Number System - Study Mode

[#361] A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be
Correct Answer

(B) 2, 3

Explanation

Solution: 4 | x xa0 xa0 xa0 xa0 xa0 xa0 y = (5 × 1 + 4) = 9 ------------ 5 | y - 1 xa0 xa0 xa0 xa0 x = (4 × y + 1) = (4 × 9 + 1) = 37 ------------ | 1 - 4 Now, 37 when divided successively by 5 and 4, we get 5 | 37 ------------- 4 | 7 - 2 ------------- | 1 - 3 Respective remainders are 2 and 3

[#362] The sum of all three digit numbers, each of which on divide by 5 leaves remainder 3, is -
Correct Answer

(D) 99090

Explanation

Solution: $$eqalign{
& {x08f{Series :}} cr
& 103 + 108, + ........ + ,998 cr
& a{ ext{ }} = { ext{ }}103 cr
& d{ ext{ }} = { ext{ }}5 cr
& { ext{Last term = 998}} cr
& { ext{Number of term }} cr
& = frac{{998 - 103}}{5} + 1 cr
& = frac{{895}}{5} + 1 cr
& = 180 cr
& { ext{Sum of n terms}} cr
& = frac{n}{2}left[ {2a{ ext{ }} + left( {n - 1}
ight)d}
ight] cr
& = frac{{180}}{2}left[ {2 imes 103 + left( {180 - 1}
ight)5}
ight] cr
& = 99090 cr} $$

[#363] A number is divisible by 11 if the difference between the sums of the digit in odd even places respectively is :
Correct Answer

(D) Zero or a multiple of 11

Explanation

Solution: Clearly, (D) is true.

[#364] 6 × 3 (3 - 1) is equal to :
Correct Answer

(C) 36

Explanation

Solution: = 6 × 3 (3 - 1) = 6 × 3(2) = 6 × 6 = 36

[#365] 325325 is a six-digit number. It is divisible by :
Correct Answer

(D) ALL 7, 11 AND 13

Explanation

Solution: (325 - 325) = 0. Which is divisible by 7 So, the given number is divisible by 7 (5 + 3 + 2) - (2 + 5 + 3) = 0 So, the given number is divisible by 11 And, $$frac{{325325}}{{13}} = 25025$$ So, 325325 is divisible by 13