0 correct out of 0 attempted (0%)
Correct answer: C
I is correct: the remainder when 2^10 is divided by 7 → 2. 2³ leaves remainder 1, so 2^10 leaves remainder 2. II is correct: the largest integer dividing both 84 and 126 → 42. 84 = 2×42 and 126 = 3×42.
Correct answer: A
On the number line -3 is the greatest integer strictly below -2.3.
Correct answer: B
I is incorrect: the number of zeros at the end of 25! → 6. Count factors of 5: floor(25/5)+floor(25/25)=5+1. II is correct: the number of distinct prime factors of 210 → 4. 210 = 2×3×5×7.
Correct answer: B
I is correct: the remainder when 1001 is divided by 13 → 0. 1001 = 13×77. II is correct: the sum of the first twenty positive odd integers → 400. The sum of the first n odd integers is n².
Correct answer: C
The digit sum is 11+x; 18 is the permitted multiple of 9.
Correct answer: A
I is incorrect: the least positive number added to 138 to make a multiple of 11 → 5. The next multiple is 143, so the difference is 5. II is correct: the integer n if n is positive and n²=169 → 13. The positive square root of 169 is 13.
Correct answer: D
84 = 2×42 and 126 = 3×42.
Correct answer: C
I is correct: the greatest integer less than -2.3 → -3. On the number line -3 is the greatest integer strictly below -2.3. II is correct: the smallest prime factor of 91 → 7. 91 = 7 × 13.
Correct answer: A
2³ leaves remainder 1, so 2^10 leaves remainder 2.
Correct answer: B
I is incorrect: the smallest positive integer divisible by 8, 12 and 18 → 72. The LCM uses 2³ and 3², giving 72. II is correct: the greatest three-digit multiple of 17 → 986. 17×58=986, whereas 17×59=1003.
Correct answer: C
The sum of the first n odd integers is n².
Correct answer: A
I is incorrect: the last digit of 7^23 → 3. The last-digit cycle is 7,9,3,1 and 23 leaves remainder 3 on division by 4. II is correct: the largest integer dividing both 84 and 126 → 42. 84 = 2×42 and 126 = 3×42.
Correct answer: D
210 = 2×3×5×7.
Correct answer: B
I is correct: the remainder when 1001 is divided by 13 → 0. 1001 = 13×77. II is correct: the least positive number added to 138 to make a multiple of 11 → 5. The next multiple is 143, so the difference is 5.
Correct answer: C
91 = 7 × 13.
Correct answer: D
I is correct: the greatest integer less than -2.3 → -3. On the number line -3 is the greatest integer strictly below -2.3. II is correct: the number of zeros at the end of 25! → 6. Count factors of 5: floor(25/5)+floor(25/25)=5+1.
Correct answer: C
1001 = 13×77.
Correct answer: A
I is incorrect: the least positive number added to 138 to make a multiple of 11 → 5. The next multiple is 143, so the difference is 5. II is correct: the missing digit x making 54x2 divisible by 9 → 7. The digit sum is 11+x; 18 is the permitted multiple of 9.
Correct answer: D
The last-digit cycle is 7,9,3,1 and 23 leaves remainder 3 on division by 4.
Correct answer: C
I is incorrect: the smallest prime factor of 91 → 7. 91 = 7 × 13. II is correct: the number of positive divisors of 36 → 9. 36 = 2² × 3², giving (2+1)(2+1)=9 divisors.
Correct answer: D
17×58=986, whereas 17×59=1003.
Correct answer: C
I is correct: the least positive number added to 138 to make a multiple of 11 → 5. The next multiple is 143, so the difference is 5. II is correct: the largest integer dividing both 84 and 126 → 42. 84 = 2×42 and 126 = 3×42.
Correct answer: A
Count factors of 5: floor(25/5)+floor(25/25)=5+1.
Correct answer: D
I is correct: the smallest prime factor of 91 → 7. 91 = 7 × 13. II is correct: the last digit of 7^23 → 3. The last-digit cycle is 7,9,3,1 and 23 leaves remainder 3 on division by 4.
Correct answer: C
The positive square root of 169 is 13.