Numbers

Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
[A].

3

5

[B].

3

10

[C].

4

5

[D].

4

3

Answer: Option C

Explanation:

Let the required fraction be x. Then	1	– x =	9
	x		20

	1 – x2	=	9
	x		20

     20 – 20×2 = 9x

     20×2 + 9x – 20 = 0

     20×2 + 25x – 16x – 20 = 0

     5x(4x + 5) – 4(4x + 5) = 0

     (4x + 5)(5x – 4) = 0

x =	4
	5

Question:
The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?

[A].

12

35

[B].

1

35

[C].

35

8

[D].

7

32

Answer: Option A

Explanation:

Let the numbers be a and b. Then, a + b = 12 and ab = 35.

	a + b	=	12			1	+	1		=	12
	ab		35			b		a			35

Sum of reciprocals of given numbers =	12
	35

Question:
In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ?

[A].

0

[B].

12

[C].

13

[D].

20

Answer: Option D

Explanation:

Number = (12 x 35)

Correct Quotient = 420 21 = 20

Question:
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

[A].

240

[B].

270

[C].

295

[D].

360

Answer: Option B

Explanation:

Let the smaller number be x. Then larger number = (x + 1365).

x + 1365 = 6x + 15

5x = 1350

x = 270

Smaller number = 270.

Question:
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?

[A].

0

[B].

1

[C].

2

[D].

4

Answer: Option D

Explanation:

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

    x = 5k + 3

    x2 = (5k + 3)2

   = (25k2 + 30k + 9)

   = 5(5k2 + 6k + 1) + 4

On dividing x2 by 5, we get 4 as remainder.

Question:
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?

[A].

0

[B].

3

[C].

5

[D].

11

Answer: Option C

Explanation:

Let x be the number and y be the quotient. Then,

x = 357 x y + 39

  = (17 x 21 x y) + (17 x 2) + 5

  = 17 x (21y + 2) + 5)

Required remainder = 5.

Question: On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ?
[A].

4

[B].

5

[C].

6

[D].

7

Answer: Option B

Explanation:

Formula: (Divisor*Quotient) + Remainder = Dividend.

Soln:

(56*Q)+29 = D ——-(1)

D%8 = R ————-(2)

From equation(2),

((56*Q)+29)%8 = R.

=> Assume Q = 1.

=> (56+29)%8 = R.

=> 85%8 = R

=> 5 = R.

Question:
On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder ?

[A].

0

[B].

1

[C].

2

[D].

3

Answer: Option B

Explanation:

Number = 269 x 68 + 0 = 18292

67) 18292 (273
134
—-
489
469
—-
202
201
—
1
—

Therefore, Required remainder = 1

Question:
In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ?

[A].

4236

[B].

4306

[C].

4336

[D].

5336

Answer: Option D

Explanation:

Divisor = (5 x 46) = 230

10 x Quotient = 230     =	230	= 23
	10

Dividend = (Divisor x Quotient) + Remainder

    = (230 x 23) + 46

    = 5290 + 46

    = 5336.

Question: What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
[A].

0 

[B].

2

[C].

3

[D].

5

Answer: Option A

Explanation:

Unit digit in (6374)1793 = Unit digit in (4)1793

    = Unit digit in [(42)896 x 4]

    = Unit digit in (6 x 4) = 4

Unit digit in (625)317 = Unit digit in (5)317 = 5

Unit digit in (341)491 = Unit digit in (1)491 = 1

Required digit = Unit digit in (4 x 5 x 1) = 0.