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241. Find the remainder when 6789 is divided by 19.
- A. 4
- B. 6
- C. 10
- D. 8
Answer: 6
Explanation: Divide 6789 by 19: 19 x 357 = 6783, and 6789 - 6783 = 6. Since 6 is less than 19, the remainder is 6.
242. Find the remainder when 4321 is divided by 13.
- A. 7
- B. 9
- C. 5
- D. 3
Answer: 5
Explanation: Divide 4321 by 13: 13 x 332 = 4316, and 4321 - 4316 = 5. Since 5 is less than 13, the remainder is 5.
243. Find the sum of squares of the first 16 natural numbers.
- A. 1506
- B. 1496
- C. 1471
- D. 1486
Answer: 1496
Explanation: The sum of squares of the first n natural numbers is n(n+1)(2n+1)/6. For n = 16: 16 x 17 x 33 / 6 = 8976 / 6 = 1496.
244. Find the sum of squares of the first 14 natural numbers.
- A. 1015
- B. 1025
- C. 1005
- D. 990
Answer: 1015
Explanation: The sum of squares of the first n natural numbers is n(n+1)(2n+1)/6. For n = 14: 14 x 15 x 29 / 6 = 6090 / 6 = 1015.
245. Find the sum of squares of the first 8 natural numbers.
- A. 194
- B. 204
- C. 214
- D. 179
Answer: 204
Explanation: The sum of squares of the first n natural numbers is n(n+1)(2n+1)/6. For n = 8: 8 x 9 x 17 / 6 = 1224 / 6 = 204.
246. Find the sum of the first 35 natural numbers.
- A. 560
- B. 595
- C. 630
- D. 665
Answer: 630
Explanation: The sum of the first n natural numbers is n(n+1)/2. For n = 35 this is 35 x 36 / 2 = 1260 / 2 = 630.
247. Find the sum of the first 28 natural numbers.
- A. 406
- B. 378
- C. 434
- D. 350
Answer: 406
Explanation: The sum of the first n natural numbers is n(n+1)/2. For n = 28 this is 28 x 29 / 2 = 812 / 2 = 406.
248. Find the sum of the first 22 natural numbers.
- A. 275
- B. 231
- C. 209
- D. 253
Answer: 253
Explanation: The sum of the first n natural numbers is n(n+1)/2. For n = 22 this is 22 x 23 / 2 = 506 / 2 = 253.
249. Find the sum of the first 18 natural numbers.
- A. 153
- B. 171
- C. 135
- D. 189
Answer: 171
Explanation: The sum of the first n natural numbers is n(n+1)/2. For n = 18 this is 18 x 19 / 2 = 342 / 2 = 171.
250. Express 0.96 as a fraction in lowest terms.
- A. 23/25
- B. 24/25
- C. 25/25
- D. 24/30
Answer: 24/25
Explanation: 0.96 = 96/100. The HCF of 96 and 100 is 4, so dividing both by 4 gives 24/25 in lowest terms. The other options are either not equal in value or not fully reduced.
251. Express 0.64 as a fraction in lowest terms.
- A. 16/30
- B. 17/25
- C. 16/25
- D. 15/25
Answer: 16/25
Explanation: 0.64 = 64/100. The HCF of 64 and 100 is 4, so dividing both by 4 gives 16/25 in lowest terms. The other options are either not equal in value or not fully reduced.
252. Express 0.55 as a fraction in lowest terms.
- A. 10/20
- B. 12/20
- C. 11/25
- D. 11/20
Answer: 11/20
Explanation: 0.55 = 55/100. The HCF of 55 and 100 is 5, so dividing both by 5 gives 11/20 in lowest terms. The other options are either not equal in value or not fully reduced.
253. Express 0.36 as a fraction in lowest terms.
- A. 10/25
- B. 8/25
- C. 9/30
- D. 9/25
Answer: 9/25
Explanation: 0.36 = 36/100. The HCF of 36 and 100 is 4, so dividing both by 4 gives 9/25 in lowest terms. The other options are either not equal in value or not fully reduced.
254. Express 0.15 as a fraction in lowest terms.
- A. 4/20
- B. 3/20
- C. 3/25
- D. 2/20
Answer: 3/20
Explanation: 0.15 = 15/100. The HCF of 15 and 100 is 5, so dividing both by 5 gives 3/20 in lowest terms. The other options are either not equal in value or not fully reduced.
255. Express 0.24 as a fraction in lowest terms.
- A. 6/25
- B. 5/25
- C. 7/25
- D. 6/30
Answer: 6/25
Explanation: 0.24 = 24/100. The HCF of 24 and 100 is 4, so dividing both by 4 gives 6/25 in lowest terms. The other options are either not equal in value or not fully reduced.
256. Find the largest 3-digit number exactly divisible by 13.
- A. 988
- B. 975
- C. 962
- D. 999
Answer: 988
Explanation: The largest 3-digit number is 999. 999 divided by 13 leaves remainder 999 - 13 x 76 = 999 - 988 = 11, so subtracting 11 gives 988 = 13 x 76.
257. Find the smallest 6-digit number exactly divisible by 61.
- A. 100000
- B. 100040
- C. 100101
- D. 100162
Answer: 100040
Explanation: The smallest 6-digit number is 100000. 100000 divided by 61 leaves remainder 100000 - 61 x 1639 = 100000 - 99979 = 21, so add 61 - 21 = 40 to get 100040 = 61 x 1640.
258. Find the largest 4-digit number exactly divisible by 53.
- A. 9858
- B. 9964
- C. 9911
- D. 9999
Answer: 9964
Explanation: Largest 4-digit number is 9999. 9999 / 53 leaves a remainder of 35, so subtract it: 9999 - 35 = 9964, which equals 53 x 188.
259. Find the smallest 5-digit number exactly divisible by 47.
- A. 10011
- B. 10105
- C. 10000
- D. 10058
Answer: 10011
Explanation: Smallest 5-digit number is 10000. 10000 / 47 leaves a remainder of 36, so add 11 to reach a multiple: 10000 + 11 = 10011, which equals 47 x 213.
260. Find the largest 3-digit number exactly divisible by 31.
- A. 999
- B. 930
- C. 961
- D. 992
Answer: 992
Explanation: Largest 3-digit number is 999. 999 / 31 leaves a remainder of 7, so subtract it: 999 - 7 = 992, which equals 31 x 32.
261. Find the smallest 4-digit number exactly divisible by 29.
- A. 1044
- B. 1073
- C. 1015
- D. 1000
Answer: 1015
Explanation: Smallest 4-digit number is 1000. 1000 / 29 leaves a remainder of 14, so add 15 to reach a multiple: 1000 + 15 = 1015, which equals 29 x 35.
262. Find the unit digit of 19^64.
- A. 8
- B. 1
- C. 4
- D. 2
Answer: 1
Explanation: Only the last digit 9 matters. Its unit digits repeat in a cycle of 2: 9, 1. Exponent 64 mod 2 = 0, which is 0, so the last term of the cycle applies, giving unit digit 1.
263. Find the unit digit of 12^45.
- A. 3
- B. 5
- C. 9
- D. 2
Answer: 2
Explanation: Only the last digit 2 matters. Its unit digits repeat in a cycle of 4: 2, 4, 8, 6. Exponent 45 mod 4 = 1, which picks term number 1 of the cycle, giving unit digit 2.
264. Find the unit digit of 23^66.
- A. 0
- B. 6
- C. 2
- D. 9
Answer: 9
Explanation: Only the last digit 3 matters. Its unit digits repeat in a cycle of 4: 3, 9, 7, 1. Exponent 66 mod 4 = 2, which picks term number 2 of the cycle, giving unit digit 9.
265. Find the unit digit of 17^53.
- A. 8
- B. 7
- C. 4
- D. 0
Answer: 7
Explanation: Only the last digit 7 matters. Its unit digits repeat in a cycle of 4: 7, 9, 3, 1. Exponent 53 mod 4 = 1, which picks term number 1 of the cycle, giving unit digit 7.
266. Find the unit digit of 13^101.
- A. 4
- B. 6
- C. 0
- D. 3
Answer: 3
Explanation: Only the last digit 3 matters. Its unit digits repeat in a cycle of 4: 3, 9, 7, 1. Exponent 101 mod 4 = 1, which picks term number 1 of the cycle, giving unit digit 3.
267. Find the unit digit of 6^44.
- A. 6
- B. 3
- C. 7
- D. 9
Answer: 6
Explanation: Only the last digit 6 matters, and every power of a number ending in 6 also ends in 6. So the unit digit of 6^44 is 6.
268. Find the unit digit of 4^88.
- A. 9
- B. 7
- C. 3
- D. 6
Answer: 6
Explanation: Only the last digit 4 matters. Its unit digits repeat in a cycle of 2: 4, 6. Exponent 88 mod 2 = 0, which is 0, so the last term of the cycle applies, giving unit digit 6.
269. Find the unit digit of 9^77.
- A. 6
- B. 0
- C. 2
- D. 9
Answer: 9
Explanation: Only the last digit 9 matters. Its unit digits repeat in a cycle of 2: 9, 1. Exponent 77 mod 2 = 1, which picks term number 1 of the cycle, giving unit digit 9.
270. Find the unit digit of 8^99.
- A. 3
- B. 2
- C. 9
- D. 5
Answer: 2
Explanation: Only the last digit 8 matters. Its unit digits repeat in a cycle of 4: 8, 4, 2, 6. Exponent 99 mod 4 = 3, which picks term number 3 of the cycle, giving unit digit 2.
271. Find the unit digit of 7^201.
- A. 4
- B. 0
- C. 8
- D. 7
Answer: 7
Explanation: Only the last digit 7 matters. Its unit digits repeat in a cycle of 4: 7, 9, 3, 1. Exponent 201 mod 4 = 1, which picks term number 1 of the cycle, giving unit digit 7.
272. Find the unit digit of 3^58.
- A. 2
- B. 6
- C. 9
- D. 0
Answer: 9
Explanation: Only the last digit 3 matters. Its unit digits repeat in a cycle of 4: 3, 9, 7, 1. Exponent 58 mod 4 = 2, which picks term number 2 of the cycle, giving unit digit 9.
273. Find the unit digit of 2^71.
- A. 5
- B. 1
- C. 8
- D. 9
Answer: 8
Explanation: Only the last digit 2 matters. Its unit digits repeat in a cycle of 4: 2, 4, 8, 6. Exponent 71 mod 4 = 3, which picks term number 3 of the cycle, giving unit digit 8.
274. Find the LCM of 22 and 33.
- A. 66
- B. 55
- C. 77
- D. 50
Answer: 66
Explanation: LCM = (product of the numbers) / HCF. HCF of 22 and 33 is 11, so LCM = 22 x 33 / 11 = 726 / 11 = 66. Hence 66 is the smallest number that both 22 and 33 divide exactly.
275. Find the LCM of 14 and 49.
- A. 74
- B. 114
- C. 82
- D. 98
Answer: 98
Explanation: HCF of 14 and 49 is 7. Using LCM = (product) / HCF = 14 x 49 / 7 = 686 / 7 = 98. Check: 98 divides evenly by both 14 and 49.
276. Find the LCM of 40 and 60.
- A. 120
- B. 140
- C. 100
- D. 90
Answer: 120
Explanation: HCF of 40 and 60 is 20. Using LCM = (product) / HCF = 40 x 60 / 20 = 2400 / 20 = 120. Check: 120 divides evenly by both 40 and 60.
277. Find the LCM of 27 and 36.
- A. 81
- B. 90
- C. 108
- D. 126
Answer: 108
Explanation: HCF of 27 and 36 is 9. Using LCM = (product) / HCF = 27 x 36 / 9 = 972 / 9 = 108. Check: 108 divides evenly by both 27 and 36.
278. Find the LCM of 32 and 48.
- A. 96
- B. 72
- C. 112
- D. 80
Answer: 96
Explanation: HCF of 32 and 48 is 16. Using LCM = (product) / HCF = 32 x 48 / 16 = 1536 / 16 = 96. Check: 96 divides evenly by both 32 and 48.
279. Find the LCM of 18 and 45.
- A. 68
- B. 75
- C. 105
- D. 90
Answer: 90
Explanation: HCF of 18 and 45 is 9. Using LCM = (product) / HCF = 18 x 45 / 9 = 810 / 9 = 90. Check: 90 divides evenly by both 18 and 45.
280. Find the LCM of 21 and 28.
- A. 70
- B. 98
- C. 63
- D. 84
Answer: 84
Explanation: HCF of 21 and 28 is 7. Using LCM = (product) / HCF = 21 x 28 / 7 = 588 / 7 = 84. Check: 84 divides evenly by both 21 and 28.
281. Find the LCM of 16 and 24.
- A. 48
- B. 36
- C. 56
- D. 40
Answer: 48
Explanation: HCF of 16 and 24 is 8. Using LCM = (product) / HCF = 16 x 24 / 8 = 384 / 8 = 48. Check: 48 divides evenly by both 16 and 24.
282. Find the HCF of 75 and 125.
- A. 25
- B. 28
- C. 23
- D. 31
Answer: 25
Explanation: Factorise: 75 = 3 x 5^2 and 125 = 5^3. The HCF is the product of the common prime factors with the lowest powers, which is 25. It divides 75 exactly 3 times and 125 exactly 5 times.
283. Find the HCF of 108 and 144.
- A. 36
- B. 34
- C. 39
- D. 42
Answer: 36
Explanation: Factorise: 108 = 2^2 x 3^3 and 144 = 2^4 x 3^2. The HCF is the product of the common prime factors with the lowest powers, which is 36. It divides 108 exactly 3 times and 144 exactly 4 times.
284. Find the HCF of 120 and 180.
- A. 66
- B. 58
- C. 63
- D. 60
Answer: 60
Explanation: Factorise: 120 = 2^3 x 3 x 5 and 180 = 2^2 x 3^2 x 5. The HCF is the product of the common prime factors with the lowest powers, which is 60. It divides 120 exactly 2 times and 180 exactly 3 times.
285. Find the HCF of 52 and 78.
- A. 32
- B. 29
- C. 26
- D. 24
Answer: 26
Explanation: Factorise: 52 = 2^2 x 13 and 78 = 2 x 3 x 13. The HCF is the product of the common prime factors with the lowest powers, which is 26. It divides 52 exactly 2 times and 78 exactly 3 times.
286. Find the HCF of 66 and 110.
- A. 28
- B. 25
- C. 22
- D. 20
Answer: 22
Explanation: Factorise: 66 = 2 x 3 x 11 and 110 = 2 x 5 x 11. The HCF is the product of the common prime factors with the lowest powers, which is 22. It divides 66 exactly 3 times and 110 exactly 5 times.
287. Find the HCF of 96 and 144.
- A. 51
- B. 46
- C. 48
- D. 54
Answer: 48
Explanation: Factorise: 96 = 2^5 x 3 and 144 = 2^4 x 3^2. The HCF is the product of the common prime factors with the lowest powers, which is 48. It divides 96 exactly 2 times and 144 exactly 3 times.
288. Find the HCF of 50 and 80.
- A. 13
- B. 10
- C. 8
- D. 16
Answer: 10
Explanation: Factorise: 50 = 2 x 5^2 and 80 = 2^4 x 5. The HCF is the product of the common prime factors with the lowest powers, which is 10. It divides 50 exactly 5 times and 80 exactly 8 times.
289. Find the HCF of 63 and 84.
- A. 19
- B. 24
- C. 27
- D. 21
Answer: 21
Explanation: Factorise: 63 = 3^2 x 7 and 84 = 2^2 x 3 x 7. The HCF is the product of the common prime factors with the lowest powers, which is 21. It divides 63 exactly 3 times and 84 exactly 4 times.
290. Find the HCF of 28 and 42.
- A. 12
- B. 17
- C. 14
- D. 20
Answer: 14
Explanation: Factorise: 28 = 2^2 x 7 and 42 = 2 x 3 x 7. The HCF is the product of the common prime factors with the lowest powers, which is 14. It divides 28 exactly 2 times and 42 exactly 3 times.
291. Find the HCF of 45 and 75.
- A. 21
- B. 18
- C. 13
- D. 15
Answer: 15
Explanation: Factorise: 45 = 3^2 x 5 and 75 = 3 x 5^2. The HCF is the product of the common prime factors with the lowest powers, which is 15. It divides 45 exactly 3 times and 75 exactly 5 times.
292. Find the remainder when 5000 is divided by 29.
- A. 12
- B. 14
- C. 10
- D. 8
Answer: 12
Explanation: Divide 5000 by 29: 29 x 172 = 4988, and 5000 - 4988 = 12. Since 12 is less than 29, the remainder is 12.
293. Find the remainder when 3000 is divided by 23.
- A. 8
- B. 12
- C. 6
- D. 10
Answer: 10
Explanation: Divide 3000 by 23: 23 x 130 = 2990, and 3000 - 2990 = 10. Since 10 is less than 23, the remainder is 10.
294. Express 0.84 as a fraction in lowest terms.
- A. 17/20
- B. 42/50
- C. 84/100
- D. 21/25
Answer: 21/25
Explanation: 0.84 = 84/100. The HCF of 84 and 100 is 4, so dividing both by 4 gives 21/25 in lowest terms. The other options are either not equal in value or not fully reduced.
295. Express 0.72 as a fraction in lowest terms.
- A. 72/100
- B. 18/25
- C. 9/10
- D. 36/50
Answer: 18/25
Explanation: 0.72 = 72/100. The HCF of 72 and 100 is 4, so dividing both by 4 gives 18/25 in lowest terms. The other options are either not equal in value or not fully reduced.
296. Find the largest 5-digit number exactly divisible by 43.
- A. 99958
- B. 99999
- C. 99975
- D. 99989
Answer: 99975
Explanation: The largest 5-digit number is 99999. 99999 divided by 43 leaves remainder 99999 - 43 x 2325 = 99999 - 99975 = 24, so subtracting 24 gives 99975 = 43 x 2325.
297. Find the smallest 6-digit number exactly divisible by 37.
- A. 100037
- B. 100007
- C. 100000
- D. 100011
Answer: 100011
Explanation: The smallest 6-digit number is 100000. 100000 divided by 37 leaves remainder 100000 - 37 x 2702 = 100000 - 99974 = 26, so add 37 - 26 = 11 to get 100011 = 37 x 2703.
298. Find the sum of squares of the first 12 natural numbers.
- A. 600
- B. 650
- C. 625
- D. 676
Answer: 650
Explanation: The sum of squares of the first n natural numbers is n(n+1)(2n+1)/6. For n = 12: 12 x 13 x 25 / 6 = 3900 / 6 = 650.
299. Find the sum of the first 25 natural numbers.
- A. 300
- B. 310
- C. 325
- D. 350
Answer: 325
Explanation: The sum of the first n natural numbers is n(n+1)/2. For n = 25 this is 25 x 26 / 2 = 650 / 2 = 325.
300. Find the unit digit of 11^200.
- A. 1
- B. 9
- C. 0
- D. 5
Answer: 1
Explanation: The unit digit of 11^n depends only on the unit digit of the base, and 1 multiplied by itself always ends in 1. So 11^200 ends in 1.
301. Find the unit digit of 6^53.
- A. 5
- B. 6
- C. 1
- D. 0
Answer: 6
Explanation: The unit digit of 6^n depends only on the unit digit of the base, and 6 multiplied by itself always ends in 6. So 6^53 ends in 6.
302. Find the unit digit of 13^88.
- A. 7
- B. 9
- C. 3
- D. 1
Answer: 1
Explanation: The unit digits of powers of 13 repeat in a cycle of 4: 3, 9, 7, 1. Since 88 divided by 4 leaves remainder 0, we take position 4 in the cycle, giving unit digit 1.
303. Find the LCM of 14, 21 and 35.
- A. 210
- B. 70
- C. 420
- D. 105
Answer: 210
Explanation: 14 = 2 x 7, 21 = 3 x 7 and 35 = 5 x 7. The LCM is the product of the highest power of each prime: 2 x 3 x 5 x 7 = 210.
304. Find the HCF of 56 and 98.
- A. 7
- B. 14
- C. 28
- D. 21
Answer: 14
Explanation: Factorise: 56 = 2^3 x 7 and 98 = 2 x 7^2. The HCF is the product of the common prime factors with the lowest powers, which is 14. It divides 56 exactly 4 times and 98 exactly 7 times.
305. Find the LCM of 72 and 120.
- A. 240
- B. 480
- C. 360
- D. 180
Answer: 360
Explanation: HCF of 72 and 120 is 24. Using LCM = (product) / HCF = 72 x 120 / 24 = 8640 / 24 = 360. Check: 360 divides evenly by both 72 and 120.
306. Find the HCF of 72 and 120.
- A. 18
- B. 12
- C. 36
- D. 24
Answer: 24
Explanation: Factorise: 72 = 2^3 x 3^2 and 120 = 2^3 x 3 x 5. The HCF is the product of the common prime factors with the lowest powers, which is 24. It divides 72 exactly 3 times and 120 exactly 5 times.
307. Convert the recurring decimal 0.666... into a fraction.
- A. 2/3
- B. 1/2
- C. 3/5
- D. 6/10
Answer: 2/3
Explanation: Let x = 0.666... Then 10x = 6.666..., and subtracting gives 9x = 6, so x = 6/9 = 2/3. Check: 2 / 3 = 0.666...
308. Find the smallest number which, when divided by 12, 15 and 20, leaves remainder 5 in each case.
- A. 55
- B. 70
- C. 60
- D. 65
Answer: 65
Explanation: The LCM of 12, 15 and 20 is 60 (2^2 x 3 x 5). The smallest number leaving remainder 5 in each case is LCM + 5 = 60 + 5 = 65. Check: 65 = 12 x 5 + 5 = 15 x 4 + 5 = 20 x 3 + 5.
309. A number when divided by 7 leaves remainder 3, and the quotient is 15. Find the number.
- A. 112
- B. 105
- C. 98
- D. 108
Answer: 108
Explanation: By the division rule, dividend = divisor x quotient + remainder = 7 x 15 + 3 = 105 + 3 = 108.
310. Find the greatest number that divides 245 and 1029 leaving remainder 5 in each case.
- A. 8
- B. 16
- C. 24
- D. 32
Answer: 16
Explanation: The required number divides 245 - 5 = 240 and 1029 - 5 = 1024 exactly, and it must be greater than 5. HCF(240, 1024) = 16, since 240 = 2^4 x 15 and 1024 = 2^10. So the answer is 16.
311. How many prime numbers are there between 1 and 20?
- A. 6
- B. 8
- C. 7
- D. 9
Answer: 8
Explanation: The primes below 20 are 2, 3, 5, 7, 11, 13, 17 and 19, which makes 8 primes. 1 is not prime and no other number up to 20 is prime.
312. Using HCF(36,90)=18, find the LCM of 36 and 90.
- A. 180
- B. 360
- C. 144
- D. 90
Answer: 180
Explanation: Using HCF x LCM = product: LCM = 36 x 90 / 18 = 3240 / 18 = 180. Check that 180 / 36 = 5 and 180 / 90 = 2 are whole numbers.
313. Find the HCF of 36 and 90.
- A. 6
- B. 12
- C. 18
- D. 9
Answer: 18
Explanation: Factorise: 36 = 2^2 x 3^2 and 90 = 2 x 3^2 x 5. The HCF is the product of the common prime factors with the lowest powers, which is 18. It divides 36 exactly 2 times and 90 exactly 5 times.
314. For two numbers, HCF × LCM = 3240 and their HCF is 18. If one number is 36, find the LCM.
- A. 198
- B. 180
- C. 144
- D. 162
Answer: 180
Explanation: Since HCF x LCM = product of the two numbers, the second number is 3240 / 36 = 90. The LCM = 3240 / HCF = 3240 / 18 = 180, and indeed LCM(36, 90) = 180.
315. Find the unit digit of 4^37.
- A. 8
- B. 4
- C. 2
- D. 6
Answer: 4
Explanation: The unit digits of powers of 4 repeat in a cycle of 2: 4, 6. Since 37 divided by 2 leaves remainder 1, we take position 1 in the cycle, giving unit digit 4.
316. Find the unit digit of 7^123.
- A. 1
- B. 3
- C. 9
- D. 7
Answer: 3
Explanation: The unit digits of powers of 7 repeat in a cycle of 4: 7, 9, 3, 1. Since 123 divided by 4 leaves remainder 3, we take position 3 in the cycle, giving unit digit 3.
317. Find √2809.
- A. 55
- B. 49
- C. 51
- D. 53
Answer: 53
Explanation: 53 x 53 = 2809 (50 x 50 = 2500, plus 2 x 50 x 3 = 300, plus 9). Also 2809 ends in 9, so the root ends in 3 or 7, and lies between 50 and 60, giving 53.
318. Find the cube root of 512.
- A. 9
- B. 7
- C. 8
- D. 6
Answer: 8
Explanation: 512 = 2^9, so its cube root is 2^3 = 8. Check: 8 x 8 x 8 = 512. 9 cubed is 729 and 7 cubed is 343, so they do not fit.
319. Find the sum of the first 15 odd numbers.
- A. 225
- B. 196
- C. 240
- D. 210
Answer: 225
Explanation: The sum of the first n odd numbers is n^2. For n = 15 the sum is 15^2 = 225 (1 + 3 + 5 + ... + 29).
320. Two numbers are in ratio 3:4 and their HCF is 5. Find the numbers.
- A. 15 and 20
- B. 12 and 16
- C. 9 and 12
- D. 18 and 24
Answer: 15 and 20
Explanation: Let the numbers be 3k and 4k where k is their HCF. With HCF 5, the numbers are 3 x 5 = 15 and 4 x 5 = 20. Check: HCF(15, 20) = 5 and 15:20 = 3:4.
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