Quantitative aptitude Question for all banking Bank PO,Clerk,IBPS PO,Railway,SSC,PSUs,IAS,OAS ,C-SAT Exams

Mathmetics

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

Q21.	What will be remainder when (67⁶⁷ + 67) is divided by 68 ?

1)	1	2)	53
3)	66	4)	67
5)	None of these

Answer : 66
Explanation :

(xⁿ + 1) will be divisible by (x + 1) only when n is odd.

(67⁶⁷ + 1) will be divisible by (67 + 1)

(67⁶⁷ + 1) + 66, when divided by 68 will give 66 as remainder.

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Q22.	The product of two numbers is 120 and the sum of their squares is 289. What is the The sum of the number ?

1)	19	2)	21
3)	23	4)	45
5)	None of these

Answer : 23
Explanation :

Let, the numbers be x and y.

Then, xy = 120 and x² + y² = 289.

(x + y)² = x² + y² + 2xy = 289 + (2 x 120) = 529

x + y = 529 = 23.

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Q23.	Find the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder ?

1)	1601	2)	2601
3)	3601	4)	3611
5)	None of these

Answer : 3601
Explanation :

Since, the number on division by 5, 6, 8, 9 and 12 leaves remainder 1 in each case, the required number is

= Multiple of LCM of ( 5, 6, 8,9,12) +1

= Multiple of 360 +1 = 360K +1 (say)

(where K is a +ve integer)

Now, 360K + 1 is divisible by 13.

But 360K +1 = 27 13K + 9K +1

Since 2713K is divisible by 13, 9K+1 should also be divisible by 13 so that the required number is (9K + 1= 9 10 + 1=91)

Required number = 360 10 + 1 = 3601

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Q24.	Two different numbers when divided by a certain divisor leave remainders 547 and 349 respectively. when the sum of the two numbers is divded by the same divisor, the remainder is 211. Find the divisor ?

1)	687	2)	685
3)	697	4)	684
5)	None of these

Answer : 685
Explanation :

Let, the two numbers be �a� and 'b'.

As per question, if �a� is divisible by a certain number 'c' (say) it leaves remainder 547 or (a) -547 is exactly divisible by c.

Also, if �b� is divided by 'c' it leaves remainder 349 (b-349) is exactly divisible by c.

Also, if (a +b) is divisible by c it leaves remainedr 211 or ( a+b-211) is exactly divisible by c.

a - 547 + b-349 = a+b -896 is also divisible by c.

[If two numbers are divisible by a certain number, their sum/difference will also be divisible by that number].

Similarly, ( a+b-211) - (a+b-896) = 685 is also divisible by c.

Prime factors of 685 are 5, 137 and 685

c may be 5, 137 or 685.

As the remainders in the three cases given in the question are 547, 349 and 211 respectively, the divisor should be greater than 547.

c is 685 (Divisor).

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Q25.	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. The number is:

1)	145	2)	253
3)	370	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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Q26.	What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?

1)	34	2)	38
3)	42	4)	46
5)	None of these

Answer : 42
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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Q27.	The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

1)	380	2)	395
3)	400	4)	425
5)	None of these

Answer : 400
Explanation : Let the numbers be x and y.
    Then, xy = 9375 and     x/y = 15.
    X = 15y
   So, y x 15y = 15y² = 9375
    or y² = 625.         y = 25.
    x = 15y = (15 x 25) = 375.
    Thus, Sum of the numbers = x + y = 375 + 25 = 400.

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Q28.	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:

1)	20	2)	30
3)	40	4)	24
5)	None of these

Answer : 20
Explanation : Let the numbers be x, y and z.
Then, x² + y² + z² = 138 and (xy + yz + zx) = 131.
or (x + y + z)² = x² + y² + z² + 2(xy + yz + zx) = 138 + 2 x 131 = 400.
or (x + y + z) = 20.

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Q29.	The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?

1)	69	2)	78
3)	96	4)	D.I
5)	None of these

Answer : D.I
Explanation : Let the ten's digit be x and unit's digit be y.
    Then, x + y = 15 and x - y = 3   or   y - x = 3.
    Solving x + y = 15   and   x - y = 3, we get: x = 9, y = 6.
    Solving x + y = 15   and   y - x = 3, we get: x = 6, y = 9.
    So, the number is either 96 or 69.
    Hence, the number cannot be determined.

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Q30.	The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

1)	3	2)	4
3)	9	4)	D.I
5)	None of these

Answer : 4
Explanation : Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
or 9(x - y) = 36 or x - y = 4.

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Mathmetics

Q21.

What will be remainder when (6767 + 67) is divided by 68 ?

Q22.

The product of two numbers is 120 and the sum of their squares is 289. What is the The sum of the number ?

Q23.

Find the least number which on being divided by 5, 6, 8, 9, 12 leaves in each case a remainder 1 but when divided by 13 leaves no remainder ?

Q24.

Two different numbers when divided by a certain divisor leave remainders 547 and 349 respectively. when the sum of the two numbers is divded by the same divisor, the remainder is 211. Find the divisor ?

Q25.

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. The number is:

Q26.

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

Q27.

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

Q28.

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:

Q29.

The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?

Q30.

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

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What will be remainder when (67⁶⁷ + 67) is divided by 68 ?