Number system
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See all →- How many numbers between 100 and 300 are exactly divisible by 7? Answer: D. 28 Answer: (D) 28 Multiples of 7 up to 299: lfloor 299/7 rfloor = 42 . Up to 100: lfloor 100/7 rfloor = 14 . Count = 42 - 14 = 28... 1
- What is the unit digit of \(3^{65} \times 7^{42}\)? Answer: B. 7 Answer: (B) 7 Unit digits of powers of 3 cycle 3, 9, 7, 1; 65 = 4 × 16 + 1 , so 3⁶⁵ ends in 3. Powers of 7 cycle 7, 9, 3, 1; 42... 1
- What is the remainder when \(7^{45}\) is divided by 5? Answer: D. 2 Answer: (D) 2 7 equiv 2 ±od 5 , so we need 2⁴⁵ bmod 5 . Powers of 2 mod 5 repeat in a cycle of 4: 2, 4, 3, 1. 45 = 4 × 11 + 1 ,... 1
- What is the smallest number that must be added to 2375 so that the sum is exactly divisible by 17? Answer: C. 5 Answer: (C) 5 2375 = 17 × 139 + 12 . Remainder 12, so add 17 - 12 = 5 : 2380 = 17 × 140 . 1
- What is the least number that must be added to 1,000 so that the sum is exactly divisible by 23? Answer: D. 12 Answer: (D) 12 1000 ÷ 23 leaves remainder 11 (23 × 43 = 989). Add 23 − 11 = 12 to get 1012 = 23 × 44. 1
- The sum of three consecutive even numbers is 138. What is the largest of the three numbers? Answer: C. 48 Answer: (C) 48 Middle number = 138 ÷ 3 = 46. The numbers are 44, 46, 48, so the largest is 48. 1