Introduction to quantitative reasoning math
Quantitative reasoning is one of the most useful application in mathematics concepts and skills.It is used to solve the real-world problems. The students must solve this quantitative reasoning for improve their skills. It is very useful to solve the real life problems also.Here some of the quantitative reasoning problems has been solved. The practice problems are very useful to the students to improve their knowledge in the quantitative reasoning mathematics.
Number Theory Problems in Quantitative Reasoning Math
Find the largest number which perfectly divide 10110-1
Solution:
Given number is 10110-1
The simple way to solve the math problem is given below
1012 = 10201.
1012 - 1 = 10200. This is divisible by 100.
Similarly for 1013 - 1 = 1030301 - 1 = 1030300.
So you can conclude that (1011 - 1) to (1019 - 1) will be divisible by 100.
(10110 - 1) to (10199 - 1) will be divisible by 1000.
Therefore, (10110 - 1) will be divisible by the large number 10^10
2.Find the minimum value of tiles required in a top floor of breadth 3 meters 78 cm and height 1 meters 74 cm?
Solution for math:
The tiles used in top floor are square. Therefore, the breadth of the tile = height of the tile. As we have to usewhole number of tiles, the side of the tiles should a factor of both 3 m 78 cm and 1m 74. And it should be the highest factor of 3m 78 cm and 1m 74.
3 m 78 cm = 378 cm and 1 m 74 cm = 174 cm.
The HCF of 378 and 174 = 6
Hence, the side of the square is 6.
The number of such tiles required =` (378xx174)/(6xx6)`
The total tiles required = 1827 marbles.
Percentage Problems in Quantitative Reasoning Math
If the price of book increases by 10% and Raj intends to spend only an additional 5% on book, by how much % will he reduce the quantity of book purchased?
Solution for math:
Let the price of 1 book be Rs.x and let Raj initially buy 'y' books.
Therefore, he would have spent Rs. xy on book
When the price of book increases by 10%, the new price per l book is 1.10x.
Raj intends to increase the amount he spends on book by 5%.
i.e., he is willing to spend xy + 5% of xy = 1.05xy
Let the new quantity of book that he can get be 'q'.
Then, `1.10x * q = 1.05xy`
Or `q = (1.05xy)/(1.10x)=(1.05)/(1.10)` y= 0.95y.
As the new quantity that he can buy is 0.95y, he gets 0.05y lesser than what he used to get earlier.
Or a reduction of 5%.
2. A student who gets 10% marks fails by 5 marks but another student who gets 21% marks gets 6% more than the passing marks. Find the maximum marks.
Solution for math
From the given data pass percentage is 21% - 6% = 15%
By hypothesis, 15% of x – 10% of x = 5 (marks)
i.e., 5% of x = 5
Therefore, x = 100 marks.
Quantitative reasoning is one of the most useful application in mathematics concepts and skills.It is used to solve the real-world problems. The students must solve this quantitative reasoning for improve their skills. It is very useful to solve the real life problems also.Here some of the quantitative reasoning problems has been solved. The practice problems are very useful to the students to improve their knowledge in the quantitative reasoning mathematics.
Number Theory Problems in Quantitative Reasoning Math
Find the largest number which perfectly divide 10110-1
Solution:
Given number is 10110-1
The simple way to solve the math problem is given below
1012 = 10201.
1012 - 1 = 10200. This is divisible by 100.
Similarly for 1013 - 1 = 1030301 - 1 = 1030300.
So you can conclude that (1011 - 1) to (1019 - 1) will be divisible by 100.
(10110 - 1) to (10199 - 1) will be divisible by 1000.
Therefore, (10110 - 1) will be divisible by the large number 10^10
2.Find the minimum value of tiles required in a top floor of breadth 3 meters 78 cm and height 1 meters 74 cm?
Solution for math:
The tiles used in top floor are square. Therefore, the breadth of the tile = height of the tile. As we have to usewhole number of tiles, the side of the tiles should a factor of both 3 m 78 cm and 1m 74. And it should be the highest factor of 3m 78 cm and 1m 74.
3 m 78 cm = 378 cm and 1 m 74 cm = 174 cm.
The HCF of 378 and 174 = 6
Hence, the side of the square is 6.
The number of such tiles required =` (378xx174)/(6xx6)`
The total tiles required = 1827 marbles.
Percentage Problems in Quantitative Reasoning Math
If the price of book increases by 10% and Raj intends to spend only an additional 5% on book, by how much % will he reduce the quantity of book purchased?
Solution for math:
Let the price of 1 book be Rs.x and let Raj initially buy 'y' books.
Therefore, he would have spent Rs. xy on book
When the price of book increases by 10%, the new price per l book is 1.10x.
Raj intends to increase the amount he spends on book by 5%.
i.e., he is willing to spend xy + 5% of xy = 1.05xy
Let the new quantity of book that he can get be 'q'.
Then, `1.10x * q = 1.05xy`
Or `q = (1.05xy)/(1.10x)=(1.05)/(1.10)` y= 0.95y.
As the new quantity that he can buy is 0.95y, he gets 0.05y lesser than what he used to get earlier.
Or a reduction of 5%.
2. A student who gets 10% marks fails by 5 marks but another student who gets 21% marks gets 6% more than the passing marks. Find the maximum marks.
Solution for math
From the given data pass percentage is 21% - 6% = 15%
By hypothesis, 15% of x – 10% of x = 5 (marks)
i.e., 5% of x = 5
Therefore, x = 100 marks.
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