The sum of the digits of two-digit number is 5. If the number is reversed, the number is decreased by 27. Find the number?
Let the number be (10a + b)
given, a +b = 5 and (10a + b) – (10b +a) = 27
a – b = 3 and a +b = 5
The ratio between a two-digit number and the sum of the digits of that number is 3:1. If the digit in the unit’s place is 5 more than digit at ten’s place, what is the number?
Let the two-digit number be 10a + b
(10a + b)/(a+b) = 3/1, 7a = 2b
And also given b = 5 + a
Solve both equations to get the number
How many numbers are there up to 1000 which are divisible by 4, 6 and 8 together?
LCM of 4,6 and 8 is 24
Divide 1000 by 24, we get quotient = 41 and 16 as remainder
so 41 numbers are there which are divisible by 4,6 and 8 together.
What is the number in the unit place of the number (129)58?
[(129)2]29 = (1)29 = 1 (92 always result in 1 on unit place)
A number when divided by 5 leaves a remainder 4. What is the remainder when the square of the same number is divided by 5?
Le the number be 5a + 4
square of the number = 25a2 + 16 + 40a
so remainder = 1 (16 divided by 5 leaves a remainder 1)
When a number is divided by 527 gives the remainder as 21. When the same number is divided by 17, the remainder will be?
Let the number be 527a + 21
when divided by 17, 527a is divisible by 17 and leaves remainder as 4 when 21 is divided by 17
If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 is added to the denominator it becomes 1/6 then find the difference between numerator and denominator is
(a +4)/b = 1/3 and a/(b+3) = 1/6 solve both the equations, u will get a = 5 and b = 27
When one-fourth of a number is added to 16, it becomes three-fourth of itself. Find the number?
a/4 + 16 = 3a/4,
2a/4 = 16, so a = 32
In the examination a candidate must get 3/8 marks to pass, out of total marks. Shyam appeared in the exam and got 300 marks and still failed by 36 marks. The maximum mark is
Let total marks = M
(3/8)*M = 300 + 36 = 336
M = 112*8 = 896
Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor?
Let us say that the two numbers are 'a' and 'b' and the divisor is 'd'
We are given that
Rem [a/d] = 11 and Rem [b/d] = 21
We are also given that the Remainder [(a + b)/d] = 4
=> Rem[(11 + 21)/d] = 4
=> Rem[32/d] = 4
=> 32 - 4 = 28 is divisible by 'd' or 'd' is a factor of 28
=> 'd' could be 1, 2, 4, 7, 14, or 28
We also know that 'd' is greater than 21 because 'b' when divided by 'd' leaves a remainder of 21.
=> The value of 'd' is 28
A number is multiplied by 561, and the result obtained is 32,582. But it was found that both 2 in the number are wrong, what should be the correct answer?
561 = 3*11*17
So the number must be divided by 3, 11 and 17
Only B option is divided by all.
If the number 10*47* is divisible by both 5 and 11, then the missing digits are respectively
Check the options in the number 10x47y
all numbers will be divisible by 5 because in end it is 5 and 0
for number to be divisible by 11, (y+4+0) – (7+x+1) should be divisible by 11
from option A, y = 5, x = 1 gives (y+4+0) – (7+x+1) as 0 which is divisible by 11
The sum of digits of a two digit number is 6. The ratio of the original number to the number formed by interchanging its digits is 4 : 7. Find the number.
Let the number is 10x+y
So x+y = 6
And (10x+y)/(10y+x) = 4/7
Solve, 2x = y and from above we have x+y = 6
Solve both equations, x = 2, y = 4
When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest product possible?
13x + 13 which is divisible by 5, or 13(x+1) should be divisible by 5. The smallest value of x = 4 to be put here to make it divisible by 5. So the number is 13(4+1)
Find the least number which must be subtracted from 103876 to make the obtained number divisible by 16.
103876/16 gives remainder 4, so 4 should be subtracted
The difference between two numbers is 2577. The quotient and remainder are respectively 26 and 2 when the larger number is divided by the smaller one. What is the largest number?
Smaller no = x, then larger = x+2577
Now x+2577 = 26x + 2
Solve, x = 103
So larger no is = 103+2577
The difference between the digits of a two digit number is 5. Also the original number is 18 more than two times the number obtained by reversing its digits. Find the original number.
Let number is 10x+y
Then x-y = 5 or y-x = 5
Now given that, 10x+y = 2(10y+x) + 18 Solve, 8x – 19y = 18
Now solve: 8x – 19y = 18 and x-y = 5. In this y = 2, x = 7
And also solve; 8x – 19y = 18 and y-x = 5. In this y come to be negative which is not possible so discard this
So number is 10*7 + 2
A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?
Let x be the quotient, then that number becomes 462*x + 25
Which = (22x * 14) + (14*1)+11
Which = 14 (22x + 1) + 11
Kavya attends 40 questions and get 96 marks. If 3 marks are given for each correct answer and 1 mark is deducted for each wrong answer, find the number of question she attended correct?
Let she attend x correct answers out of 40, then incorrect = 40-x
So x*3 – (40-x)*1 = 96
Solve, x = 34
When 1 is added to the numerator of a fraction it becomes 1/4 and 1 is subtracted from the denominator of that fraction it becomes 1/5. Find the fraction.
Let fraction = x/y
Then (x+1)/y = 1/4
And x/(y-1) = 1/5
Solve both equations, x = 3, y = 16