math & puzzles Online Quiz - 214

Pramita's daughter-in-law's son's son is Pramita's great-grandson. Pramita's daughter-in-law is married to Pramita's son. Their son is Pramita's grandson. His son (the great-grandson) is Pramita's husband's great-grandson as well. Option C is correct.

The sequence is (n^3)/3 for n=1, 2, 3, 4... 1^3/3 = 0.333; 2^3/3 = 2.666 (Wait, the sequence says 2). If the sequence is n*(n+1)(n+2)/18? No. The pattern is (n^3 + n)/6? No. If we use (n^3 + n^2)/12: (1+1)/12=0.16. The pattern is (n^3 + n^2 + n)/9? No. Actually, (n^3 + n)/3: (1+1)/3=0.66. Let's try n^2 * (n+1) / 12: 12/12=0.16. The correct pattern is n^3 / 3 + (n-1). 1/3+0=0.333; 8/3+1=3.66 (No). The logic for 17.857 usually comes from a specific polynomial or fractional series; 17.857 is 125/7 or similar.

The pattern is n * (n-1)^n? No. The pattern is: 1^11=1, 2^11=2, 3^22=18, 4^33=192, 5^4*4=2500. The next term is 6^5 * 5. 7776 * 5 = 38880.

In the given sequence (2, 1.5, 1.333, 1.25, 1.2,....), we can see that each subsequent term is getting closer to the value of 1.1666.

Now, let's go through each option and determine which one matches the pattern:

A. 1.1666: This option matches the pattern and is the correct answer. Each term in the sequence is getting closer to the value of 1.1666, and this option represents that value accurately.

B. 1.2666: This option does not match the pattern. The terms in the sequence are not getting closer to the value of 1.2666.

C. 1.5666: This option does not match the pattern. The terms in the sequence are not increasing and are not getting closer to the value of 1.5666.

D. 1.6666: This option does not match the pattern. The terms in the sequence are not getting closer to the value of 1.6666.

Therefore, the correct answer is A. 1.1666.

The sequence represents 1 + n/(n+1) or similar fractions. Specifically: 1 + 1/2 (1.5), 1 + 2/3 (1.666), 1 + 3/4 (1.75), 1 + 4/5 (1.8), 1 + 5/6 (1.8333). The next term is 1 + 6/7, which is approximately 1.8571.

The sequence follows the pattern n(n+1)/2: 0.5(1×1/2), 2(2×2/2), 4.5(3×3/2), 8(4×4/2), 12.5(5×5/2), 18(6×6/2), 24.5(7×7/2). The next term is 8×8/2 = 32. The differences between terms increase by 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, so the next difference is 7.5, making 24.5+7.5=32.

The sequence follows the formula n^2 - 1, starting from n=2. 2^2-1=3, 3^2-1=8, 4^2-1=15, 5^2-1=24, 6^2-1=35. The next term is 7^2-1, which is 49 - 1 = 48.

The sequence uses the same four digits (8, 7, 2, 3) and shifts the last digit to the front: 8723 -> 3872 -> 2387. Following this rotation, the next number moves the 7 to the front, resulting in 7238.

This is an alternating sequence. The first, third, and fifth terms are 7, 8, 9 (increasing by 1). The second, fourth, and sixth terms are 5, 4, 3 (decreasing by 1). The next term in the first sequence (7th term) should be 9 + 1 = 10.

The pattern is (n * 2) - 1, (n * 2) - 1... no. The pattern is: 232 - 1 = 45; 452 - 1 = 89; 892 - 1 = 177; 1772 - 1 = 353. Each subsequent number is double the previous number minus one.

Let the first day be x. The sum of an arithmetic progression is (n/2)(2a + (n-1)d). Here, 5/2(2x + 4*6) = 100. This simplifies to 5(x + 12) = 100, so x + 12 = 20, which means x = 8. The man ate 8, 14, 20, 26, and 32 bananas respectively.

The function follows the pattern f(x, y) = (x * y) + (x + y). For (2, 7): (14) + (9) = 23 (doesn't match). Another pattern is f(x, y) = (x+y)5 + 12. For (2,7): 95+12=57. For (1,6): 75+12=47 (doesn't match). The intended logic is f(x, y) = (x+y)10 + (y-x). For (2,7): 90+5=95 (no). Correct pattern: f(x,y) = (x+y)7 + 1. For (2,7): 97-6? No. Actually, 27=14, 16=6. The logic is f(x,y) = (x+y)5 + 12. Wait, 310=30. The pattern is (x+y)10 - (x+y+x). For (3,10): 1310 - 3 = 127.

This is a classic heads and legs problem. Let h = horses and p = pigeons. Then h + p = 80 (heads) and 4h + 2p = 260 (legs, since horses have 4 legs and pigeons have 2). Multiply first equation by 2: 2h + 2p = 160. Subtract from second equation: 2h = 100, so h = 50. Verification: 50 horses + 30 pigeons = 80 heads, and 50×4 + 30×2 = 200 + 60 = 260 legs. Options A (40), B (30), and D (60) don't satisfy both conditions.

After a 25% reduction, the price becomes 75% of original. After a further 20% reduction on the reduced price, the final price is 75% × 80% = 60% of original. Therefore, total reduction = 100% - 60% = 40%. The reductions compound multiplicatively, not additively. Options A (45%), C (35%), and D (30%) don't represent the correct combined reduction.

1/8 = 0.125. The number 0.127 - 0.125 = 0.002 = 2/1000 = 1/500. Therefore, 0.127 is greater than 1/8 by 1/500. Options A (1/2 = 0.5), B (2/10 = 0.2), and C (1/50 = 0.02) are all too large to be the correct difference.

This is a classic trick question - all 12 months have at least 28 days. February has exactly 28 days in non-leap years, but every single month has 28 days (some have 30 or 31, but all have 28). The question tests reading comprehension rather than calendar knowledge.

The family consists of 2 parents (mother + father), 7 daughters, and 1 son who is the brother to all daughters. Total: 2 + 7 + 1 = 10 people. The key insight is that each daughter shares the same one brother, not that each has a separate brother.

We compare (3t+4r)/rt and (3t+4r)/(r+t). Since r>0 and t>0, (3t+4r) is positive and cancels out. The comparison reduces to comparing denominators: rt vs (r+t). The relationship depends on values - if r+t > rt, Col A > Col B; if r+t < rt, Col B > Col A. Example: r=t=2 gives equality; r=3,t=2 gives Col A < Col B; r=1,t=3 gives Col A > Col B. Thus, it cannot be determined.

Let the number be 10a + b where a is tens digit and b is units digit. Half of 52 is 26. The units digit of 52 (which is 2) equals the tens digit of 26 (which is 2). Also, the tens digit of 52 (which is 5) equals the units digit of 26 (which is 6) minus 1. The sum of digits 5 + 2 = 7. All conditions are satisfied.

Single-digit prime numbers are 2, 3, 5, and 7. Consecutive single-digit primes are 2 and 3, making their product X = 6. Checking option E, 6X = 36, which is 6 times 6, not the product of two consecutive integers. Thus, 6X is not a product of consecutive integers.