Number System - Study Mode

[#341] The unit's digit in the product 274 × 318 × 577 × 313 is :
Correct Answer

(A) 2

Explanation

Solution: Unit digit in the given product = Unit digit of (4 × 8 × 7 × 3), which is 2

[#342] Which one of the following is the common factor of (47 43 + 43 43 ) and (47 47 + 43 47 ) = ?
Correct Answer

(B) (47 + 43)

Explanation

Solution: When n is odd, (x n + a n ) is always divisible by (x + a). ∴ Each one of (47 43 + 43 43 ) and (47 47 + 43 47 ) is divisible by (47 + 43)

[#343] If a number 774958A96B is divisible by 8 and 9, the respective values of A and B will be :
Correct Answer

(C) 8 and 0

Explanation

Solution: Since 774958A96B is divisible by 8, so the number 96B must be divisible by 8. So, B = 0, as 960 is divisible by 8. Now, 774958A960 is divisible by 9. So, (55 + A) must be divisible by 9. This happens when A = 8 Hence, A = 8 and B = 0

[#344] The number of two digit prime numbers which remain prime even inverting the position of its digits is:
Correct Answer

(C) 9

Explanation

Solution: These numbers are 11, 13, 31, 17, 71, 37, 73, 79, 97.

[#345] The number of numbers from 1 to 200 which are divisible by neither 3 nor 7 is :
Correct Answer

(A) 115

Explanation

Solution: The required number = Number of numbers, which are (divisible by 3 + divisible by 7 - divisible by 21) Number of number divisible by 3, $$eqalign{
& { ext{ = }} {frac{{ {198 - 3} }}{3}} + 1 cr
& = 66 cr} $$ Number of number divisible by 7 $$eqalign{
& = {frac{{ {196 - 7} }}{7}} + 1 cr
& = 28 cr} $$ Number of number divisible by 21, $$eqalign{
& = {frac{{ {189 - 21} }}{{21}}} + 1 cr
& = 9 cr} $$ Thus, the divisible value $$eqalign{
& = {66 + 28 - 9} cr
& = 85 cr} $$ Thus, number of numbers which are not divisible by 3 or 7 $$eqalign{
& = { ext{ }}200{ ext{ }} - { ext{ }}85 cr
& = { ext{ }}115 cr} $$