Question
What is the remainder when 32025 is divided
by 7?Solution
ATQ, Powers of 3 modulo 7: 3¹ ≡ 3 3² ≡ 9 ≡ 2 3³ ≡ 3·2 = 6 3⁴ ≡ 3·6 = 18 ≡ 4 3⁵ ≡ 3·4 = 12 ≡ 5 3⁶ ≡ 3·5 = 15 ≡ 1 (mod 7) So, 3⁶ ≡ 1 (mod 7), cycle length 6. 2025 ÷ 6 = 337 remainder 3. So 3^2025 ≡ 3³ (mod 7) ≡ 27 ≡ 6 (mod 7).
Statements:
I. All pins are bins.
II. All bins are not papers.
Conclusions:
I. Some papers are pins.
II. All ...
Statement: W < X; W ≥ Y > Z; T ≥ U > X
Conclusion:
I. Z ≥ X
II. U ≥ W
3 In the following question below are given some statements followed by some conclusions based on those statements. Taking the given statements to be t...
Statements: X > V ≥ A = I ≤ R > G = H ≤ Q
Conclusion
I: Q ≤ A
II: Q > A
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at varianc...
Statement:
No one is two.
A few two are three.
Only one is four.
Conclusion:
1. All two being three is a possibilit...
Statements: H ≤ L< S ≤ K , S = G ≥ I > Q, U ≤ B < N = C = I
Conclusions: I. B < S II. H < Q
In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is/are definitely true and then...
Statements: M ≥ X ≥ B > V ≤ G = Y > K > U < N
Conclusion
I: G > U
II: V ≤ M
The Sahariyas are members of an indigenous tribe which has for centuries occupied an area now located partly within the state of Rajasthan and partly wi...
