Numbers

Question: If the number 42573 * is exactly divisible by 72, then the minimum value of * is:

[A].

4

[B].

5

[C].

6

[D].

7

Answer: Option C

Explanation:

72 = 9 x8, where 9 and 8 are co-prime.

The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6.

Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.

Required value of * is 6.

Question:
Which one of the following numbers is completely divisible by 99?

[A].

3572404

[B].

135792

[C].

913464

[D].

114345

Answer: Option D

Explanation:

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisibleby 11 as well as 9. So, it is divisible by 99.

Question: Which one of the following numbers is completely divisible by 45?

[A].

181560

[B].

331145

[C].

202860

[D].

2033555

Answer: Option C

Explanation:

45 = 5 x 9, where 5 and 9 are co-primes.

Unit digit must be 0 or 5 and sum of digits must be divisible by 9.

Among given numbers, such number is 202860.

Question:
If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:

[A].

1

[B].

2

[C].

3

[D].

4

Answer: Option C

Explanation:

Then number 6×2 must be divisible by 8.

   x = 3, as 632 is divisible 8.

Question:
If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be:

[A].

3

[B].

2

[C].

1

[D].

5

Answer: Option A

Explanation:

Given number = 97215×6

(6 + 5 + 2 + 9) – (x + 1 + 7) = (14 – x), which must be divisible by 11.

  x = 3

Question:
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:

[A].

2

[B].

5

[C].

6

[D].

7

Answer: Option D

Explanation:

Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.

   x = 7.

Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
[A].

0 

[B].

1

[C].

2

[D].

None of these

Answer: Option C

Explanation:

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.

  x = 2.

Question:
What is the unit digit in 7105 ?

[A].

1

[B].

5

[C].

7

[D].

9

Answer: Option C

Explanation:

Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]

But, unit digit in (74)26 = 1

Unit digit in 7105 = (1 x 7) = 7

Question:
If (64)2 – (36)2 = 20 x x, then x = ?

[A].

70

[B].

120

[C].

180

[D].

140

Answer: Option D

Explanation:

20 x x = (64 + 36)(64 – 36) = 100 x 28

x =	100 x 28	= 140
	20

Question:
397 x 397 + 104 x 104 + 2 x 397 x 104 = ?

[A].

250001

[B].

251001

[C].

260101

[D].

261001

Answer: Option B

Explanation:

Given Exp.	= (397)2 + (104)2 + 2 x 397 x 104
	= (397 + 104)2
	= (501)2 = (500 + 1)2
	= (5002) + (1)2 + (2 x 500 x 1)
	= 250000 + 1 + 1000
	= 251001