Number System - Study Mode

[#486] The remainder when 75 75 75 is divide by 37.
Correct Answer

(B) 1

Explanation

Solution: $$frac{{{{75}^{{{75}^{75}}}}}}{{37}}$$ When 75 is divided by 37, it leaves remainder of 1. So, the expression will become, $$frac{{{1^{{{75}^{75}}}}}}{{37}}$$ Now, for any power of 1, we always get 1 and expression becomes $$frac{1}{{37}}$$ that leaves remainder 1

[#487] The product of the digits of a three digit number is a perfect square and perfect cube both is :
Correct Answer

(A) 126

Explanation

Solution: The only possible number which is both perfect square and perfect cube is 729 which is cube of 9 and square of 27
So, 7 × 2 × 9 = 126

[#488] The LCM of two numbers is 1020 and their HCF is 34 the possible pair of number is:
Correct Answer

(C) 204, 170

Explanation

Solution: Going through options:
LCM of 204 and 170 = 1020.

[#489] Sunny gets $$frac{7}{9}$$ times as many marks in QA as in ENGLISH. If his total combined marks in both the papers is 90. His marks in QA is:
Correct Answer

(C) 70

Explanation

Solution: $$eqalign{
& { ext{Total}},{ ext{Marks}} = 90 cr
& { ext{Marks}},{ ext{in}},{ ext{QA}} = frac{7}{9}, ext{of},,90 cr
& = frac{{left( {7 imes 90}
ight)}}{9} cr
& = 7 imes 10 cr
& = 70 cr} $$

[#490] Sum of three consecutive even integers is 54. Find the least integer among them.
Correct Answer

(D) 16

Explanation

Solution: $$eqalign{
& x + left( {x + 2}
ight) + left( {x + 4}
ight) = 54 cr
& 3x + 6 = 54 cr
& 3x = 48 cr
& x = 16 cr
& cr
& {x08f{Alternate: }} cr
& { ext{Middle number = }}frac{{54}}{3} = 18 cr
& { ext{then number is 16,18,20}} cr
& { ext{Smallest number is 16}} cr} $$