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Number System Examples
Answer - B
Explanation
Step 1. Find a whole number k such that k2 > n for each number. 142 > 187. 302 > 811. 192 > 341. 212 > 437. Step 2. Get all prime numbers which are < k 14 - 2 , 3, 5, 7, 11, 13 30 - 2 , 3, 5, 7, 11, 13, 17, 19, 23, 29 19 - 2 , 3, 5, 7, 11, 13, 17 21 - 2 , 3, 5, 7, 11, 13, 17, 19 Step 3. Check divisiblity of each number with prime numbers which are < k. 187 is divisible by 11. 811 is not divisible by any prime number. 341 is divisible by 11. 437 is divisible by 19. Result: 811 is the prime number.
Q 2 - Which of the following is the output of 6894 x 99 ?
Answer - B
Explanation
6894 x 99 = 6894 x (100 - 1) = 6894 x 100 - 6894 x 1 = 689400 - 6894 = 682506
Q 3 - Which of the following is the output of 685798 x 125 ?
Answer - A
Explanation
685798 x 125 = 685798 x 53 = 685798 x (10/2)3 = (685798 x 103) / 23 = 685798000 / 8 = 85724750
Q 4 - Which of the following is the output of 43986 x 625 ?
Answer - C
Explanation
43986 x 625 = 43986 x 54 = 43986 x (10/2)4 = (43986 x 104) / 24 = 439860000 / 16 = 27491250
Q 5 - Which of the following is the output of 869 x 738 + 869 x 262 ?
Answer - D
Explanation
869 x 738 + 869 x 262 = 869 x (738 + 262) = 869 x 1000 = 869000
Q 6 - Which of the following is the output of 936 x 587 - 936 x 487 ?
Answer - A
Explanation
936 x 587 - 936 x 487 = 936 x (587 - 487) = 936 x 100 = 93600
Q 7 - Which of the following is the output of 1496 x 1496 ?
Answer - B
Explanation
1496 x 1496 = 14962 = (1500-4)2 = 15002 + 42 - 2 x 1500 x 4 = 2250000 + 16 - 12000 = 2238016
We've used following formula here:
(a-b)2 = a2 + b2 - 2ab.
Q 8 - Which of the following is the output of 1607 x 1607 ?
Answer - C
Explanation
1607 x 1607 = 16072 = (1600+7)2 = 16002 + 72 + 2 x 1600 x 7 = 2560000 + 49 +22400 = 2582449
We've used following formula here:
(a+b)2 = a2 + b2 + 2ab.
Q 9 - Which of the following is the output of 596 x 596 - 104 x 104 ?
Answer - D
Explanation
596 x 596 - 104 x 104 = 5962 - 1042 = (596 + 104) x (596 - 104) = 700 x 492 = 344400
We've used following formula here:
a2 - b2 = (a + b)(a - b).
Q 10 - Which of the following is the output of 57 x 57 + 43 x 43 + 2 x 57 x 43 ?
Answer - A
Explanation
57 x 57 + 43 x 43 + 2 x 57 x 43 = (57 + 43)2 = (100)2 = 10000
We've used following formula here:
(a + b)2 = a2 + b2 + 2ab.
Q 11 - Which of the following is the output of 93 x 93 + 73 x 73 - 2 x 93 x 73 ?
Answer - B
Explanation
93 x 93 + 73 x 73 - 2 x 93 x 73 = (93 - 73)2 = (20)2 = 400
We've used following formula here:
(a - b)2 = a2 + b2 - 2ab.
Q 12 - Which of the following is the output of (578 x 578 x 578 + 432 x 432 x 432) / (578 x 578 - 578 x 432 + 432 x 432) ?
Answer - D
Explanation
(578 x 578 x 578 + 432 x 432 x 432) / (578 x 578 - 578 x 432 + 432 x 432) Let's have a = 578, b = 432 Now expression is (a3 + b3) / (a2 - ab + b2) = a + b = 578 + 432 = 1000
We've used following formula here:
a3 + b3 = (a + b)(a2 - ab + b2).
Q 13 - Which of the following is the output of (141 x 141 x 141 - 58 x 58 x 58) / (141 x 141 + 141 x 58 + 58 x 58) ?
Answer - A
Explanation
(141 x 141 x 141 - 58 x 58 x 58) / (141 x 141 + 141 x 58 + 58 x 58) Let's have a = 141, b = 58 Now expression is (a3 - b3) / (a2 + ab + b2) = a - b = 141 - 58 = 83
We've used following formula here:
a3 - b3 = (a - b)(a2 + ab + b2).
Q 14 - Which of the following is the output of 213 x 213 + 187 x 187 ?
Answer - B
Explanation
213 x 213 + 187 x 187 Let's have a = 213, b = 187 Now expression is a2 + b2 Using following formula, (a + b)2 + (a - b)2 = 2 x (a2 + b2) 2 x ( 213 x 213 + 187 x 187) = (213 + 187)2 + (213 - 187)2 2 x ( 213 x 213 + 187 x 187) = 4002 + 262 2 x ( 213 x 213 + 187 x 187) = 160000 + 676 213 x 213 + 187 x 187 = 160676 / 2 = 80338
Q 15 - Which of the following is the output of ((637 + 478)2 - (637 - 478)2) /(637 x 478) ?
Answer - C
Explanation
((637 + 478)2 - (637 - 478)2)/(637 x 478) Let's have a = 637, b = 478 Now expression is ((a + b)2 - (a - b)2) / ab = (a2 + b2 + 2ab - (a2 + b2 - 2ab)) / ab = (a2 + b2 + 2ab - a2 - b2 + 2ab) / ab = 4ab / ab = 4
We've used following formulae here:
(a + b)2 = a2 + b2 + 2ab. (a - b)2 = a2 + b2 - 2ab.
Q 16 - Which of the following is the output of ((964 + 578)2 + (964 - 578)2) /(964 x 964 + 578 x 578) ?
Answer - D
Explanation
((964 + 578)2 + (964 - 578)2) /(964 x 964 + 578 x 578) Let's have a = 964, b = 578 Now expression is ((a + b)2 + (a - b)2) / (a2 + b2) = (a2 + b2 + 2ab + (a2 + b2 - 2ab)) / (a2 + b2) = (a2 + b2 + 2ab + a2 + b2 - 2ab) / (a2 + b2) = 2(a2 + b2) / (a2 + b2) = 2
We've used following formulae here:
(a + b)2 = a2 + b2 + 2ab. (a - b)2 = a2 + b2 - 2ab.
Q 17 - On dividing a number by 342, 47 is the remainder. What will be remainder if same number is divided by 18?
Answer - A
Explanation
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.
We've used following formulae here:
Dividend = (Divisor x Quotient) + Reminder
Answer - B
Explanation
unit digit in (3157)754 = unit digit in (7)754 = unit digit in (74)188 x 72 = unit digit in (1 x 49) = 9 Thus Unit digit in (3157)754 is 9.
We've used following formulae here:
Unit digit in 71 = 7 Unit digit in 72 = 9 Unit digit in 73 = 3 Unit digit in 74 = 1 Unit digit in 75 = 7 Unit digit in 76 = 9 Unit digit in 77 = 3 Unit digit in 78 = 1 So pattern is 7-9-3-1. This pattern works for all numbers. So Unit digit in ((7)4)n) will be 1.
Answer - C
Explanation
Multiply unit digits of each number. Unit digit in 658 x 539 x 436 x 312 = Unit digit in 8 x 9 x 6 x 2. = Unit digit in 864. = 4.
Answer - C
Explanation
357 = (34)14 x 3 So Unit digit in 357 = Unit digit in 1 x 3 = 3 641 = (64)10 x 6 So Unit digit in 641 = Unit digit in 6 x 6 = 6 763 = (74)15 x 73 So Unit digit in 761 = Unit digit in 1 x 343 = 3 So Unit digit in 357 x 641 x 763 = Unit digit in 3 x 6 x 3 = 4
We've used following formulae here:
Unit digit in 34 = 1 Unit digit in 64 = 6 Unit digit in 74 = 1 So Unit digit - in ((3)4)n) will be 1. - in ((6)4)n) will be 6. - in ((7)4)n) will be 1.