Number System - Study Mode
[#351] The sum of two numbers is 18. The greatest product of these two number can be:
Correct Answer
(B) 81
Explanation
Solution: a + b = 18 So, maximum of (a × b) will be only when a = b Thus, a = b = 9 Maximum of (a × b) = 9 × 9 = 81.
[#352] The unit digit of (316) 3 4n + 1 is :
Correct Answer
(D) 7
Explanation
Solution: The unit digit of (316) 3 4n , depends on the power of 6. See the pattern, 6 2 = 36 6 3 = 216 6 4 = 1296 Any power of 6 will give unit digit 6. So The unit digit of (316) 3 4n always 6. So, unit digit of (316) 3 4n + 1 will be 7
[#353] A number when divided by 14 leaves reminder of 8, but when the same number is divided by 7, it will leave the remainder :
Correct Answer
(C) 1
Explanation
Solution: When the number is divided by 14 it gives a remainder of 8, The number = 14N + 8 (14N is divisible by 14) When same number is divided by 7 it will give remainder 1
[#354] 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:
Correct Answer
(C) 8 and 5
Explanation
Solution: Let the number be 476ab0 476ab0 is divisible by 3 ⇒ 4 + 7 + 6 + a + b + 0 is divisible by 3 ⇒ 17 + a + b is divisible by 3 - - - - - - - (i) 476ab0 is divisible by 11 [(4 + 6 + b) - (7 + a + 0)] is 0 or divisible by 11 ⇒ [3 + (b - a)] is 0 or divisible by 11 - - - - - - - -(ii) Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation (i) and Equation (ii). if a = 6 and b = 2, 17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer if a = 8 and b = 2, 17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i) [3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11 --- Does not meet equation(ii).Hence this is not the answer if a = 6 and b = 5, 17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer if a = 8 and b = 5,
17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1
[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2
Since these values satisfies both equation 1 and equation 2, this is the answer
[#355] When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
Correct Answer
(B) 349
Explanation
Solution: $$eqalign{
& x = 13p + 11,{ ext{and}},x = 17q + 9 cr
& herefore 13p + 11 = 17q + 9 cr
& Rightarrow 17q - 13p = 2 cr
& Rightarrow q = frac{{2 + 13p}}{{17}} cr
& { ext{Thr}},{ ext{least}},{ ext{value}},{ ext{of}},p,{ ext{for}},{ ext{which}} cr
& q = frac{{2 + 13p}}{{17}},{ ext{is}},{ ext{a}},{ ext{whole}},{ ext{number}},{ ext{is}},p = 26 cr
& herefore x = left( {13 imes 26 + 11}
ight) cr
& ,,,,,,,,,,, = left( {338 + 11}
ight) cr
& ,,,,,,,,,,, = 349 cr} $$