Math Test 1
The average of 9 observations was 9, that of the first 5 being 10 and that of the last 5 being 8. What was the fifth observation ?
  • 8
  • 7
  • 9
  • 10
Explanation: Given: • Average of 9 numbers = 9 - Total = 9 × 9 = 81 • Average of first 5 numbers = 10 - Total = 10 × 5 = 50 • Average of last 5 numbers = 8 - Total = 8 × 5 = 40 The 5th number is counted in both the first and last 5 numbers. So: Add both totals:50 + 40 = 90 But the real total is only 81, so the 5th number was counted twice. To fix that, subtract the extra 5th number once: 90 - x = 81 → x = 9 Answer: 5th observation is 9.
Consider the five numbers given here : (i) 736 (ii) 269 (iii) 958 (iv) 219 (v) 793 Arrange the digits of each number in descending order. What would be the difference between the highest number and the lowest one ?
  • 222
  • 716
  • 618
  • 12
Explanation: Given Numbers: 736, 269, 958, 219, 793 Rearrange digits in descending order: • 736 - 763 • 269 - 962 • 958 - 985 • 219 - 921 • 793 - 973 Find highest and lowest: • Highest = 985 • Lowest = 763 Find the difference: 985 − 763 = 222 Ans: 222
The longest diagonal that can be found in a regular cube of side 1 cm is :
  • 2 cm
  • sqrt 2 cm
  • 3 cm
  • sqrt 3 cm
Explanation: Formula: Longest diagonal of a cube = side × √3 Given: Side = 1 cm Calculation: 1 × √3 = √3 cm Ans: √3 cm
Three numbers A, B and C are such that the HCF of A and B is same as the HCF of B and C. If the LCM of A and B is three times the LCM of B and C, then the ratio C : A is :
  • 1 : 9
  • 3 : 1
  • 9 : 1
  • 1 : 3
Explanation: Given: • HCF(A, B) = HCF(B, C) • LCM(A, B) = 3 × LCM(B, C) • We need to find the ratio C : A Let: • A = d × a • B = d × b • C = d × c (Where d is the common HCF, and a, b, c are co-prime) LCM(A, B) = d × a × b LCM(B, C) = d × b × c Given: LCM(A, B) = 3 × LCM(B, C) d × a × b = 3 × d × b × c Cancel d × b from both sides: a = 3c So: A = d × a = d × 3c C = d × c Therefore: C / A = (d × c) / (d × 3c) = 1 / 3 Ans: C : A = 1 : 3
At a class test for 50 students, the average score was found to be 45.5 out of 100. Upon checking, it was found that an incorrect data-entry had occurred where 85 was incorrectly entered as 58. What should be the correct class average ?
  • 54.50
  • 46.04
  • 46.40
  • 55.40
Explanation: Total score using wrong average • 45.5 × 50 = 2275 Correct the wrong score • Wrong entry: 58 • Correct score: 85 • Difference = 85 − 58 = 27 Correct total score • 2275 + 27 = 2302 Correct average • 2302 ÷ 50 = 46.04 Correct average is: 46.04
If cosθ= 5/13 , then the value of sinθ is :
  • 5/12
  • 12/5
  • 12/13
  • 13/12
Explanation: Given: Cosθ = 5/13 Use identity: sin2θ + cos2θ = 1 Plug in value: sin2θ+(5/13)2=1 = sin2θ+25/169 = 1 Solve for sin2θ: sin2θ=1−25/169=144/169 Take square root: Sinθ = 12/13 Ans: Sinθ=12/13
The remainder when −46 is divided by 3 is :
  • −2
    • Explanation: Find a number that multiplies with 3 close to – 46 • 3 × (–16) = –48 Now: – 46 – (– 48) = –46 + 48 = 2 Ans: The remainder is 2