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Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

Q11.	What is the total numbers of 3-digit numbers which are completely divisible by 6 ?

1)	140	2)	150
3)	152	4)	159
5)	None of these

Answer : 150
Explanation :

The 3-digit number divisible by 6 are : 102, 108, 114,... , 996

It is an A.P. series where a = 102, d = 6 and l = 996

Let, the number of terms be n. Then tn = 996.

or a + (n - 1) d = 996

or 102 + (n - 1) x 6 = 996

or 6 x (n - 1) = 894

or (n - 1) = 149

or n = 150

So, number of terms = 150.

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Q12.	If the number 653 xy is divisible by 90, then (x + y) = ?

1)	2	2)	3
3)	4	4)	6
5)	None of these

Answer : 4
Explanation :

90 = 10 x 9

Clearly, 653xy is divisible by 10, so y = 0

Now, 653x0 is divisible by 9.

So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4.

Hence, (x + y) = (4 + 0) = 4.

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Q13.	If n is a natural number, then (6n² + 6n) is always divisible by:

1)	6 only	2)	6 and 12 both
3)	12 only	4)	by 18 only
5)	None of these

Answer : 6 and 12 both
Explanation : (6n² + 6n) = 6n (n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.

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Q14.	What would be the unit digit of the following expressions. (123)¹²⁵ + (234) ¹²⁷ = ?

1)	4	2)	6
3)	7	4)	9
5)	None of these

Answer : 7
Explanation : We know that, any digit multiply four times, that product's unit digit will be same digit.

So,125/4 =31 quotient and 1 reminder and 127/4 = 31 divisor and 3 reminder.

Now, (123)¹ + (234)³ = 3 + 4 = 7

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Q15.	A number, when divided by 135, the reminder is 45. If the same number is divided by 27, what would be the reminder ?

1)	15	2)	18
3)	21	4)	Data Inadequate
5)	None of these

Answer : 18
Explanation : We know that, Dividend = (Divisor x Quotient) + Reminder.

So, Dividend = (135 x Quotient) + 45

Or Dividend = [ (27 x 5 x Quotient )+ (27 x 1 +18)]

When above Dividend is divided by 27, 18 will be reminder.

Short-Cut Method:

If the second divisor is a factor of the first divisor, then you just divide the second divisor with reminder.

i.e. (R₁/d₂) = R₂

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Q16.	What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?

1)	24	2)	38
3)	42	4)	48
5)	Non of these

Answer : 38
Explanation :

Let, the numbers be x and x + 2.

Then, (x + 2)² - x² = 84

or 4x + 4 = 84 or 4x = 80

or x = 20. The required sum = x + (x + 2) = 2x + 2 = 42.

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Q17.	A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. What is the number ?

1)	235	2)	253
3)	273	4)	352
5)	None of these

Answer : 253
Explanation :

Let, the middle digit be x.

Then, 2x = 10 or x = 5. So, the number is either 253 or 352.

Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.

Hence, required number = 253.

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Q18.	A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. What is the number ?

1)	18	2)	24
3)	42	4)	81
5)	None of these

Answer : 24
Explanation :

Let, the ten's and unit digit be x and y respectively.

So, xy = 8 and the number be 10x+y

When 18 is added, the number be 10x+ y +18.

Then, 10x + y + 18 = 10 y + x

or 9x - 9y = -18 x - y = - 2

We know that (x+y)²=( x-y)² + 4xy = (-2)² + 4 x 8 =36

or x+y = 6

By solving we get x = 2 and y = 4

Thus, the number is 24.

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Q19.	A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by-

1)	3	2)	5
3)	10	4)	11
5)	None of these

Answer : 11
Explanation :

Let, the ten's digit be x and unit's digit be y.

Then, number = 10x + y.

Number obtained by interchanging the digits = 10y + x.

(10x + y) + (10y + x) = 11(x + y), which is divisible by 11

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Q20.	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 ?

1)	4	2)	8
3)	12	4)	14
5)	None of these

Answer : 8
Explanation :

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

Let, ten's and unit's digits be 2x and x respectively.

Then, (10 x 2x + x) - (10x + 2x) = 36

or 9x = 36

or x = 4.

So, required difference = (2x + x) - (2x - x) = 2x = 8.

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Mathmetics

Q11.

What is the total numbers of 3-digit numbers which are completely divisible by 6 ?

Q12.

If the number 653 xy is divisible by 90, then (x + y) = ?

Q13.

If n is a natural number, then (6n² + 6n) is always divisible by:

Q14.

What would be the unit digit of the following expressions.
(123)¹²⁵ + (234) ¹²⁷ = ?

Q15.

A number, when divided by 135, the reminder is 45. If the same number is divided by 27, what would be the reminder ?

Q16.

What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?

Q17.

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. What is the number ?

Q18.

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. What is the number ?

Q19.

A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by-

Q20.

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 ?

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Mathmetics

Q11.

What is the total numbers of 3-digit numbers which are completely divisible by 6 ?

Q12.

If the number 653 xy is divisible by 90, then (x + y) = ?

Q13.

If n is a natural number, then (6n2 + 6n) is always divisible by:

Q14.

What would be the unit digit of the following expressions.(123)125 + (234) 127 = ?

Q15.

A number, when divided by 135, the reminder is 45. If the same number is divided by 27, what would be the reminder ?

Q16.

What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?

Q17.

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. What is the number ?

Q18.

A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. What is the number ?

Q19.

A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by-

Q20.

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 ?

Study Materials +

Quick Links

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If n is a natural number, then (6n² + 6n) is always divisible by:

What would be the unit digit of the following expressions.
(123)¹²⁵ + (234) ¹²⁷ = ?