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CAT 2025 Lesson : Quant: Jan '25 to Feb '25 - Numbers 1 Solving - 9 Jan 2025
Numbers 1
1) The sum of seven consecutive odd integers is 175. What is the sum of the two largest integers among them?
Answer:
2) In 30 consecutive even integers, what is the maximum possible difference between any two of the integers?
Answer:
3) How many 3-digit numbers exist such that the product of their hundreds and units digits is not a composite number?
Answer:
4) Where x, y and z are distinct positive integers such that x and y are odd and z is even and greater than the sum of x and y. Which of the following is never even?
(1) (x – z)(y – z)(x + y - z)
(2) (x – y)(y – z)(z - x)
(3) (x + z)(y + z)(2x - y)
(4) (x + z)(y + z)(2x - z)
5) Which of the following equals 2.343343343343... ?
(1)
(2)
(3)
(4)
6) Where and , what is = ?
Answer:
7) The largest natural number that will perfectly divide the product of any 6 consecutive natural numbers is
Answer:
8) Where x is an integer that perfectly divides 7056, how many different solutions
(i) exist for x?
(ii) exist for x, where x is positive?
(iii) exist for x, where x is positive and odd?
(iv) exist for x, where x is even?
Answer:
9) In how many different ways can 7056 be written as
(i) a product of two integers?
(ii) a product of two positive integers?
(iii) a product of two distinct positive integers?
Answer:
10) What is the product of all the factors of 7056?
(1)
(2)
(3)
(4)
11) How many consecutive integers exist between -23 and 71 (both included)?
Answer:
12) How many terms are there in the series -341, -333, -325, ... , 75?
Answer:
13) When you reverse the digits of a 2-digit positive integer, the value increases by 27. How many such 2-digit positive integers exist?
Answer:
14) How many 3-digit positive integers exist such that the difference between the integer and the integer formed by reversing its digits is 198?
Answer:
15) If and , then equals
Answer:
16) () is definitely divisible by
(i) 26
(ii) 24
(iii) 156
(iv) 312
(1) (i) and (iii)
(2) (ii) and (iv)
(3) (i), (ii) and (iii)
(4) (i), (ii), (iii) and (iv)
17) How many factors of are perfect cubes greater than 1?
Answer:
18) A, B and C take seconds, seconds and 10 seconds to go around a circular track. A, B and C start from the a point P at the same time, and stop when all three of them meet at P once again. What is the total number of laps covered by the three of them?
Answer:
19) Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17
(2) 16
(3) 18
(4) 15
(5) 19
20) Vishwa divides a positive integer with another integer and gets 3.4954954954... If the largest positive integer that perfectly divides and is 1, then =
(1) 498
(2) 499
(3) 4491
(4) 4492
1) The sum of seven consecutive odd integers is 175. What is the sum of the two largest integers among them?
Answer:
2) In 30 consecutive even integers, what is the maximum possible difference between any two of the integers?
Answer:
3) How many 3-digit numbers exist such that the product of their hundreds and units digits is not a composite number?
Answer:
4) Where x, y and z are distinct positive integers such that x and y are odd and z is even and greater than the sum of x and y. Which of the following is never even?
(1) (x – z)(y – z)(x + y - z)
(2) (x – y)(y – z)(z - x)
(3) (x + z)(y + z)(2x - y)
(4) (x + z)(y + z)(2x - z)
5) Which of the following equals 2.343343343343... ?
(1)
(2)
(3)
(4)
6) Where and , what is = ?
Answer:
7) The largest natural number that will perfectly divide the product of any 6 consecutive natural numbers is
Answer:
8) Where x is an integer that perfectly divides 7056, how many different solutions
(i) exist for x?
(ii) exist for x, where x is positive?
(iii) exist for x, where x is positive and odd?
(iv) exist for x, where x is even?
Answer:
9) In how many different ways can 7056 be written as
(i) a product of two integers?
(ii) a product of two positive integers?
(iii) a product of two distinct positive integers?
Answer:
10) What is the product of all the factors of 7056?
(1)
(2)
(3)
(4)
11) How many consecutive integers exist between -23 and 71 (both included)?
Answer:
12) How many terms are there in the series -341, -333, -325, ... , 75?
Answer:
13) When you reverse the digits of a 2-digit positive integer, the value increases by 27. How many such 2-digit positive integers exist?
Answer:
14) How many 3-digit positive integers exist such that the difference between the integer and the integer formed by reversing its digits is 198?
Answer:
15) If and , then equals
Answer:
16) () is definitely divisible by
(i) 26
(ii) 24
(iii) 156
(iv) 312
(1) (i) and (iii)
(2) (ii) and (iv)
(3) (i), (ii) and (iii)
(4) (i), (ii), (iii) and (iv)
17) How many factors of are perfect cubes greater than 1?
Answer:
18) A, B and C take seconds, seconds and 10 seconds to go around a circular track. A, B and C start from the a point P at the same time, and stop when all three of them meet at P once again. What is the total number of laps covered by the three of them?
Answer:
19) Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?
(1) 17
(2) 16
(3) 18
(4) 15
(5) 19
20) Vishwa divides a positive integer with another integer and gets 3.4954954954... If the largest positive integer that perfectly divides and is 1, then =
(1) 498
(2) 499
(3) 4491
(4) 4492
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