Powers of 3 mod 7: 3^1=3, 3^2=2, 3^3=6, 3^4=4, 3^5=5, 3^6=1. Pattern repeats every 6. 100 = 16×6 + 4, so 3^100 ≡ 3^4 ≡ 4 (mod 7). Actually 3^4 = 81, 81 mod 7 = 4. Let me verify: 3^6 ≡ 1, so 3^100 = 3^(96+4) = (3^6)^16 × 3^4 ≡ 1 × 81 ≡ 4 (mod 7). Wait, checking again: 3^2=9≡2, 3^3≡6, 3^4≡4, 3^5≡5, 3^6≡1. So answer is 4.

Rate of filling = 1/6 + 1/8 - 1/12 = (4+3-2)/24 = 5/24. Time = 24/5 = 4.8 hours. Hmm, let me recalculate: (1/6 + 1/8 - 1/12) = (4+3-2)/24 = 5/24. So time = 1/(5/24) = 24/5 = 4.8. But 3.43 is closest to our options, let me verify the calculation once more with LCM 24: 1/6 = 4/24, 1/8 = 3/24, 1/12 = 2/24. Net = (4+3-2)/24 = 5/24. Time = 24/5 = 4.8. None match exactly, but checking: could the answer key have error?

From 'all roses are flowers' and 'some flowers are red', we can conclude that some roses might be red, but we cannot definitively say all roses are red. The safest conclusion from the logical overlap is that some roses could be red.

Differences: 5-2=3, 10-5=5, 17-10=7, 26-17=9. Next difference = 11. So 26+11 = 37. Pattern: n^2 + 1 for n=1,2,3,4,5: 2,5,10,17,26,37.

a:b = 2:3 means a/b = 2/3. b:c = 4:5 means b/c = 4/5. To find a:b:c, make b equal: a:b = 8:12 and b:c = 12:15. So a:b:c = 8:12:15.

If some programmers are graduates, and all graduates are educated, then by logical deduction, some programmers must be educated.

O=6, R=3, A=5, N=1, G=7, E=8. So RAGE = R(3), A(5), G(7), E(8) = 3578. Wait, that's not in options. Let me recheck: If ORANGE=635178, then O=6,R=3,A=5,N=1,G=7,E=8. RAGE would be 3,5,7,8 = 3578. Hmm, none match exactly. Closest is option A if there's a typo.

When 'team' is used with 'are', it should be followed by 'have' not 'has'. 'The team are playing well and have won three matches.'

If a decision is welcomed by all, it means everyone agrees. Unanimous means complete agreement.

The logical order is: C (John driving), B (road blocked), A (takes different route), D (reaches on time).