# Practice Problems on Numbers – Set 1

Practice Problems on Numbers – Set 1
1. The difference between a number and its three- fifth is 50. What is the number ?
a) 50
b) 75
c) 100
d) 125
e) None of these
Explanation: Let the number be x.
Then, x-3/5x = 50 <=> 2/5x = 50 <=> x = (50*5/2) = 125

2. If a number is decreased by 4 and divided by 6, the result is 8. What would be the result if 2 is subtracted from the number and then it is divided by 5.
a) 6
b) 10
c) 2
d) 11 1/5
e) None of these
Explanation: Let the number be x. Then, x-4/6 = 8 <=> x-4 = 48 <=> x=52.
x-2/5 = 52-2/5 = 50/5 = 10.

3. If one-third of one fourth of a number is 15, then three-tenth of that number is :
a) 35
b) 36
c) 45
d) 54
e) None of these
Explanation: Let the number be x.
Then, 1/3 of 1/4 of x=15 <=> x = 15 * 12 = 180.
So, required number = (3/10 * 180) = 54.

4. A number is doubled and nine is added. If the resultant is trebled, it becomes 75. What is that number ?
a) 3.5
b) 6
c) 8
d) 9.5
e) None of these
Explanation: Let the number be x.
Then, 3(2x + 9) = 75 <=> 2x + 9 = 25 <=> 2x=16 <=> x=8.

5. Three-fourth of a number is 60 more than its one third. The number is :
a) 84
b) 108
c) 144
d) 169
e) None of these
Explanation: Let the number be x.
Then, 3/4x-1/3x = 60 <=> 5x/12 = 60 <=> x=(60*12/5) = 144.

6. What is the four digit number in which the first digit is 1/3 of the second, the third is the sum of the first and second, and the last is three times the second?
a) 1349
b) 6286
c) 2686
d) 1341
e) None of these
Explanation: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349.

7. What least number must be added to 859622, to get a number exactly divisible by 456?
a) 485
b) 394
c) 62
d) 387
e) None of these
Explanation: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.

8. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
a) 6
b) 8
c) 4
d) 5
e) 7
Explanation: Let the number be  xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x >  unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8

9. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
a) 10
b) 30
c) 40
d) Can’t be determined
e) None of these