Q 1-Which f the following numbers is exactly divisible by 11?

A - 499774

B - 47554

C - 466654

D - 4646652

Answer - A Explanation "Reference : Divisibility by 11 Rule Take 47554 4 + 5 + 4 = 13 7 + 5 = 12 13 - 12 = 1 1 is not divisible by 11 Hence 47554 is not divisible by 11 Take 466654 4 + 6 + 4 = 14 6 + 5 = 11 14 - 11 = 3 3 is not divisible by 11 Hence 466654 is not divisible by 11 Take 4646652 4 + 4 + 6 + 2 = 16 6 + 6 + 5 = 17 17 - 16 = 1 1 is not divisible by 11 Hence 4646652 is not divisible by 11 Take 499774 4 + 9 + 7 = 20 9 + 7 + 4 = 20 20 - 20 = 0 We got the difference as 0. Hence 499774 is divisible by 11 "

Q 2-What is the sum all even natural numbers between 1 and 101?

A - 5050

B - 2550

C - 5040

D - 2540

Answer - B Explanation "Reference 1: Natural Numbers Reference 2: Arithmetic Progression (AP) and Related Formulas Required sum = 2 + 4 + 6+ . . . + 100 This is an arithmetic progression with a = 2 d = (4 - 2) = 2 n=( l − a ) / d+1 =(100−2)/2+1 =98/2+1 =49+1 =50 2+4+6+⋯+100 = n/2 (a+l) =50/2(2+100) =50×51 =2550 "

Q 3-A boy multiplies 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong , but the other digits are correct, then what will be the correct answer?

A - 556581

B - 555681

C - 555181

D - 553681

Answer - B Explanation "The answer is divisible by 987. So we can use hit and trial method to find out the number divisible by 987 from the given choices. 553681 ÷ 987 gives a remainder not equal to 0 555181 ÷ 987 gives a remainder not equal to 0 556581 ÷ 987 gives a remainder not equal to 0 But 555681 ÷ 987 gives 0 as remainder. Hence this is the answer "

Q 4-Which one of the following cannot be the square of a natural number ?

A - 15186125824

B - 49873162329

C - 14936506225

D - 60625273287

Answer - D Explanation "Square of a natural number cannot end with 7. Hence 60625273287 is the answer"

Q 5-7128+1252=1202+?

A - 6028

B - 1248

C - 2348

D - 7178

Answer - D Explanation "?=7128+1252−1202 =7128+50 =7178 "

Q 6-73411×9999=?

A - 724836589

B - 724036589

C - 734036589

D - 734036129

Answer - C Explanation "73411×9999 =73411(10000−1) =734110000−73411 =734036589 "

Q 7-32+33+34+⋯+42=?

A - 397

B - 407

C - 417

D - 427

Answer - B Explanation "1+2+3+⋯+n =∑n=n(n+1)/2 (Reference: Power Series) 32+33+34+⋯+42 =(1+2+3+⋯+42) − (1+2+3+⋯+31) =(42×43/2)−(31×32/2) = 21×43−31 × 16 =903−496 =407 "

Q 8-1234+123+12−?=1221

A - 148

B - 158

C - 168

D - 178

Answer - A Explanation ? = 1234+123+12−1221=148

Q 9-9312×9999=?

A - 93110688

B - 93010688

C - 93110678

D - 83110688

Answer - A Explanation "9312×9999 =9312(10000−1) =93120000−9312 =93110688 "

Q 10-A three-digit number 4a3 is added to another three-digit number 984 to give a four digit number 13b7, which is divisible by 11. What is the value of (a + b)?

A - 9

B - 10

C - 11

D - 12

Answer - B Explanation "(Reference : Divisibility by 11 rule) 4 a 3 9 8 4 13 b 7 => a + 8 = b ...(1) 13b7 is divisible by 11 => (1 + b) - (3 + 7) is 0 or divisible by 11 => (b - 9) is 0 or divisible by 11 ...(2) Assume that (b - 9) = 0 => b = 9 Substituting the value of b in (1), a + 8 = b a + 8 = 9 => a = 9 - 8 = 1 If a = 1 and b= 9, (a + b) = 1 + 9 = 10 10 is there in the given choices. Hence this is the answer. "

Q 11-The sum of the two numbers is 11 and their product is 24. What is the sum of the reciprocals of these numbers ?

A - 42563

B - 42686

C - 42698

D - 42559

Answer - C Explanation "Let the numbers be xx and y Then x+y=11 xy=24 Hence, x+y/xy=11/24 ⇒1/y+1/x=11/24 "

Q 12-What is the difference between the place values of two sevens in the numeral 54709479 ?

A - 699930

B - 699990

C - 99990

D - None of these

Answer - A Explanation "Required Difference = 700000 - 70 = 699930 "

Q 13-A number when divided by 75 leaves 34 as remainder. What will be the remainder if the same number is divided by 65?

A - 1/2

B - 12/31

C - 1/5

D - 1/8

Answer - D Explanation "Let the number be x Let x÷75 =p and remainder = 34 ⇒x=75p+34 ⇒x=(25p×3)+25+9 ⇒x=25(3p+1)+9 Hence, if the number is divided by 25, we will get 9 as remainder "

Q 14-The number 7490xy7490xy is divisible by 90. Find out (x+y)(x+y)

A - 4

B - 5

C - 6

D - 7

Answer - D Explanation "If a number is divisible by two co-prime numbers, then the number is divisible by their product also. A number is divisible by 10 if the last digit is 0. A number is divisible by 9 if the sum of its digits is divisible by 9. 10×9=90 where 10 and 9 are co-prime numbers. Hence, if 7490xy is divisible by 9 and 10, it will also be divisible by 90 Suppose 7490xy is divisible by 10. We know that a number is divisible by 10 if the last digit is 0. Hence y=0y=0 Thus we have the number 7490x0. If this is divisible by 9, 7+4+9+0+x+0 is divisible by 9 => 20+x is divisible by 9 (where x is a digit) => x=7 Hence, (x+y)=(7+0)=7 "

Q 15-What is the smallest 3 digit prime number?

A - 107

B - 100

C - 102

D - 101

Answer - D Explanation ". Prime Numbers . Divisibility Rules 102 is divisible by 2 => 102 is not a prime number 100 is divisible by 2 => 100 is not a prime number. √101<11 101 is not divisible by the prime numbers 2, 3, 5, 7 Hence 101 is a prime number. Since 100 is not a prime number, 101 is the smallest 3 digit prime number. √107<11 107 is also not divisible by the prime numbers 2,3,5,7 Hence 107 is also a prime number. But the smallest 3 digit prime number is 101 "