Numbers

0
2036

Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. What is the smallest prime number?

A. 0

B. 1

C. 2

D. 3


Answer

                  Ans: Option C

       Explanation:

       Smallest prime number is 2.

       0 and 1 are neither prime numbers nor composite numbers.


2. (1000)9 ÷ 1024 =?

A.10000

B.1000

C.100

D.10


Answer

                  Ans: Option B

       Explanation:

       Given Exp. = (1000)9 / 1024 = (103)/ 1024 = (10)27 / 1024 = 10(27-24) = 103 = 1000


3. What is the largest 5 digit number exactly divisible by 94?

A. 99922

B. 99924

C. 99926

D. 99928


Answer

                  Ans: Option A

       Explanation:

       Largest 5 digit number = 99999

       99999 ÷ 94 = 1063, remainder = 77

       Hence largest 5 digit number exactly divisible by 94 = 99999 – 77 = 99922 


4. 287 x 287 + 269 x 269 – 2 x 287 x 269 =?

A.534

B.446

C.354

D.324


Answer

                  Ans: Option D

       Explanation:

       Given Exp. = a2 + b2 – 2ab, where a = 287 and b = 269

        = (a – b)2 = (287 – 269)2

        = (182)

        = 324


5. If P and Q are odd numbers, then which of the following is even?

A. P + Q

B. PQ

C. P + Q + 1

D. PQ + 2


Answer

                  Ans: Option A

       Explanation:

       The sum of two odd numbers is an even number

       Hence P + Q is an even number


6. The sum of all two digit numbers divisible by 5 is:

A.1035

B.1245

C.1230

D.945


Answer

                  Ans: Option D

       Explanation:

       Required numbers are 10, 15, 20, 25… 95

       This is an A.P. in which a = 10, d = 5 and l = 95.

       tn = 95        

       a + (n – 1)d = 95

       10 + (n – 1) x 5 = 95

       (n – 1) x 5 = 85

       (n – 1) = 17

        n = 18

        Required Sum = n/2 (a + l) = 18/2 x (10 + 95)   = (9 x 105)   = 945.


7. 108 + 109 + 110 + … + 202 =?

A. 14615

B. 14625

C. 14715

D. 14725


Answer

                  Ans: Option D

       Explanation:

        Number of terms of an arithmetic progression

       n= (l−A.d+1

       where, n = number of terms, a= the first term , l = last term, d= common difference

       Sum of first n terms in an arithmetic progression

       Sn=n2[ 2a+(n−1)d ] =n2[ a+l ]where a = the first term, d= common difference, l=tn=nth term = a+(n−1)d

       a=108l=202d=109−108=1n=(l−A.d+1=(202−108)1+1=94+1=95Sn=n2[ a+l ]=952[ 108+202 ]=95×3102=95×155=14725


8. (854 x 854 x 854 – 276 x 276 x 276) / (854 x 854 + 854 x 276 + 276 x 276) =?

A.1130

C.565

D.1156

E. None of these 


Answer

                  Ans: Option B 

       Explanation:

       Given Exp. = (a3 – b3)/ (a2 + ab + b2)

        = (a – B. = (854 – 276) = 578


9. Which one of the following numbers is completely divisible by 99?

A. 115909

B. 115919

C. 115939

D. 115929


Answer

                  Ans: Option D

           If a number is divisible by two co-prime numbers, then the number is divisible by their product also.

           If a number is divisible by more than two pairwise co-prime numbers, then the number is divisible by their product also.

            If a number is divisible by another number, then it is also divisible by all the factors of that number.

            We know that 99 = 9 × 11 where 9 and 11 are co-prime numbers. Also 9 and 11 are factors of 99. Hence if a number is divisible by 9 and 11, the number will be divisible by their product 99 also.  If a number is                not divisible by 9 or 11, it is not divisible by 99. So,

            115929 is divisible by both 9 and 11 => 115929 is divisible by 99

           115939 is not divisible by 9 and 11 => 115939 is not divisible by 99

           115919 is not divisible by 9 and 11 => 115919 is not divisible by 99

           115909 is not divisible by 9 and 11 => 115909 is not divisible by 99

             Hence, 115929 is the answer


10. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?

A. 2 or 6

B.4

C.4 or 8

D.8

E.None of these 


Answer

                  Ans: Option A

       Explanation:

       80 = 2 x 5 x 8

       Since 653xy is divisible by 2 and 5 both, so y = 0.

       Now, 653x is divisible by 8, so 13x should be divisible by 8.

       This happens when x = 6.

        x + y = (6 + 0) = 6.


11. 12 + 22 + 32 + … + 82 =?

A. 204

B. 200

C. 182

D. 214


Answer

                  Ans: Option A

       Explanation:

       (Reference: Power Series : Important formulas)

        12+22+32+⋯+n2=∑n2=n(n+1)(2n+1)6

         12+22+32+⋯+82=n(n+1)(2n+1)6=8(8+1)[(2×8)+1]6=8×9×176=4×9×173=4×3×17=204


12.  The sum of even numbers between 1 and 31 is:

A.6

B.28

C.240

D.512


Answer

                  Ans: Option C

       Explanation:

       Let Sn = (2 + 4 + 6 + … + 30). This is an A.P. in which a = 2, d = 2 and l = 30

       Let the number of terms be n. Then,

       a + (n – 1)d = 30

        2 + (n – 1) x 2 = 30

        n = 15.

        Sn = n/2 (a + l) = 15/2 x (2 + 30) = (15 x 16) = 240.


13. What least number should be subtracted from 13601 such that the remainder is divisible by 87?

A. 27

B. 28

C. 29

D. 30


Answer

                  Ans: Option C

       Explanation:

       13601 ÷ 87 = 156, remainder = 29

        Hence 29 is the least number which can be subtracted from 13601 such that the remainder

        is divisible by 87


14. 3251 + 587 + 369 – ? = 3007

A.1250

B.1300

C.1375

D.1200

E.None of these 


Answer

                  Ans: Option D

       Explanation:

          3251          Let 4207 – x = 3007

       + 587          Then, x = 4207 – 3007 = 1200

       + 369

          —-

         4207

           —-


15. If (64)2 – (36)2 = 10x, then x = ?

A. 200

B. 220

C. 210

D. 280


Answer

                  Ans: Option D 

       Explanation:

       a2−b2=(a−b)(a+b)

       (64)2 – (36)2 = (64 – 36)(64 + 36) = 28 × 100

       Given that (64)2 – (36)2 = 10x

        28 × 100 = 10x

         x = 280


1
2
3
4
SHARE
Previous articleMixtures
Next articlePercentage

LEAVE A REPLY

Please enter your comment!
Please enter your name here