Question 1

How many remainders are possible if 16n is divided by 9 for any positive integral value of n ?

Accepted Answer

When 16 n is divided by 9, we have 16 1 9 , remainder = 7 16 2 9 , remainder = 4 16 3 9 , remainder = 1 16 4 9 , remainder = 7 16 5 9 , remainder = 4 16 6 9 , remainder = 1 So, we have cyclicity of 3 factors i.e 7,4,1. Hence only 3 remainders are possible.

Question 2

Find the remainder when 1234 x 1235 x 1237 is divided by 8.

Accepted Answer

When we divide 1234 by 8, remainder is 2 When we divide 1235 by 8, remainder is 3 When we divide 1237 by 8, remainder is 5 ---> 2 x 3 x 5 = 30 As 30 will not be the remainder because it is greater than 8, when 30 divided by 8, remainder = 6.

Question 3

A six-digit number is formed by repeating a three-digit number; for example, 404404 or 415415 etc. Any number of this form is always exactly divisible by

Accepted Answer

Here by trial and error method, we can obseve that 404404 = 404 x 1001; 415415 = 415 x 1001, etc. So, any number of this form is divisible by 1001.

Question 4

A teacher multiplies 987 by a certain number and obtains 556781 as her answer. If in the answer, both 6 and 7 are wrong but the other digits are correct, then the correct answer will be

Accepted Answer

Given number is 987 = 3 x 7 x 47. So, required number must be divisible by each one of 3, 7, 47. None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7. Correct answer is 555681.

Question 5

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 6

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 7

How many digits will be there to the right of the decimal point in the product of 85.44 and .08455 ?

Accepted Answer

Sum of decimal places = 7. Since the last digit to the extreme right will be zero (since 4 x 5 = 20), so there will be 6 significant digits to the right of the decimal point.

Question 8

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 9

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 10

If n is even, which of the following cannot be odd?

Accepted Answer

In case B, odd times even will give even

Question 11

A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?

Accepted Answer

A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5 Consider the answer choices in turn. 8 is the cube of 2, and p is a cube, and so the product will also be a cube. pq will also be a cube as shown above. pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube. -p will be a cube. Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

Question 12

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 13

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 14

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 15

If 1/a+1/b+1/c = 1/(a+b+c) where a+b+c not equals '0', abc not equals '0', What is the value of (a+b) (b+c) (a+c) ?

Accepted Answer

Let assume the value of a,b &c that will satisfy the equation. so a=1,b=1,c= -1 or a=1,b= -1 &c=1 or a= -1,b=1,c=1 here all three cases satisfy the equation assume any one a=1,b=1,c= -1 Hence (a+b)(b+c)(c+a)=(1+1)(1-1)(-1+1) = 0

Question 16

Which of the following is a rational number?

Accepted Answer

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero. Every integer is a rational number since Q can be 1. Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions. Hence, 4 is a rational number in the given options.

Question 17

Which of the following is the largest?

Accepted Answer

In the given options, 12/49 can be written as 1/(49/12) = 1/4.083 7/30 can be written as 1/(30/7) = 1/4.285 13/56 can be written as 1/(56/13) = 1/4.307 11/46 can be written as 1/(46/11) = 1/4.1818 Here in the above, 1/4.083 has the smallest denominator and so 12/49 is the largest number or fraction.

Question 18

If a2 = 12, then a4 =?

Accepted Answer

Given a x a = 12 asked to find a x a x a x a = (a x a) x (a x a) a4 = a2 x a2 = 12 x 12 = 144. More :: Mathematical operations questions and answers.

Question 19

A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?

Accepted Answer

When the larger cube is cut into smaller cubes, the corner cubes will have paint on three sides. The cubes in the middle of the faces will have paint on only one side, but the cubes cut from the edges will have paint on two sides. In this case, there will be only one cube one each edge (excluding the corners), and since there are 12 edges, there will be 12 cubes with paint on two sides.

Question 20

Which of the following can be used to illustrate that not all prime numbers are odd?

Accepted Answer

The only even numbers in the list are 2 and 4, but 4 is not a prime. So 2 can be used to illustrate the statement that all primes are not odd.

Numbers Questions