## Number System MCQ's1) Every rational number is a - - Whole number
- Real number
- Natural number
- None of the above
2) Between any two numbers, there are - - Two rational numbers
- No rational number
- Infinite rational numbers
- None of the above
3) What will be the value of x - 3xyz
- 2xyz
- xyz
- xyz(xy + yz + zx)
x + y + z = 0 On cubing both sides, we will get (x + y + z) x So, the value of x 4) Digit 1 is occurring 136 times on writing all of the page numbers of a book. What will be the number of pages in the book? - 194
- 195
- 200
- 295
So, from 1 to 199, the digit 1 occurs - 20 + 120 = 140 times According to question 1 is occurring only 136 times, which means we need to remove 196, 197, 198, and 199. So, the required number of pages will be 195. 5) Which of the following is the unit digit in the product of 853 x 452 x 226 x 1346? - 2
- 5
- 6
- 7
3 in 853 2 in 452 6 in 226 6 in 1346 ∴ 3 x 6 x 2 x 6 = 216 (consider the unit digit in the product) So, the unit digit in the product of 853 * 1346 * 452 * 226 is 6. 6) The sum of odd numbers upto 240 is - - 11400
- 12400
- 13400
- 14400
Sum of first n odd numbers = n n = 120 Required sum = 120 7) Which of the following number is divisible by 9? - 56785
- 45678
- 65889
- 67578
The Sum of the digits of the given numbers are; 6+7+5+7+8= 33 5+6+7+8+5= 31 4+5+6+7+8= 30 6+5+8+8+9= 36 The sum of the digits of the number 65889 is 36, which is divisible by 9, so the correct answer is 65889. 8) What smallest number should be subtracted from 9805 so that it is divisible by 8? - 6
- 7
- 5
- 8
9) Which of the following is the unit digit in the product of {(341) - 3
- 7
- 0
- 8
Unit digit in (341) = Unit digit in (1) Unit digit in (625) = Unit digit in (5) Unit digit in (6374) = (4) = unit digit in [(4 = unit digit in 6 x 4 = 4 So, on multiplying the unit digits, we will get - 1 x 5 x 4 = 20 (consider the unit digit in the product) So, the unit digit in the product of {(341) 10) Which of the following is completely divisible by 45? - 331145
- 306990
- 181660
- None of the above
So, we check the divisibility of given numbers by the following rules - A number is divisible by 3 if the sum of its entire digits is divisible by 3. The number which ends with 0 or 5 is divisible by 5. A number is divisible by 9 if the sum of its entire digits is divisible by 9. The number 306990 fulfills all the requirements, so the answer is 306990. 11) If the two-third of three - fourth of a number is 34, what will be the 20% of that number? - 13.4
- 13.6
- 13.7
- 14
According to the question, 2/3 * 3/4 * X = 34 6/12 * X = 34 Or, 1/2 * X = 34 So, X = 68 Now, 20% of 68 is = 68 * 20/100 = 13.6 12) 7X2 is a three-digit number in which X is a missing digit. If the number is divisible by 6, the missing digit is - - 4
- 3
- 7
- 5
Now, 7 + X + 2 = 9 + X, must be divisible by 3. So, X = 3 makes the number divisible by 3, so 3 is the required digit. 13) Which is the largest 4-digit number that can be exactly divisible by 66? - 9987
- 9912
- 9913
- 9966
So, the largest 4-digit number divided by 66 = 9999 - 33 = 9966 14) Which is the largest 4-digit number that can be exactly divisible by 66? - 9987
- 9912
- 9913
- 9966
So, the largest 4-digit number divided by 66 = 9999 - 33 = 9966 15) What will be the remainder when 6 - 3
- 2
- 1
- None of the above
(6 Or, we can say 216 We will always get remainder 1 on dividing 216 by 215 = 1 So, the remainder will be 1. 16) Which of the following is the least number which will leave the remainder 5, when divided by 8, 12, 16, and 20? - 245
- 255
- 265
- None of the above
8 = 2 x 2 x 2 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 20 = 2 x 2 x 5 LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240 240 is the least number that is exactly divisible by 8, 12, 16, and 20. So, the required number that will leave remainder 5 is - 240 + 5 = 245 17) Which of the following is largest among others? - √0.0004
- √0.0121
- (0.1)
^{2} - 0.12
√0.0004 = 0.02 √0.0121 = 0.11 (0.1) 0.12 = 0.12 From the above examination, we can see 0.12 is the largest among others. 18) What will be the unit digit of (2153)167? - 1
- 7
- 3
- 9
As we know, 3 3 3 3 The cycle will continue. On the dividing the power of 3 by 4, we will get - 167/4 = remainder is 3 So, 3 19) If the sum of two numbers is considered as 'a' and their product is considered as 'b', then what will be the sum of their reciprocals? - a/b
- 1/b + 1/b
- b/a
- ab
So, according to the question - P + Q = a P * Q = b Sum of reciprocals of P and Q is = 1/P + 1/Q = Q + P/PQ = a/b 20) From the list of below options, which of the fraction is the smallest? - 14/33
- 7/13
- 11/13
- 8/15
So, according to the question - P + Q = a P * Q = b Sum of reciprocals of P and Q is = 1/P + 1/Q = Q + P/PQ = a/b 21) If the number A381 is divisible by 11, then what is the value of A? - 7
- 3
- 1
- 8
Hence, (A + 8) - (3 + 1) = either 0 or multiple of 11 If we put A = 7, then we get (7 + 8) - (3 + 1) = 15 - 4 = 11 (Which is divisible by 11). 22) Suppose a number 381A is divisible by 9, then what is the value of A? - 6
- 3
- 1
- 8
Hence, 3 + 8 + 1 + A = multiple of 9 If we put A = 6, then we get 3 + 8 + 1 + 6 = 18 (which is a multiple of 9) 23) Suppose there is a number 'n'. When 'n' is divided by 5, the remainder will be 2. What will be the remainder when n2 is divided by 5? - 6
- 4
- 1
- 8
n/5 = remainder 2 On putting n =7, and on dividing it with 5 we will get remainder 2 So, n = 7, and n n 24) If the difference between three times and seven times of a number is equal to 36, what will be the number? - 9
- 4
- 1
- 8
So according to the question - 7X - 3X = 36 4X = 36 Or, X = 36/4 = 9 So, the required number is 9. 25) What will be the value of x, if 5 - 11/5
- 11/6
- 5/11
- 6/11
We can write it as - 5 Or, x + 3 = 2(3x - 4) x + 3 = 6x - 8 or, 5x = 11 So, x = 11/5 26) If the sum of two numbers is 12 and their product is 35, then what will be the sum of their reciprocals? - 12/35
- 1/5
- 2/3
- None of the above
So, according to the question - P + Q = 12 P * Q = 35 Sum of reciprocals of P and Q is = 1/P + 1/Q = Q + P/PQ = 12/35 27) What will be the value of a - 126
- -125
- -126
- 125
On putting the values in the given equation, we will get - (-4) = -64 - 48 - 12 - 6 + 12 - 8 = -126 28) If the sum and reciprocal of a number is equal to 2, the number is - - 1
- -1
- -2
- 2
So, according to the question - a + 1/a = 2 (a a Or, a We can say that (a - 1) So, a =1 Hence the required number is 1, whose sum and reciprocal are equal to 2. 29) If the ratio of two positive numbers is 7 : 9 and their product is 1575, then the greatest number is - - 45
- 15
- 35
- 55
So, let the numbers be 7a and 9a. According to the question - 7a * 9a = 1575 63a a Or a And a =5 So, the two numbers will be - 7a = 7 * 5 = 35 And 9a = 9 * 5 = 45 Hence, the greater number is 45 between the given numbers. 30) The sum of two numbers is equal to the thrice of their difference. What will be the ratio between them? - 1 : 3
- 3 : 1
- 1 : 2
- 2 : 1
(a + b) = 3(a - b) (a + b) = 3a - 3b 2a = 4b a = 2b So, a/b = 2 : 1 31) Which of the following is equal to x - x
^{6}x^{3} - x
^{6}+ x^{3} - x
^{6}/ x^{3} - (x
^{6})^{3}
x 32) The sum of four consecutive even numbers is 748, then which is the smallest number among them? - 184
- 186
- 174
- None of the above
So, according to the question - (a) + (a + 2) + (a + 4) + (a + 6) = 748 4(a) + 12 = 748 4a = 736 Or, a = 184 So, the smallest number be 184
We can use an alternative solution of it Middle term = 748/4 = 187 So, the numbers will 184, 186, 188, and 190 And the smallest number between them is 184. 33) If (64) - 120
- 140
- 112
- None of the above
So, after applying the formula, we will get (64 + 36) (64 - 36) = 20 * x 100 * 28 = 20 * x x = 100 * 28/ 20 = 140 34) What is the value of (a - b), if (a - 36
- 22
- 45
- 25
a It is given that (a So, it can be written as (a + b) (a - b)/(a + b) = 25 Hence, (a - b) = 25 35) What will be the result of 1397 x 1397? - 1951609
- 1951608
- 1951699
- None of the above
We can also write it as (1397) Or, (1400 - 3) On expanding we get, = (1400) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609 36) Which of the following is the unit digit in (1570) - 2
- 4
- 6
- 7
0 1 2 3 On adding the unit digits, we will get, 0 + 1 + 4 + 9 = 14 (unit digit = 4) So, on adding (1570) 37) Suppose x = a(b - c), y = b(c - a), z = c(a - b), then what is the value of (x/a) - 3xyz/abc
- 2xyz/abc
- xyz/abc
- None of the above
x = a(b - c) or, x/a = (b - c) …..(i) y = b(c - a) or, y/b = (c - a) …..(ii) z = c(a - b) or, z/c = (a - b) …..(iii) Add equation (i), (ii), and (iii), we will get x/a + y/b + z/c = b - c + c - a + a - b x/a + y/b + z/c = 0 So, (x/a) = 3xyz/abc 38) The sum of three numbers is 2, if the first number is � times of the 2nd number, and the third number is � times of the 2nd number. What will be the second number? - 8/7
- 7/8
- 6/7
- 7/6
a + b + c = 2 and, a = ½b ….(i) c = ¼b ….(ii) From equation (i), a/b = ½ and from equation (ii) b/c = 4/1 Ratio between a, b, c is a : b : c = 2x : 4x : 1x (2x + 4x + 1x) = 2 7x = 2 So, x = 2/7 Then a = 2x = 2 * 2/7 = 4/7 b = 4x = 4 * 2/7 = 8/7 c = x = 2/7 So, the second number is 8/7. 39) The sum of the squares of three consecutive positive numbers is 365. What will the sum of numbers? - 36
- 33
- 45
- None of the above
According to the question, (x) On expanding, we will get, x 3x Or, x => (x - 10) (x + 12) = 0 So, x = 10 First number x = 10 Second number x + 1 = 11 Third number x + 2 = 12 So, sum of the numbers is = 10 + 11 + 12 = 33 40) The sum of three numbers is 252. What is the value of the second number if the first number is thrice of the second number, and the third number is two-third of the first number? - 36
- 42
- 45
- None of the above
According to the question, a = 3b or, a/b = 3/1 c = 2/3a or, a/c = 3/2 Ratio between a, b, c is a : b : c = 3x : x : 2x (3x + x + 2x) = 252 6x = 252 So, x = 252/6 = 42 Then, first number a = 3x = 3 * 42 = 126 Second number, b = x = 42 Third number, c = 2x = 42 * 2 = 84 So, the second number is 42. 41) If x, y, and z are said to be the real numbers, then what is the value of (x - y) - 0
- (x - y)
- 3(x - y) (y - z) (z - x)
- (x - y) (y - z) (z - x)
On adding a, b, and c we will get a + b + c = x -y + y - z + z - x => a + b + c =0 So, a We can say that (x - y) 42) If the sum of the digits of a two-digit number is 12, and the difference between the digits of that number is 6, what will be the number? - 36 or 63
- 22 or 22
- 39 or 93
- 25 or 52
We can also get the answer using the specified options. We can check the digits of the numbers mentioned in the options. As in the option 'C', there are 39 or 93, and on adding their digits, we will get 12, and on subtracting the digits, we will get 6.
Suppose the digits of the two-digit number be 'a' and 'b'. So, according to the question a + b = 12 ….(i) a - b = 6 ……(ii) Add equation (i) and (ii), we get 2a = 18 Or, a = 9 Put a = 9 in eq b = 3 So, the two-digit number is 93 (when a > b) Or 39 (when b > a) 43) If the three-fifth of a number is equal to 70% of another number, what is the ratio between the first number and second number? - 6 : 7
- 7 : 6
- 3 : 4
- 4 : 3
So, according to the question, a * 3/5 = 70% of b 3a/5 = 70b/100 a/b = (70 * 5)/(100 * 3) = 7/6 So, the ration between a and b is 7 : 6. 44) If the sum of the cubes of three numbers is 4500, and their ratio is 1 : 2 : 3, what is the value of the smallest number between them? - 6
- 5
- 3
- 4
So, the numbers will be 1a : 2a : 3a Then, a 36a Or, a So, a = 5 The smallest number is 5. 45) The denominator of a fraction is 3 more than its numerator. If the denominator is decreased by 2, and the numerator is increased by 7, we will get 2. What will be the sum of the numerator and denominator of that fraction? - 6
- 13
- 31
- 14
According to the question, (a + 7)/ ((a + 3) - 2) = 2/1 (a + 7)/(a + 1) = 2/1 2a + 2 = a + 7 => a = 5 So, the fraction is a/a + 3 = 5/ 5 + 3 = 5/8 And the sum of the numerator and denominator of the fraction is 13. 46) Which of the following is the result of 1505 x 1505? - 2265015
- 2265035
- 2265025
- None of the above
= 1505 = (1500 + 5) Apply formula; (a + b) = 1500 = 2250000 + 25 + 15000 = 2265025 47) A boy has mistakenly multiplied a number by 45 instead of multiplying it with 25. Due to this, the answer was 200 more than the correct answer. What was the number? - 15
- 10
- 7
- None of the above
= 200/45 - 25 = 10 48) If a = (0.4) - c > a > b
- a > b > c
- a < b < c
- None of the above
b = 0.04 c = 2/5 = 0.4 So, the relationship is c > a > b. 49) The sum of the numerator and denominator of a fraction is 11. If we add 2 to both numerator and denominator, the fraction will be increased by 1/24. What is the difference between the numerator and denominator of that fraction? - 1
- 2
- 6
- 8
So, the fraction = x/11 - x On adding 2 in both numerator and denominator, according to the question, the fraction will be - (x + 2)/(11 - x + 2) = (x)/(11 - x) + 1/24 (x + 2)/(13 - x) - (x)/(11 - x) = 1/24 [11x + 22 - x After solving the above equation, we will get => 528 - 96x = 143 - 24x + x x (x + 77) (x - 5) = 0 So, x =5 So, numerator = 5 and, denominator = 11 - 5 = 6 Difference between both is = 6 - 5 = 1 50) If a and b are two odd numbers, then which of the following is even? - a + b + 2ab
- a + b + ab
- a + b + 1
- None of the above
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