Advanced No. Questions : Advanced No. Questions
Learning Objectives : Learning Objectives 1. No. of Zeroes
2. The Last digit problems
3. The remainder questions.
4. Highest power that can
divide a number.
5. Some advanced no. ques.
6. Certain Actual CAT ques.
Ques. 1: What is the number of zeroes at the end of 120!? (CAT 1993). : Ques. 1: What is the number of zeroes at the end of 120!? (CAT 1993).
Slide 4 : Answer is 28
Ques. 2: M is an odd integer & N is an even integer, which of the following is always true? 1. M(N – 1) is even. 2. (M – 1)N is odd. 3. MN is odd. 4. (M – 1)(N – 1) is even : Ques. 2: M is an odd integer & N is an even integer, which of the following is always true? 1. M(N – 1) is even. 2. (M – 1)N is odd. 3. MN is odd. 4. (M – 1)(N – 1) is even
Slide 6 : Answer is 4th option
Ques. 3: What will be the remainder when 7123 is divided by 8? : Ques. 3: What will be the remainder when 7123 is divided by 8?
Slide 8 : Answer is 7
Ques.4: The remainder when 784 is divided by 342 is (CAT 1999):1. 0 2. 1 3. 49 4. 341 : Ques.4: The remainder when 784 is divided by 342 is (CAT 1999):1. 0 2. 1 3. 49 4. 341
Slide 10 : Answer is
2nd option
Ques.5 : What is the remainder when 496 is divided by 6 (CAT 2003)? 1. 0 2. 2 3. 3 4. 4 : Ques.5 : What is the remainder when 496 is divided by 6 (CAT 2003)? 1. 0 2. 2 3. 3 4. 4
Slide 12 : Answer is 4th option
Ques. 6 : What is the remainder when 2! + 4! + 6! + 8! + … 100! is divided by 3? : Ques. 6 : What is the remainder when 2! + 4! + 6! + 8! + … 100! is divided by 3?
Slide 14 : Answer is 2
Ques. 7: On a paper first 100 natural no. are written, then all the no. which are multiples of 3 or 4 but not both are erased. What is the number of remaining natural numbers on the paper? : Ques. 7: On a paper first 100 natural no. are written, then all the no. which are multiples of 3 or 4 but not both are erased. What is the number of remaining natural numbers on the paper?
Slide 16 : Answer is 50.
Answer is 42.
Answer is 58.
Ques. 8: What isthe unit’s digit of the expression 327301 8572 – 21421? : Ques. 8: What isthe unit’s digit of the expression 327301 8572 – 21421?
Slide 18 : Answer is 1
Ques. 9: What is the greatest power of 3 that will divide 41! completely? : Ques. 9: What is the greatest power of 3 that will divide 41! completely?
Slide 20 : Answer is 18
Ques. 10: When 2 numbers are divided by a divisor, 17 & 21 are obtained as remainders, when the sum of these 2 no. is divided by the same divisor the remainder is 7. Find the divisor. : Ques. 10: When 2 numbers are divided by a divisor, 17 & 21 are obtained as remainders, when the sum of these 2 no. is divided by the same divisor the remainder is 7. Find the divisor.
Slide 22 : Answer is 31
Ques. 11 : If a, a + 2, and a + 4 are prime numbers, then the number of possible solutions for a is (CAT 2003):1. one 2. two 3. three 4. more than three : Ques. 11 : If a, a + 2, and a + 4 are prime numbers, then the number of possible solutions for a is (CAT 2003):1. one 2. two 3. three 4. more than three
Slide 24 : Answer is 1st option
Ques. 12 : A merchant had gold coins. One day, his wife asked, "How many gold coins do we have?" After a moment, he replied, "If I divide the coins into 2 unequal no., then 48 times the d/f b/w the 2 no. equals the d/f b/w the squares of the 2 no. Find the no. of gold coins (CAT 2002). 1. 96 2. 53 3. 43 4. None of these : Ques. 12 : A merchant had gold coins. One day, his wife asked, "How many gold coins do we have?" After a moment, he replied, "If I divide the coins into 2 unequal no., then 48 times the d/f b/w the 2 no. equals the d/f b/w the squares of the 2 no. Find the no. of gold coins (CAT 2002). 1. 96 2. 53 3. 43 4. None of these
Slide 26 : 4th option (48)
Slide 27 : THANK YOU