## Number Systems | Test 1

Number of Questions: 34 | Difficulty: Moderate

Q.1 Which of the following is the smallest?
(a) 51/2
(b) 613
(c) 81/4
(d) 121/6

Q.2 A number N is divisible by 6 but not divisible by 4. Which of the following will not be an integer?
(a) N/3
(b) 1/2
(c) N/6
(d) N/12

Q.3 If a, b, and c are consecutive positive integers, then the largest number that always divides (a2 + b2 + c)
(a) 14
(b) 55
(C) 3
(d) None of these

Q.4  (3.134)3 +(1.866)3
(3.134) – 3.134×1.866+(1.866)2
(a) 2.5
(b) 2.68
(c) 1.038
(d) 5

Q.5 If n2 is a perfect cube, then which of the following statements is always true?
(a) n is odd.
(b) n is even.
(c) n is a perfect square.
(d) n is a perfect cube.

Q.6 If (5x + 1ly) is a prime number for natural number values of x and y, then what is the minimum value of (x + y)?
(a) 2
(b) 3
(c) 4
(d) 5

Q.7 For what values of x is (25x + 1) divisible by 13?
(a) All real values of x
(b) Odd natural values of x
(c) Even values of x
(d) All the integral values of x

Q.8 Which of the following numbers lies between 5/6 and 6/7?
(a) 71/84
(b) 31/42
(c) 1297168
(d) 157/339

Q.9 By multiplying with which of the following numbers, does the product of 8 x 9 x 10 x 11 x 12 become a perfect square?
(a) 55
(b) 11
(C) 165
(d) 310

Q.10 What is the difference between the sum of the cubes and that of squares of the first 10 natural numbers?
(a) 5280
(b) 2640
(c) 3820
(d) 4130

Q.11 If 3 – 9+ 15 – 21 + … up to 19 terms = x then x is a/ an
(a) odd number
(b) even number
(c) prime number
(d) irrational number

Q.12 What is the units digit of 213 x 212 x 347 x 468 x 778?
(a) 4
(b) 8
(c) 6
(d) 2

Q.13 If the units digit in the product (47n x 729 x 345 x 343) is 5, what is the maximum number of values that n may take?
(a) 9
(b) 3
(c) 7
(d) 5

Q.14 In how many ways, can 846 be resolved into two factors?
(a) 9
(b) 11
(c) 6
(d) None of these

Q.15 If a number is divided by 15, it leaves a remainder of 7.If thrice the number is divided by 5, then what is the remainder?
(a) 5
(b) 6
(c) 7
(d) 1

Q.16 A number when divided by 391 gives a remainder of 49.Find the remainder when it is divided by 39.
(a) 10
(b) 9
(c) 11
(d) Cannot be determined

Q.17 p and q are two prime numbers such that p<q <50. In how many cases, would (q + p) be also a prime number?
(a) 5
(b) 6
(c) 7
(d) None of these

Q.18 How many distinct factors of 1600 are perfect cubes?
(a) 3
(b) 4
(c) 6
(d) 2

Q.19 The LCM of 96, 144 and N is 576. If their HCF is 48,then which of the following can be one of the values of N?

(a) 168
(b) 192
(c) 144
(d) 244

Q.20 If p and q are consecutive natural numbers in (in-creasing order), then which of the following is true?
(a) q2 <p
(b) 2p > p2
(c) (q + 1)2>p2
(d) (p + 2)3<q3

Q.21 (1721 + 1921) is not divisible by
(a) 36
(b) 8
(c) 9
(d) 18

Q.22 Which of the following will divide 1112296– 1?
(a) 11 and 12
(b) 11 and 10
(c) 10 and 12
(d) 11 only

Q.23. If a, b, c, and d are consecutive odd numbers, then (a2 + b2 + c2 + d2) is always divisible by
(a) 5
(b) 7
(c) 3
(d) 4

Q.24. Three bells toll at intervals of 14, 21, and 42 min, respectively. If they toll together at 11:22 am, when will they toll together for the first time after that?
(a) 11:56 am
(b) 12:04 pm
(c) 12:06 pm
(d) 11:48 am

Q.25 When x is divided by 6, remainder obtained is 3. Find the remainder when (x4+x3+x2+x+1) is divided by
(b) 5
(b) 4
(c) 1
(d) 5

Q.26 I have 77 sweets and I want to distribute them equally among 24 students. After each of the student got maximum integral sweets, how many sweets are
left with me?
(a) 8
(b) 5
(c) 1
(d) None of these

Q.27 When I distribute some chocolates to my 40 students, three chocolates will be left. If I distribute the same number of chocolates to my students and my colleague Manoj Dawrani, seven chocolates are left. Find the minimum number of chocolates I have.
(a) 1443
(b) 1476
(c) 1480
(d) None of these

Q.28 The LCM of two numbers is 40 times of their HCF. The sum of the LCM and HCF is 1476. If one of the numbers is 288, find the other numbers.
(a) 169
(b) 180
(c) 240
(d) 260

Q.29.  1010101…94 digits is a 94-digit number. What will be the remainder obtained when this number is divided by 375?
(a) 10
(b) 320
(c) 260
(d) None of these

Q.30 Chandrabhal adds first N natural numbers and finds the sum to be 1850. However, actually one number was added twice by mistake. Find the difference between N and that number.
(a) 40
(b) 33
(c) 60
(d) 17

Q.31 When I distribute a packet of chocolates to 7 students, I am left with 4 chocolates. When I distribute the same packet of chocolates to 11 students, I am left with 6 chocolates. How many chocolates will be left with me if I distribute the same packet of chocolates among 13 students (a packet of chocolate contains total number of N chocolates, where 1000 <N< 1050)?
(a) 2
(b) 0
(c) 6
(d) 7

Q.32 How many prime numbers are there between 80 and 105?
(a) 3
(b) 4
(c) 5
(d) 8

Q.33 If x and y are consecutive natural numbers in an in-creasing order, then which of the following is always true?
(a) YY    > YX
(b) YX  > Xy
(c) XX   > YY
(d) YY  >  XX

Q.34 What is the remainder when 579 is divided by 7?
(a) 1
(b) 0
(c) 5
(d) 4