Daily Practice Questions

Explanation: We have A:B = 3:7, B:C = 14:5, C:D = 15:11. First, combine A:B and B:C. Since B is common, make B equal: LCM of 7 and 14 is 14. So A:B = 6:14 (multiply by 2), and B:C = 14:5. So A:B:C = 6:14:5. Now combine with C:D = 15:11. Since C=5 in the ratio, and C=15 in the other, multiply A:B:C by 3 to get C=15: A:B:C = 18:42:15. Then D=11 (from C:D=15:11). So A:D = 18:11? Wait—C:D=15:11, so if C=15, D=11. So A:D = 18:11. But options are 1:2, 2:3, etc. Did I misread? A:B=3:7 → A/B=3/7. B:C=14:5 → B/C=14/5 → C/B=5/14. So A/C = (A/B)*(B/C) = (3/7)*(14/5)=6/5. So A:C=6:5. Now C:D=15:11 → C/D=15/11 → D/C=11/15. So A/D = (A/C)*(C/D) = (6/5)*(15/11)=18/11. So A:D=18:11, not in options. Wait—maybe B:C is 14:5 means B/C=14/5? Yes. But let's compute numerically: Let A=3k, B=7k (from A:B=3:7). From B:C=14:5, so 7k/C=14/5 → C=(7k*5)/14= (35k)/14=2.5k=5k/2. From C:D=15:11, so (5k/2)/D=15/11 → D=(5k/2)*(11/15)= (55k)/(30)=11k/6. So A=3k, D=11k/6 → A:D=3k : 11k/6 = 18:11. Not in options. But existing_answer is B (2:3). Did I misread ratios? Maybe A:B=3:7 means A/B=7/3? No, standard is first:second = A:B. Alternative interpretation: maybe the ratios are A to B is 3 to 7, so A=3a, B=7a. B:C=14:5 → 7a:C=14:5 → C=(7a*5)/14=2.5a. C:D=15:11 → 2.5a:D=15:11 → D=(2.5a*11)/15= (27.5a)/15=11a/6. So A:D=3a : 11a/6 = 18:11. Still not matching options. Unless the problem says A:B=7:3? Then A=7a, B=3a. B:C=14:5 → 3a/C=14/5 → C=15a/14. C:D=15:11 → (15a/14)/D=15/11 → D=(15a/14)*(11/15)=11a/14. So A:D=7a : 11a/14 = 98:11. No. Maybe B:C=5:14? Then B/C=5/14 → C=14B/5. A:B=3:7 → B=7A/3. So C=14*(7A/3)/5=98A/15. C:D=15:11 → (98A/15)/D=15/11 → D=(98A/15)*(11/15)=1078A/225. A:D=225:1078, no. Alternatively, perhaps the ratios are chained differently. Let's try to find A:D directly: A/B=3/7, B/C=14/5, C/D=15/11. So A/D = (A/B)*(B/C)*(C/D) = (3/7)*(14/5)*(15/11). Compute: 3*14*15 / (7*5*11) = (630)/(385) = 126/77 = 18/11. So A:D=18:11. Not in options. But existing_answer is B (2:3). Maybe the problem has a typo? Let's check if A:D=2:3 is possible. Suppose A=2, D=3. Then from C:D=15:11, C= (15/11)*3=45/11. From B:C=14:5, B= (14/5)*C= (14/5)*(45/11)=126/11. From A:B=3:7, A/B=3/7 → A= (3/7)B= (3/7)*(126/11)=54/11 ≠2. So no. Unless the ratios are reversed: B:A=3:7, etc. If A:B=7:3 (i.e., A/B=7/3), B:C=5:14, C:D=11:15. Then A/D=(7/3)*(5/14)*(11/15)= (385)/(630)=11/18. Still not 2:3. Try A:D=2:3 → A/D=2/3. Compute (A/B)*(B/C)*(C/D)= (3/7)*(14/5)*(15/11)=18/11≠2/3. So no match. But perhaps the problem meant A:B=3:7, B:C=5:14 (not 14:5), and C:D=15:11. Then A/B=3/7, B/C=5/14 → C/B=14/5. So A/C=(3/7)*(5/14)=15/98. Then C/D=15/11 → A/D=(15/98)*(15/11)=225/1078. No. Alternatively, if B:C=14:5 means C:B=14:5? Unlikely. Given standard interpretation, answer should be 18:11, not listed. But existing_answer is B (2:3). Let's see if any option fits with common mistake. Common error: multiply numerators and denominators separately: A:C = 3*15 : 7*? Wait—A:B=3:7, B:C=14:5 → A:C = 3*14 : 7*5? No, correct is A:B:C = 3*14 : 7*14 : 7*5? No—standard chain: A/B * B/C = A/C → (3/7)*(14/5)=6/5, so A:C=6:5. Then C:D=15:11 → A:D = 6*15 : 5*11? No—A/C=6/5, C/D=15/11 → A/D = (6/5)*(15/11)=18/11. If someone does A:C=3:7 * 14:5 = 42:35=6:5, then A:D=6*15 : 5*11=90:55=18:11. Still same. Maybe the problem has a typo and C:D=5:11? Then A/D=6/5 * 5/11=6/11. Not in options. Or if B:C=7:5? Then A:B=3:7, B:C=7:5 → A:B:C=3:7:5. C:D=15:11 → multiply first by 3: A:B:C=9:21:15, so D=11 → A:D=9:11. Not in options. If C:D=3:11? Then A:D=9*3 : 5*11=27:55. No. Wait—maybe the answer is B (2:3) if ratios are different. Let's solve for A:D=2:3. Set A=2k, D=3k. From C:D=15:11 → C= (15/11)*3k=45k/11. From B:C=14:5 → B= (14/5)*C= (14/5)*(45k/11)=126k/11. From A:B=3:7 → A/B=3/7 → 2k / (126k/11) = 22/126=11/63 ≠ 3/7. So impossible. Given this, the existing answer is likely wrong. But since the question is provided with existing_answer=B, and we must validate, we note discrepancy.

Explanation: Prokaryotic genomes consist of a single, circular DNA molecule that lacks histones and is not enclosed within a membrane-bound nucleus. Instead, this genetic material is concentrated in an irregularly shaped area called the nucleoid region within the cytoplasm. In contrast, eukaryotic cells possess linear chromosomes housed inside a distinct nucleus, making options involving linearity or a nucleus incorrect for prokaryotes.

Explanation: Following the definition of logarithms, log x 81 = 4 can be rewritten as x 4 = 81. Take the fourth root of both sides to get ; which simplifies to x = 3, which is (B).

Explanation: 5. (E) If s.length() < 4 for all strings in wordList , then SHORT WORD will be printed on each pass through the for loop. Since there are wordList.size() passes through the loop, the maximum number of times that SHORT WORD can be printed is wordList.size() .

Explanation: Choice (B) is correct because it directly proposes a constructive strategy—building on successful NASA asteroid orbital modification—to mitigate the specific threat of large asteroid strikes mentioned in the notes. This option effectively uses relevant information by focusing on proven scientific methods rather than extreme measures like colonization or militarization, which are not supported by the provided context.

Explanation: C —The quantities of more than one reactant are given; therefore it is necessary to determine which reactant is limiting. To determine the limiting reactant, it is necessary to convert the mass of the reactants to moles: