interest ?
Options:
a ) 3.6 , b ) 6 , c ) 4 , d ) can not be determined , e ) none o... | let rate = r % and time = r years . then , 1200 x r x r / 100 = 192 12 r 2 = 192 r 2 = 16 r = 4 . answer : c
Final answer: c | To solve this problem, let's use the simple interest formula:
I = P * r * t
where:
I = Interest paid
P = Principal (initial amount)
r = Rate of interest
t = Time
Given:
P = $1200
I = $192
t = ? (time)
We need to find the rate of interest (r).
Rearrange the formula to isolate r:
r = I / (P * t)
r = 192 / (1200 * t... |
Solve the following multiple choice question.
Question:
reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 192 as interest at the end of the loan period , what was the rate of interest ?
Options:
a ) 3.6 , b ) 6 , c ) 4 , d ) can not be determined , e ) none o... | let rate = r % and time = r years . then , 1200 x r x r / 100 = 192 12 r 2 = 192 r 2 = 16 r = 4 . answer : c
Final answer: c | To solve this problem, we can use the simple interest formula:
I = P * r * t
Where I is the interest, P is the principal amount, r is the rate of interest and t is the time.
Given:
P = $1200
I = $192
t = ? (we are also given that the time is equal to the rate, i.e., r)
To find the rate of interest, we can substit... |
Solve the following multiple choice question.
Question:
reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 192 as interest at the end of the loan period , what was the rate of interest ?
Options:
a ) 3.6 , b ) 6 , c ) 4 , d ) can not be determined , e ) none o... | let rate = r % and time = r years . then , 1200 x r x r / 100 = 192 12 r 2 = 192 r 2 = 16 r = 4 . answer : c
Final answer: c | To solve this problem, let's use the simple interest formula:
I = (P × R × T) / 100
Where:
I = Interest paid
P = Principal amount ($1200)
R = Rate of interest
Rearranging the formula to find the rate of interest, we get:
R = (I × 100) / (P × T)
Given that I = $192 and P = $1200, and T = amount of time (years)
R... |
Solve the following multiple choice question.
Question:
find number which is 60 % less than 80 .
Options:
a ) 18 , b ) 32 , c ) 28 , d ) 26 , e ) 98
Answer (choose one of a, b, c, d, e): | explanation : 60 % less is 40 % of the given number therefore , 40 % of 80 is 32 . answer : b
Final answer: b | To find the number which is 60% less than 80, we need to find 40% of 80 and subtract it from 80.
40% of 80 = 0.40 * 80 = 32
So, the number is 80 - 32 = 48
The correct answer is (a) 18. |
Solve the following multiple choice question.
Question:
tom , working alone , can paint a room in 10 hours . peter and john , working independently , can paint the same room in 5 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work... | let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 10 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 5 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 10 * ( t + 4 ) + 1 / 5 * ( t... | To solve this problem, we can use the concept of work done by each person per hour.
Let's denote the total work done by Tom in 8 hours of painting (2 hours solo + 6 hours with Peter and John).
In one hour, Tom does 1/10 of the work (since he can paint 1 room in 10 hours).
In 2 hours of painting with Peter and John, ... |
Solve the following multiple choice question.
Question:
tom , working alone , can paint a room in 10 hours . peter and john , working independently , can paint the same room in 5 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work... | let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 10 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 5 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 10 * ( t + 4 ) + 1 / 5 * ( t... | To solve this problem, let's calculate the work done by Tom, Peter, and John separately before and after combining.
Tom works alone for 2 hours, so he does 2/10 of the job.
Peter works independently for 2 hours, so he does 2/5 of the job.
The combined work rate of Tom and Peter working together is 2/10 + 2/5 = 12/10... |
Solve the following multiple choice question.
Question:
tom , working alone , can paint a room in 10 hours . peter and john , working independently , can paint the same room in 5 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work... | let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 10 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 5 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 10 * ( t + 4 ) + 1 / 5 * ( t... | To solve this problem, let's break it down step by step.
Let the total time to paint the room be 12 hours (4 hours by Tom, 2 hours by Peter, and 6 hours by John).
1. Tom paints for 2 hours alone (1/6 of the total job).
2. After 2 hours, Tom is left with 2/6 of the job.
- Since the rate is 1/6, Tom can paint 1/6 of... |
Solve the following multiple choice question.
Question:
oy started cycling along the boundaries of a square field from corner point a . after half an hour he reached the corner point c , diagonally opposite to a . if his speed was 8 km / hr , the area of the filed in square km is ?
Options:
['a ) 64', 'b ) 4', 'c ) 1... | explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 × 2 = 4 square km answer : b
Final answer: b | To solve this problem, we need to find the area of the square field.
The distance between points A and C is equal to the side length of the square. Since the diagonal AC forms a right angle and the points A, B and C are on the axes, we can use the Pythagorean theorem to find the distance between points A and C.
Let'... |
Solve the following multiple choice question.
Question:
oy started cycling along the boundaries of a square field from corner point a . after half an hour he reached the corner point c , diagonally opposite to a . if his speed was 8 km / hr , the area of the filed in square km is ?
Options:
['a ) 64', 'b ) 4', 'c ) 1... | explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 × 2 = 4 square km answer : b
Final answer: b | To solve this problem, we can use the concept of speed, distance, and area of a square.
Distance between point A and C =
(0.5 * side)^2 = 0.25s
Now, as the field is a square, each side has the same length.
So, side = 0.25 s
Speed = 8 km/hr
Distance = 0.25 s
Area of Square = side^2
= (0.25)^2
= 0.0625... |
End of preview. Expand in Data Studio
No dataset card yet
- Downloads last month
- 25