Subject: ASF Assistant Director Past Papers

Explanation
⇒  Let total examines is x. ⇒  65% of total examines has passed.  ⇒  student failed =100%−65%=35% Then, 35% of examines have failed. ⇒  Number of failures is 420 ∴  35% of x=420 ∴   35x/100 = 420  x=(420 * 100)/35 ∴  x=1200 Thus, Total number of examines are 1200.

Explanation
Given: (x1 + x2 + x3 + x4) / 4 = 16 Multiply both sides by 4: x1 + x2 + x3 + x4 = 64 ... (Equation 1) Also, (x2 + x3 + x4) / 2 = 23 Multiply both sides by 2: x2 + x3 + x4 = 46 ... (Equation 2) Now, substitute Equation 2 into Equation 1: x1 + 46 = 64 Subtract 46 from both sides: x1 = 18 Therefore, the correct answer is: 18

Explanation
Given: a^2 + b^2 = 8 ... (Equation 1) (a - b)^2 = 4 Expanding the left side of the equation: a^2 - 2ab + b^2 = 4 Now, substitute Equation 1 into this equation: 8 - 2ab = 4 Subtract 8 from both sides: -2ab = -4 Divide both sides by -2: ab = 2 So, the value of ab is 2.

Explanation
Let N of 1/12 = 3/48. Then, N = 3/48 x 12 = 3/4

Explanation
Savings % = (100 – 65) % = 35 % Saving = 35 % of Rs. 720 = Rs(35/100 ×720) = Rs. 252

Explanation
Vladimir Putin announced that Russia was suspending its participation in the NEW START treaty on February 21, 2023 . This move was part of escalating tensions between Russia and the US regarding nuclear arms control.

Explanation
2/7 = (2/7) x (100/100) = 200/7 = 28.57% 1/35 = (1/35) x (100/100) = 100/35 = 2.86% Now, divide the percentage equivalent of 1/35 by the percentage equivalent of 2/7 and multiply by 100 : (2.86 ÷ 28.57) x 100 = 10% So, 1/35 is 10% of 2/7. The correct answer is: 10%

Explanation
The sum of five numbers is 555. The average of the first two numbers is 75, so their sum is 2 x 75 = 150. The third number is 115. So, the sum of the first three numbers is 150 + 115 = 265. Since the sum of all five numbers is 555 , the sum of the last two numbers is 555 - 265 = 290. Therefore, the average of the last two numbers is 290 / 2 = 145. The correct answer is: 145

Explanation
Vladimir Putin announced that Russia was suspending its participation in the NEW START treaty on February 21, 2023 . This move was part of escalating tensions between Russia and the US regarding nuclear arms control.

Explanation
2/7 = (2/7) x (100/100) = 200/7 = 28.57% 1/35 = (1/35) x (100/100) = 100/35 = 2.86% Now, divide the percentage equivalent of 1/35 by the percentage equivalent of 2/7 and multiply by 100 : (2.86 ÷ 28.57) x 100 = 10% So, 1/35 is 10% of 2/7. The correct answer is: 10%

Explanation
The sum of five numbers is 555. The average of the first two numbers is 75, so their sum is 2 x 75 = 150. The third number is 115. So, the sum of the first three numbers is 150 + 115 = 265. Since the sum of all five numbers is 555 , the sum of the last two numbers is 555 - 265 = 290. Therefore, the average of the last two numbers is 290 / 2 = 145. The correct answer is: 145

Explanation
To evaluate the expression 2^2n + 1 , we need to follow the order of operations (PEMDAS): Calculate the exponent: 2^2n = 2^(2*3) = 2^6 Calculate the value of 2^6: 2^6 = 64 Add 1 to the result: 64 + 1 = 65 Therefore, the correct answer is: 65

Explanation
Given expression = (3a + 2b) / (3a - 2b) = [3(a/b) + 2] / [3(a/b) - 2] = [3 x 1/3 + 2] / [3 x 1/3 - 2] = 3 / -1 =-3

Explanation
⇒  Let total examines is x. ⇒  65% of total examines has passed.  ⇒  student failed =100%−65%=35% Then, 35% of examines have failed. ⇒  Number of failures is 420 ∴  35% of x=420 ∴   35x/100 = 420  x=(420 * 100)/35 ∴  x=1200 Thus, Total number of examines are 1200.

Explanation
Given: (x1 + x2 + x3 + x4) / 4 = 16 Multiply both sides by 4: x1 + x2 + x3 + x4 = 64 ... (Equation 1) Also, (x2 + x3 + x4) / 2 = 23 Multiply both sides by 2: x2 + x3 + x4 = 46 ... (Equation 2) Now, substitute Equation 2 into Equation 1: x1 + 46 = 64 Subtract 46 from both sides: x1 = 18 Therefore, the correct answer is: 18

Explanation
Given: a^2 + b^2 = 8 ... (Equation 1) (a - b)^2 = 4 Expanding the left side of the equation: a^2 - 2ab + b^2 = 4 Now, substitute Equation 1 into this equation: 8 - 2ab = 4 Subtract 8 from both sides: -2ab = -4 Divide both sides by -2: ab = 2 So, the value of ab is 2.

Explanation
Let N of 1/12 = 3/48. Then, N = 3/48 x 12 = 3/4

Explanation
Savings % = (100 – 65) % = 35 % Saving = 35 % of Rs. 720 = Rs(35/100 ×720) = Rs. 252

Explanation
Vladimir Putin announced that Russia was suspending its participation in the NEW START treaty on February 21, 2023 . This move was part of escalating tensions between Russia and the US regarding nuclear arms control.

Explanation
2/7 = (2/7) x (100/100) = 200/7 = 28.57% 1/35 = (1/35) x (100/100) = 100/35 = 2.86% Now, divide the percentage equivalent of 1/35 by the percentage equivalent of 2/7 and multiply by 100 : (2.86 ÷ 28.57) x 100 = 10% So, 1/35 is 10% of 2/7. The correct answer is: 10%

Explanation
The sum of five numbers is 555. The average of the first two numbers is 75, so their sum is 2 x 75 = 150. The third number is 115. So, the sum of the first three numbers is 150 + 115 = 265. Since the sum of all five numbers is 555 , the sum of the last two numbers is 555 - 265 = 290. Therefore, the average of the last two numbers is 290 / 2 = 145. The correct answer is: 145

Explanation
To evaluate the expression 2^2n + 1 , we need to follow the order of operations (PEMDAS): Calculate the exponent: 2^2n = 2^(2*3) = 2^6 Calculate the value of 2^6: 2^6 = 64 Add 1 to the result: 64 + 1 = 65 Therefore, the correct answer is: 65

Explanation
Given expression = (3a + 2b) / (3a - 2b) = [3(a/b) + 2] / [3(a/b) - 2] = [3 x 1/3 + 2] / [3 x 1/3 - 2] = 3 / -1 =-3

Explanation
⇒  Let total examines is x. ⇒  65% of total examines has passed.  ⇒  student failed =100%−65%=35% Then, 35% of examines have failed. ⇒  Number of failures is 420 ∴  35% of x=420 ∴   35x/100 = 420  x=(420 * 100)/35 ∴  x=1200 Thus, Total number of examines are 1200.

Explanation
Given: (x1 + x2 + x3 + x4) / 4 = 16 Multiply both sides by 4: x1 + x2 + x3 + x4 = 64 ... (Equation 1) Also, (x2 + x3 + x4) / 2 = 23 Multiply both sides by 2: x2 + x3 + x4 = 46 ... (Equation 2) Now, substitute Equation 2 into Equation 1: x1 + 46 = 64 Subtract 46 from both sides: x1 = 18 Therefore, the correct answer is: 18

Explanation
Given: a^2 + b^2 = 8 ... (Equation 1) (a - b)^2 = 4 Expanding the left side of the equation: a^2 - 2ab + b^2 = 4 Now, substitute Equation 1 into this equation: 8 - 2ab = 4 Subtract 8 from both sides: -2ab = -4 Divide both sides by -2: ab = 2 So, the value of ab is 2.

Explanation
Let N of 1/12 = 3/48. Then, N = 3/48 x 12 = 3/4

Explanation
Savings % = (100 – 65) % = 35 % Saving = 35 % of Rs. 720 = Rs(35/100 ×720) = Rs. 252