Q 1 - What is the unit digit in (384)1793 x (1035)317 x (261)491?
A. 5
B. 7
C. 1
D. 0
Unit Digit in (384)1793 = Unit Digit in (4)1793 = Unit Digit in (42)896 x 4 = Unit Digit in (6 x 4) = 4 Unit Digit in (1035)317 = Unit Digit in (5)317 = 5 Unit Digit in (261)491 = Unit Digit in (1)491 = 1 Therefore, unit digit in (384)1793 x (1035)317 x (261)491 = Unit Digit in (4 x 5 x 1) = 0
Q 2 - The sum of first 25 natural numbers is?
A. 125
B. 325
C. 20
D. 750
Sn = (1 + 2 + 3 + 4 + ... + 25) A.P -> a = 1, d = 1, n = 25 where n = terms Sn = S25 = n⁄2[2a + (n-1)d] = 25⁄2 [2 x 1 + (25 - 1) x 1] = 25 x 13 = 325
Q 3 - The difference of the squares of two consecutive even integers is divisible by which of the following integers?
A. 1
B. 5
C. 4
D. 2
Let the consecutive integers(even) be 2p and (2p + 2): = (2p + 2)2 - 2p2 = (2p + 2 + 2p)(2p + 2 -2p) = 2(4p + 2) = 4 (2p + 1) Therefore, divisible by 4.
Q 4 - How many natural numbers are there between 17 and 90 which are exactly divisible by 6?
A. 13
B. 15
C. 14
D. 16
Numbers -> 18, 24, 30, ... , 90 A.P: a = 18, d = 6, l = 90 tn = a + (n-1)d 90 = 18 + (n-1)6 90 = 18 + 6n -6 n = 13
Q 5 - I how many ways can 22500 be written as a product of two different factors?
A. 10
B. 32
C. 22
D. 12
1502 = 22500 Therefore, 1502 = ((2)(5)(3)(5))2 = 225432 = 1⁄2{(2 + 1)(4 + 1)(2 + 1) - 1} = 22
Q 6 - If unit digit in 549 x 56 x 28p x 684 is 8 then what is p?
A. 4
B. 3
C. 2
D. 1
Multiply unit digits of each number. Unit digit in 549 x 56 x 28p x 684 = 8 Unit digit in 9 x 6 x p x 4 = 8 Unit digit in 216 x p = 8 Thus p must be 3.
Q 7 - 587 x 999 = y. What is y?
A. 586413
B. 586423
C. 586433
D. 586443
y = 587 x 999 = 587 x (1000 - 1) = 587 x 1000 - 587 = 587000 - 587 = 586413
Q 8 - Which of the following is not a prime number?
A. 31
B. 61
C. 71
D. 91
91. As it is divisible by 7.
Q 9 - 517p324 is divisible by 3. What is minimum p?
A. 0
B. 1
D. 3
5 + 1 + 7 + p + 3 + 2 + 4 = 22 + x which is divisible by 3 ∴ x = 2
Q 10 - On dividing a number by 342, 47 is the remainder. What will be remainder if same number is divided by 18?
A. 11
B. 6
C. 8
Let's quotient is a and given number be b. b = 342a + 47 = (18 x 19)a + 36 + 11 = (18 x 19)a + (18 x 2) + 11 = 18 x (19a + 2) + 11 Thus, if same number is divided by 18, remainder will be 11.