Question
Let ‘x’ be the least number divisible by 18, 20, 27,
30, and 50, and also ‘x’ is a perfect square. Find the remainder when ‘x’ is divided by 77.Solution
ATQ,
Prime factors
18 = 2 × 3²
20 = 2² × 5
27 = 3³
30 = 2 × 3 × 5
50 = 2 × 5²
LCM (take highest powers)
LCM = 2² × 3³ × 5² = 2700
Make it a perfect square
2700 = 2² × 3³ × 5² → exponent of 3 is odd
Multiply by 3 to make exponent of 3 even:
x = 2700 × 3 = 2² × 3⁴ × 5² = 8100
Remainder when x is divided by 77
8100 ÷ 77 → 77 × 105 = 8085
8100 − 8085 = 15
Remainder = 15
Statements: P = W > Y; U < W = X; T ≤ G ≤ Y
Conclusions:
I. T < P
II. P = X
III. U > G
Statements: G > N > P = E ≥ H < L; M < E < B < C = Q > X; U > W > Y = Q > H
Conclusions:
I). U > P
II). Y > P
...In the following question the relationship between different elements is given in the statements followed by three conclusions I, II and III. Read the...
Statements:
A < B = C; D = E ≤ F ≤ G; E ≤ B
Conclusions:
I). G ≥ C
II). D ≤ B
III). C ≥ D
Statement: G ≤ L ≥ O ≥ W ≥ I < N
Conclusion: I. O > G II. W < N
...Statements: A $ B, B * C, D % A
Conclusions: a) C # D b) D $ B
In the question, assuming the given statements to be true, find which of the following conclusion(s) among the two conclusions is/are true and then give...
Which of the following symbols should replace the sign ($) and (*) respectively in the given expression in order to make the expression F ≥ J and P...
Statements: E # L, L @ U, U $ N, N % K
Conclusions: I. K @ U II. K % U III. E @ U
...Statements: M * T, D % T, D # K, K $ R
Conclusions: I. M * D II. T # K II...
