Number System - Study Mode

[#591] Let, p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression $$frac{{p - q - 1}}{{r - s}}$$ xa0is:
Correct Answer

(C) -s - 1

Explanation

Solution: q > p and r > s q > p > r > s All number have three prime factor One digit → s, r s → 2 xa0 xa0 xa0 xa0 2 2 = 4 r → 3 xa0 xa0 xa0 xa0 3 2 = 9 Two digit → p, q p → 5 xa0 xa0 5 2 = 25 q → 7 xa0 xa0 7 2 = 49 $$eqalign{
& frac{{p - q - 1}}{{r - s}} = frac{{25 - 49 - 1}}{{9 - 4}} = frac{{ - 25}}{5} = - 5 cr
& - 5 = - 4 - 1 = - s - 1 cr} $$

[#592] What decimal of a week is an hour?
Correct Answer

(A) .0059

Explanation

Solution: $$frac{1}{{24 imes 7}} = 0.0059$$

[#593] The sum of three consecutive natural numbers each divisible by 5, is 225. The largest among them is?
Correct Answer

(D) 80

Explanation

Solution: Let numbers are x, x + 5, x + 10 So, x + x + 5 + x + 10 = 225 3x + 15 = 225 3x = 210 x = 70 Largest number = 70 + 10 = 80

[#594] A six-digit number is divisible by 198. If the digits are rearranged, even then the number will be divisible by:
Correct Answer

(A) 3

Explanation

Solution: Let, 6 digit number after rearranging the digit divisible by 198 is = 0000891 This number is divisible by 3

[#595] If A = $$frac{{sqrt {0.0004} imes
oot 3 of {0.000008} }}{{
oot 4 of {16000} imes
oot 3 of {125000} imes
oot 4 of {810} }}$$ xa0 xa0 xa0and B = $$frac{{
oot 3 of {0.729} imes
oot 4 of {0.0016} }}{{sqrt {0.16} }},$$ xa0 xa0what is A × B?
Correct Answer

(A) $$6 imes {10^{ - 8}}$$

Explanation

Solution: $$eqalign{
& { ext{A}} = frac{{sqrt {0.0004} imes
oot 3 of {0.000008} }}{{
oot 4 of {16000} imes
oot 3 of {125000} imes
oot 4 of {810} }} cr
& = frac{{0.02 imes 0.02}}{{
oot 4 of {16000 imes 810} imes
oot 3 of {125000} }} cr
& = frac{{0.02 imes 0.02}}{{20 imes 3 imes 50}} cr
& = frac{1}{{75 imes {{10}^5}}} cr
& { ext{B}} = frac{{
oot 3 of {0.729} imes
oot 4 of {0.0016} }}{{sqrt {0.16} }} cr
& = frac{{0.9 imes 0.2}}{{0.4}} cr
& = frac{9}{{20}} cr
& herefore A imes B = frac{1}{{75 imes {{10}^5}}} imes frac{9}{{20}} cr
& = frac{3}{{25 imes 2}} imes frac{1}{{{{10}^6}}} cr
& = frac{3}{5} imes frac{1}{{{{10}^7}}} cr
& = frac{3}{5} imes {10^{ - 7}} cr
& = 6 imes {10^{ - 8}} cr} $$