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Q.11 The quotient of π is an odd integer and there is no remainder. Which must be the correct 7 statement from below? A. B. C. D. E. a is a prime integer a is consecutive integer a is an even integer a is an odd integer a is multiple of 3 Solution; The odd integers are 1, 3, 5, 7β¦β¦β¦β¦β¦β¦β¦. Here it is given that the quotient of π If 7 π 7 π 7 π 7 is an odd integer that means = 1; then a = 7 = 3; then a = 21 = 5; then a = 35 That means for any value of π 7 to be odd the value of βaβ must be odd. So the correct answer choice is βDβ. Q.12 What are the multiple of 3, 6, & 9? Choose all the options from the following. A. B. C. D. E. 12 15 18 36 54 Solution; If we check option choice one by one we can easily get the answer. A. B. C. D. E. 12 = Multiple of 3 and 6 15 = Multiple of 3 18 = Multiple of 3, 6 and 9 36 = Multiple of 3, 6 and 9 54 = Multiple of 3, 6 and 9 So, correct answer will be C, D Q.13 and E. m is an even integer and n is an odd integer Quantity A Quantity B m 3 n A. If Quantity A is greater B. If Quantity B is greater C. If Quantity A and Quantity B are equal D. The relationship cannot be determined from given information Solution; Let us take values for m and n If m = 2, n = 1 then m/n = 2/1 = 2 Quantity A is greater If m = 12, n =3 then m/n = 12/3 = 4 Quantity B is greater So, Both the Quantity A & Quantity B cannot be compared from given data, Hence Answer is βDβ. Q.14 Dividend βxβ = 36. βxβ is square of its quotient Quantity A Quantity B Divisor of βxβ 6 A. If Quantity A is greater B. If Quantity B is greater C. If Quantity A and Quantity B are equal D. The relationship cannot be determined from given information Solution; Here it is given that Dividend = x = 36, which is square of its quotient. That means 36 is square of its quotient which should be β6β. So if we divide 36 with 6 then only βxβ can be square of quotient. So in above condition; Dividend = x = 36 Divisor = 6 Quotient = 6 The value for Quantity A will be 6. Now if we compare The value of Quantity B which is also 6 , it comes out equal so correct answer choice will be βCβ. Q.15 The integer m is even and integer n is even and prime. The square of βmβ is addition of m and n. Find the least possible value for βmβ? Solution; The possible values for βmβ could be 2, 4, 6, 8β¦β¦β¦β¦β¦β¦β¦β¦β¦.. The value for βnβ will be = 2, as 2 is only even and prime number. Now if we take βmβ = 2, βnβ = 2, then m2 = m x m = 2 x 2 = 4 Now addition of m + n = 2 + 2 = 4. As the least possible value is being asked, so this condition justifies the asked question. So the least possible value for βmβ will be =2. Q.16 If βxβ is double to the next number of sum of first three prime numbers. Quantity A Quantity B x 23 A. If Quantity A is greater B. If Quantity B is greater C. If Quantity A and Quantity B are equal D. The relationship cannot be determined from given information Solution; The first three prime numbers are 2, 3 and 5 The Sum = 2 + 3 + 5 = 10 Next number to 10 is 11. Double of 11, so βxβ = 2 x 11 = 22 If we compare Quantity A = x = 22 and Quantity B = 23, Quantity B is always greater. The correct answer choice is βBβ. Q.17 If βxβ is even and prime. It is one of the factors and digit at tenβs place of the number of another factor with a digit at oneβs place is square of 3. What is that number? Solution; βxβ is even and prime i.e. x = 2 , Now there is one integer with two factors . One of the factors is 2. And for second factor it is given that digit at tens place is 2 and oneβs place is square of 3 which is 9. So, the second factor is 29. Hence the number = 2 x 29 = 58. The correct answer is 58. Q. 18 If βmβ is a positive integer and βnβ is a negative integer then which of the following value must be true for m - n? A. B. C. D. E. Positive Negative Positive and even Prime Only even Solution; Let us take the positive value for (i) m = 1 and negative value for n = -1; Then m-n = 1 β (-1) = 1 + 1 = 2 (ii) Now take next value for m = 3 and n = -5 Then m-n = 3 β (-5) = 3 + 5 = 8 (iii) For m = 5 and n = -4 Then m β n = 5 β (- 4) = 5 + 4 = 9 (iv)Take one more value for m = 6 and n= -8 Then m β n = 6 β (- 8) = 6 + 8 =14 Every time the result is positive integer only. So correct answer is βAβ. Q. 19 If βmβ is multiplied to βnβ the result is 1. If βmβ is divided by βnβ the result is 4 what is m + n? A. B. C. D. E. 1 5 3 4 5 6 1 2 5 2 Solution; m x n = 1 β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.Equation 1 m n = 4 so, m = 4n β¦β¦β¦β¦β¦β¦β¦β¦. Equation 2 Now put value of βmβ in equation 1 4n x n = 1 n2 = 1 4 ; Taking square root both side; n= π βπ = π π π m = 4n = 4 x π =2 Therefore, m + n = 2 + π π = π π The correct answer choice is βEβ. Q.20 If a is square of integer t Quantity A Quantity B a t t a A. If Quantity A is greater B. If Quantity B is greater C. If Quantity A and Quantity B are equal D. The relationship cannot be determined from given information Solution; The best rule to solve this problem is taking one positive and one negative value for given variables and compare the Quantity A with Quantity B. Let us start by putting the values for integerβtβ. If t = 2 then a = 22 = 2 x 2 = 4 (i) a t = 4 2 t =2 a = 2 4 = 1 2 = 0.5 Quantity A is greater, Eliminate Choice βCβ If t = -3 then a = (-3)2 = 9 (ii) a t = 9 β3 = -3 Quantity B is greater t a = β 3 9 = - 0.33 As it is difficult to reach to any conclusion after comparing Quantity A and Quantity B, The correct answer choice will be βDβ.