Numbers- Aptitude Questions and Answers

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Evaluate 743 x 999 ?

A)

724457


B)

784527


C)

742257


D)

74257



Correct Answer :

742257


Explanation :

743 × 999
=743 × (1000 – 1)
=743000 – 743
=742257

How many three digit numbers are divisible by 5?

A)

200


B)

180


C)

175


D)

10



Correct Answer :

180


Explanation :

smallest 3 digit number divisible by 5 is first term, a =100
common difference ,d =5
greatest 3 digit number divisible by 5 is nth term, an =995

AP(Arithmetic Progression)
an=a+(n-1)d
995=100+(n-1)5
995=95+5n
900=5n
n=180

So , the three digits number which is divisible by 5 is 180

X is a whole number. If the only common factors of X and X2 are 1 and X, then X is _______?

A)
1

B)
a perfect square

C)
an odd number

D)
a prime number


Correct Answer :

a prime number


Explanation :

A number that is divisible only by itself and 1 is called prime number.
so here X is a prime number.

What least number must be added to 3000 to obtain a number exactly divisible by 19?

A)
1

B)
2

C)
3

D)
4


Correct Answer :

2


Explanation :

On dividing 3000 by 19 we get 17 as remainder
Therefore number to be added = 19-17=2

means 3000+2 = 3002 is fully divided by 19
3002/19=158

Find the unit's digit in the product 2467153 * 34172?

A)
1

B)
3

C)
7

D)
9


Correct Answer :

7


Explanation :

2467153 * 34172
Unit's digit in the given product=Unit's digit in 7 153 * 172
Now 7 4 gives unit digit 1
7 152 gives unit digit 1
7 153 gives 1*7=7
Also 172 gives 1
Hence unit's digit in the product ,7 153 * 172=7*1=7

Find the total number of prime factors in 411 *7 5 *112 ?

A)
17

B)
23

C)
27

D)
29


Correct Answer :

29


Explanation :

411 *7 5 *112= (2*2) 11 *7 5 *112
= 222 *7 5 *112
Total number of prime factors=22+5+2=29

A positive number which when added to 1000 gives a sum , which is greater than when it is multiplied by 1000. The positive integer is?

A)
1

B)
3

C)
5

D)
7


Correct Answer :

1


Explanation :

1000+N>1000N
clearly N=1

How many numbers between 11 and 90 are divisible by 7?

A)
10

B)
11

C)
12

D)
7


Correct Answer :

11


Explanation :

The required numbers are 14,21,28,...........,84
This is an A.P with a=14,d=7
Let it contain n terms
then T =84=a+(n-1)d
=14+(n-1)7
=7+7n
7n=77 =>n=11

Find the sum of all odd numbers up to 100?

A)
1700

B)
2200

C)
2500

D)
2800


Correct Answer :

2500


Explanation :

The given numbers are 1,3,5.........99.
This is an A.P with a=1,d=2.
Let it contain n terms 1+(n-1)2=99
=>n=50
Then required sum =n/2(first term +last term)
=50/2(1+99)=2500

How many terms are there in 2,4,6,8..........,1024?

A)
10

B)
14

C)
18

D)
22


Correct Answer :

10


Explanation :

Clearly 2,4,6........1024 form a G.P with a=2,r=2
Let the number of terms be n
then 2*2 n-1=1024
2n-1 =512=29
n-1=9
n=10

Find the sum of 2+22+23+24+25..........+28=?

A)
430

B)
440

C)
510

D)
560


Correct Answer :

510


Explanation :

Given series is a G.P with a=2,r=2 and n=8.
Sum Sn=a( r n - 1) / r-1 if |r| > 1
Sn=2(28 - 1)/ 2-1
=2*(256-1)/1
=2*255
=510

Find the number of zeros in 27! (Factorial of 27)?

A)
2

B)
4

C)
5

D)
6


Correct Answer :

6


Explanation :

Number of Trailing Zeros at the end of a factoria-
To determine the number of zeros at the end of a factorial, recursively divide the number by 5 until the quotient is less than 5, and sum the results after applying the greatest integer function.
For example,
8! = 40320 , the number of trailing zeros in 8! is ([8/5]=1) = 1
10! = 3628800, the number of trailing zeros in 10! is ([10/5]=2) = 2
the number of trailing zeros in 50! is ([50/5]=10) + ([10/5]=2) = 12

the number of trailing zeros in 27! is ([27/5]=5) + ([5/5]=1) = 6 zeros

Find the remainder when 231 is divided by 5?

A)
3

B)
4

C)
5

D)
7


Correct Answer :

270


Explanation :

210 =1024.
unit digit of 210 * 210 * 210 is 4
as 4*4*4= 64 gives unit digit 4
unit digit of 231 is 4*2= 8.
Now 8 when divided by 5 gives 3 as remainder.
231 when divided by 5 gives 3 as remainder.

In doing a division of a question with zero remainder,a candidate took 12 as divisor instead of 21.The quotient obtained by him was 35. The correct quotient is?

A)

0


B)
12

C)
13

D)
20


Correct Answer :

20


Explanation :

Number = Quotient x Divisor + Remainder
Here remainder = 0
So, Number = Quotient x Divisor

Divisor taken = 12
Quotient obtained = 35,
Remainder = 0
So, Number = (35 x 12) = 420

Now, the divisor was wrongly taken as 12 instead of 21
Number = 420,
Divisor = 21
Remainder = 0
So, for correct divisor we have
420 = Quotient x 21

So, Quotient = 420/21 = 20
The correct quotient is 20

If a number is multiplied by 22 and the same number is added to it then we get a number that is half the square of that number. Find the number?

A)

45


B)
46

C)
47

D)
48


Correct Answer :

46


Explanation :

Let the required number be x.
Given that 22*x+x = x2/ 2
23x = x2/ 2
23 = x/ 2
x = 2*23= 46
the required number is 46

Find the number of zeros in the factorial of the number 18?

A)

1


B)
2

C)
3

D)
4


Correct Answer :

3


Explanation :

Number of Trailing Zeros at the end of a factoria-
To determine the number of zeros at the end of a factorial, recursively divide the number by 5 until the quotient is less than 5, and sum the results after applying the greatest integer function.
For example,
8! = 40320 , the number of trailing zeros in 8! is ([8/5]=1) = 1
10! = 3628800, the number of trailing zeros in 10! is ([10/5]=2) = 2
the number of trailing zeros in 50! is ([50/5]=10) + ([10/5]=2) = 12

18! = 6402373705728000 , the number of trailing zeros in 18! is ([18/5]=3) = 3

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