# Number System Questions Pg1

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442 1. When the number x is divided by a divisor it’s seen that the divisor = 4 times the quotient = double the remainder. If the remainder is 80 then the worth of x is
1.  9680
2. 8460
3. 6480
4. 4680

### Answer is c

From the question
Divisor=4 × Quotient = 2 × reminder
Given reminder = 80
Divisor = 2 × 80 = 160
Quotient =160 ÷ 4 = 40
We have, Dividend = Divisor × Quotient + Remainder
Dividend = 160 × 40 + 80 =6480

2. A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it’s successively divided by 5 and 4 the respective remainders are going to be

1.  3, 2
2. 1, 2
3. 2, 3
4. 4, 1

### Answer is c

Let the number be x

x ÷ 4 leaves remainder 1 and quotient y
y ÷ 5 leaves remainder 4 and quotient 1
y=5 × 1 + 4 = 9
x=4 × y + 1 = 4 × 9 + 1 =37
37 ÷ 5 leaves remainder 2 and quotient 7
7 ÷ 4 leaves remainder 3 and quotient 1

3. When a student was asked to multiply a number by 3/2 instead he divided that number by 3/2. His result was 10 less than the right answer. The number was:

1.  15
2. 12
3. 5
4. 20

### Answer is b

Let, Given number be x.
Student was asked to multiply number with 3/2 =x × (3/2)
But, Student divided with 3/2 =x ÷ (3/2)
According to problem difference of these two is equal to 10
[x × (3/2) ]- [3/2 =x ÷ (3/2)] = 10
(3x/2)-(2x/3) = 10
(9x-4x)/6 = 10
X = 12

4. A number, when divided by 52, gives remainder 45. If this number is divided by 13, the remainder is going to be

1.  6
2. 7
3. 12
4. 5

### Answer is a

Here 13 is a factor of 52.
So, we can directly divide the remainder by 45 to get resultant remainder
45/13 quotient is 3 and remainder is 6

5. When two numbers each divided by the same divisor, give remainders 3 and 4 respectively. If the sum of the 2 numbers is divided by the same divisor, the remainder is 2. The divisor is

1.  3
2. 9
3. 7
4. 5

### Answer is d

Divisor = First Reaminder + Second Remainder – Third Remainder
Divisor = 3 + 4 – 2 = 5

Read More: Number System Concepts