Question 1

What is the right most integer of the expression 65776759 + 54697467 ?

Accepted Answer

Last digit for the power of 6 is 6 (always) Power cycle of 7 is 7, 9, 3, 1. Now 467/4 gives a remainder of 3 Then the last digit is 7 3 = 3 Last digit is 6 + 3 = 9.

Question 2

A box contains 90 screws each of 100 gms and 100 bolts each of 150 gms. If the entire box weighs 35.5 kg, then the weight of the empty box is ?

Accepted Answer

Screws weight = 90x100 = 9000gms bolts weight = 100 x 150 = 15000gms weight = screws + bolts => 24000 gms =>24 kg Given entire box weight = 35.5kg empty box = entire box weight - weight => 35.5kg - 24kg => 11.5kg so the empty box is 11.5kg.

Question 3

A sequence of natural number 2,3,5,6,10. Such that no square and no cube occurs in the term. Find the 300th term of sequence ?

Accepted Answer

1 to 300 = 300 numbers squares btwn 1 to 300 = 1,4,9,16,25,36,49.....289 i.e, total 17 cubes = 1,8,27,64,125,216 i.e, 5 now 1 and 64 are common so total numbers that should be removed ( 17+5-2= 20 ) total 20 term removed so 300th term would be 320

Question 4

Which of the following is not a prime number?

Accepted Answer

A prime number is a whole number greater than 1 whose only factors are 1 and itself. Factors of 5 are 1, 5 Factors of 11 are 1, 11 Factors of 21 are 1, 3, 7, 21 Factors of 37 are 1, 37. Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.

Question 5

What should be the maximum value of B in the following equation? 8A9 – 6B2 + 4C6 = 723

Accepted Answer

1 1 8 A 9 + 4 C 6 - 6 B 2 7 2 3 We may represent the given sum, as shown below: 1 + A + C - B = 12 A + C - B = 11 Now,giving the maximum values to A and C, i.e. A = 9 and C = 9, we get B = 7.

Question 6

How many prime numbers exist in 65×359×113 ?

Accepted Answer

Given 6 5 × 35 9 × 11 3 ⇒ 2 × 3 5 × 5 × 7 9 × 11 3 ⇒ 2 5 × 3 5 × 5 9 × 7 9 × 11 3 Thus, there are (5 + 5 + 9 + 9 + 3)= 31 prime numbers.

Question 7

There are several peacocks and deers in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many peacocks are there, and how many deers ?

Accepted Answer

Let x = peacocks y = deers 2x + 4y = 200 x + y = 72 y = 72 - x 2x + 288 - 4x = 200 x = 44 peacocks y = 28 deers

Question 8

What least number must be subtracted from 13601, so that the remainder is divisible by 87 ?

Accepted Answer

87)13601(156 87 ----- 490 435 ----- 551 522 ----- 29 ----- Required number is 29.

Question 9

The sum of all two digit numbers divisible by 5 is

Accepted Answer

Required numbers are 10,15,20,25,...,95 This is an A.P. in which a=10,d=5 and l=95. Let the number of terms in it be n.Then t=95 So a+(n-1)d=95. 10+(n-1)*5=95,then n=18. Required sum=n/2(a+l)=18/2(10+95)=945.

Question 10

The difference between the place value and the face value of 7 in the numeral 967452 is

Accepted Answer

(Place value of 7)-(face value of 7) =7000-7=6993.

Question 11

A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be:

Accepted Answer

Let the Number be Y. Then Y = 296 q + 75 = (37 x 8)q +( 37 x 2) + 1 = 37 (8q + 2) + 1 Thus, when the number is divided by 37, the remainder is 1

Question 12

On dividing 2272 as well as 875 by 3-digit number N,we get the same remainder.The sum of the digits of N is:

Accepted Answer

(2272-875) = 1397, is exactly divisible by N. Now , 1397 = 11 x 127 The required 3-digit number is 127,the sum of digits is 10.

Question 13

If the product 4864*9 P 2 is divisible by 12, the value of p:

Accepted Answer

Clearly 4864 is divisible by 4 So, 9 P 2 must be divisible by 3. So (9+P+2) must be divisible by 3. So P=1.

Question 14

A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :

Accepted Answer

987 = 3 * 7 * 47. So, the required number must be divisible by each one of 3, 7, 47 553681 => (Sum of digits = 28, not divisible by 3) 555181 => (Sum of digits = 25, not divisible by 3) 555681 is divisible by each one of 3, 7, 47.

Question 15

The difference between the squares of two consecutive odd integers is always divisible by ?

Accepted Answer

Let the two consecutive odd integers be (2x + 1) and (2x + 3) Then, (2x + 3)2 - (2x + 1)2 = (2x + 3 + 2x + 1) (2x + 3 - 2x - 1) = (4x + 4)(2) = 8 (x + 1), which is always divisible by 8

Question 16

On dividing 4150 by a certain number , the quotient is 55 and the remainder is 25, the divisor is

Accepted Answer

Let Divisor be x. We know that Dividend = Remainder+Divisor×Quotient So Divisor = (Dividend - Remainder)/Quotient ⇒ x = (4150 - 25)/55 ⇒ x = 4125/55 ⇒ x = 75 Hence Divisor is 75.

Question 17

Find the next number in the series 125, 80, 45, 20, ....

Accepted Answer

The pattern is -45, -35, -25, -15 The next number = 20-15= 5

Question 18

The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :

Accepted Answer

Let the required fraction be x. Then, (1 / x )- x = 9/20 1 - x^(2) / x = 9 / 20 => 20 - 20 * x^(2) = 9 * x. 20 * x^(2) + 9 *x - 20 = 0. => (4 * x + 5) (5 * x - 4) = 0. => x = 4 / 5.

Question 19

What is the greatest of 3 consecutive integers whose sum is 24 ?

Accepted Answer

The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3 If the sum is 24, we need to solve the equation 3n + 3 = 24; => 3n = 21; => n = 7 The greatest of the three numbers is therefore 7 + 2 = 9

Question 20

If 60% of 35 of a number is 36, then the number is

Accepted Answer

Let the number be x.Then 60% of 3 5 of x=36. => 60 100 * 3 5 * x = 36 => 9 x 25 = 36 => x= 25 * 36 9 = 100 Required number is 100.

Numbers Questions