Number System - Study Mode

[#176] Product of three consecutive odd numbers is 1287. What is the largest of the three numbers?
Correct Answer

(C) 13

Explanation

Solution: Let three consecutive odd numbers be x, x + 2 & x + 4 x(x + 2)(x + 4) = 1287 Let take x = 9, x + 2 = 11 & x + 4 = 13 satisfy the equation Therefore, Largest number = 13

[#177] Arrangement of the fractions $$frac{4}{3},, - frac{2}{9},, - frac{7}{8},,frac{5}{{12}}$$ xa0 xa0into ascending order:
Correct Answer

(B) $$ - frac{7}{8},, - frac{2}{9},,frac{5}{{12}},,frac{4}{3}$$

Explanation

Solution: $$eqalign{
& frac{4}{3},,frac{{ - 2}}{9},,frac{{ - 7}}{8},,frac{5}{{12}} cr
& frac{4}{3} = 1.33 cr
& frac{{ - 2}}{9} = - 0.22 cr
& frac{{ - 7}}{8} = - 0.875 cr
& frac{5}{{12}} = 0.416 cr
& { ext{So, }}frac{{ - 7}}{8},,frac{{ - 2}}{9},,frac{5}{{12}},,frac{4}{3} cr} $$

[#178] Let a, b and c be the fractions such that a < b < c. If c is divided by a, the result is $$frac{5}{2}$$, which exceeds b by $$frac{7}{4}$$. If a + b + c = $$1frac{{11}}{{12}}$$ , then (c - a) will be equal to:
Correct Answer

(C) $$frac{1}{2}$$

Explanation

Solution: $$eqalign{
& frac{c}{a} = frac{5}{2} cr
& b = frac{5}{2} - frac{7}{4} cr
& b = frac{3}{4} cr
& a + b + c = frac{{23}}{{12}} cr
& a + c = frac{{23}}{{12}} - frac{3}{4} cr
& a + c = frac{{14}}{{12}} cr
& a + c = frac{7}{6} cr
& 2x + 5x = frac{7}{6},,,,,,left{ {frac{c}{a} = frac{{5x}}{{2x}}}
ight. cr
& 7x = frac{7}{6} cr
& x = frac{1}{6} cr
& c - a = 3x = 3 imes frac{1}{6} = frac{1}{2} cr} $$

[#179] The sum of the digits of the least number which when divided by 36, 72, 80 and 88 leaves the remainders 16, 52, 60 and 68, respectively, is:
Correct Answer

(A) 16

Explanation

Solution: 36 - 16 = 20 72 - 52 = 20 80 - 60 = 20 88 - 68 = 20 LCM of 36, 72, 80, 88 = 7920 Least number = 7920 - 20 = 7900 Sum of the digits = 7 + 9 + 0 + 0 = 16

[#180] The numbers 2272 and 875 are divided by a three-digit numbers N, giving the same remainder. The sum of the digits of N is :
Correct Answer

(A) 10

Explanation

Solution: Clearly, (2272 - 875) = 1397, is exactly divisible by N. Now, 1397 = 11 × 127 ∴ The required 3-digit number is 127, the sum of whose digits is 10