Quantitative Aptitude (Averages - Part 2)
Below are questions 11 to 20 from the document, presented in the same format with accurate mathematical explanations.
11. The average of x numbers is y² and the average of y numbers is x². Find the average of all the numbers taken together?
Correct Answer: (a) xy
Explanation:
Step 1: Sum of x numbers = x × y² = xy² Step 2: Sum of y numbers = y × x² = yx² Step 3: Total Sum = xy² + yx² = xy(y + x) Step 4: Average =
Explanation:
Step 1: Sum of x numbers = x × y² = xy² Step 2: Sum of y numbers = y × x² = yx² Step 3: Total Sum = xy² + yx² = xy(y + x) Step 4: Average =
xy(x + y)
(x + y)
= xy
12. There are three fractions A, B and C. If A = 1/3 and B = 1/6 and the average of A, B and C is 1/12. What is the value of C?
Correct Answer: (d) -1/4
Explanation:
Step 1:
Explanation:
Step 1:
A + B + C
3
=
1
12
Step 2: A + B + C =
3
12
=
1
4
Step 3:
1
3
+
1
6
+ C =
1
4
Step 4:
3
6
+ C =
1
4
⇒
1
2
+ C =
1
4
Step 5: C =
1
4
-
1
2
= -
1
4
13. The average temperature for Wednesday, Thursday and Friday was 40°C. The average for Thursday, Friday and Saturday was 41°C. If the temperature on Saturday was 42°C, what was the temperature on Wednesday?
Correct Answer: (a) 39°C
Explanation:
Step 1: Wed + Thu + Fri = 40 × 3 = 120 Step 2: Thu + Fri + Sat = 41 × 3 = 123 Step 3: (Thu + Fri + Sat) - (Wed + Thu + Fri) = 123 - 120 Step 4: Sat - Wed = 3 Step 5: 42 - Wed = 3 ⇒ Wed = 39°C
Explanation:
Step 1: Wed + Thu + Fri = 40 × 3 = 120 Step 2: Thu + Fri + Sat = 41 × 3 = 123 Step 3: (Thu + Fri + Sat) - (Wed + Thu + Fri) = 123 - 120 Step 4: Sat - Wed = 3 Step 5: 42 - Wed = 3 ⇒ Wed = 39°C
14. If average of a, b and c is M and ab + bc + ca = 0, then the average of a², b² and c² is:
Correct Answer: (b) 3M²
Explanation:
Step 1: a + b + c = 3M Step 2: Formula: (a+b+c)² = a² + b² + c² + 2(ab + bc + ca) Step 3: (3M)² = (a² + b² + c²) + 2(0) Step 4: a² + b² + c² = 9M² Step 5: Required Average =
Explanation:
Step 1: a + b + c = 3M Step 2: Formula: (a+b+c)² = a² + b² + c² + 2(ab + bc + ca) Step 3: (3M)² = (a² + b² + c²) + 2(0) Step 4: a² + b² + c² = 9M² Step 5: Required Average =
9M²
3
= 3M²
15. Find the average of all prime numbers between 30 and 50.
Correct Answer: (a) 39.8
Explanation:
Step 1: Prime numbers between 30 and 50 are: 31, 37, 41, 43, 47 Step 2: Sum = 31 + 37 + 41 + 43 + 47 = 199 Step 3: Total count = 5 Step 4: Average =
Explanation:
Step 1: Prime numbers between 30 and 50 are: 31, 37, 41, 43, 47 Step 2: Sum = 31 + 37 + 41 + 43 + 47 = 199 Step 3: Total count = 5 Step 4: Average =
199
5
= 39.8
16. The average of x successive natural numbers is N. If the next natural number is included in the group, the average increases by:
Correct Answer: (d) 0.5
Explanation:
Step 1: In any consecutive natural number series (AP with difference 1), adding the next number increases the average by
Explanation:
Step 1: In any consecutive natural number series (AP with difference 1), adding the next number increases the average by
d
2
.
Step 2: Here, difference (d) = 1.
Step 3: Increase =
1
2
= 0.5
17. In a hotel where rooms are numbered from 101 to 130, each room gives an earning of 3000 for the first fifteen days of a month and for the latter half 2000 per room. Find the average earning per room per day over the month. (Assume 30 day month)
Correct Answer: (b) 2500
Explanation:
Step 1: Since the number of days for both rates are equal (15 days each), we can take the direct average of rates. Step 2: Average =
Explanation:
Step 1: Since the number of days for both rates are equal (15 days each), we can take the direct average of rates. Step 2: Average =
3000 + 2000
2
Step 3: Average =
5000
2
= 2500
18. The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven papers is 35. Find the marks obtained in the 7th paper.
Correct Answer: (c) 19
Explanation:
Step 1: Total of 13 papers = 13 × 40 = 520 Step 2: Sum of first 7 = 7 × 42 = 294 Step 3: Sum of last 7 = 7 × 35 = 245 Step 4: 7th Paper = (Sum of First 7 + Sum of Last 7) - Total Step 5: 7th Paper = (294 + 245) - 520 = 539 - 520 = 19
Explanation:
Step 1: Total of 13 papers = 13 × 40 = 520 Step 2: Sum of first 7 = 7 × 42 = 294 Step 3: Sum of last 7 = 7 × 35 = 245 Step 4: 7th Paper = (Sum of First 7 + Sum of Last 7) - Total Step 5: 7th Paper = (294 + 245) - 520 = 539 - 520 = 19
19. The average of n consecutive even numbers is 201. Find the sum of first and last numbers?
Correct Answer: (d) None
Explanation:
Step 1: For any Arithmetic Progression (AP), Average =
Explanation:
Step 1: For any Arithmetic Progression (AP), Average =
First Term + Last Term
2
Step 2: 201 =
First + Last
2
Step 3: First + Last = 201 × 2 = 402
Step 4: Since 402 is not in options A, B, or C, the answer is None.
20. The average age of the Indian cricket team (11 players) is 30. The average age of 5 of the players is 27 and that of another set of 5 players is 29. Find the age of the captain (who is remaining).
Correct Answer: (c) 50
Explanation:
Step 1: Total age of 11 players = 11 × 30 = 330 Step 2: Sum of first 5 players = 5 × 27 = 135 Step 3: Sum of next 5 players = 5 × 29 = 145 Step 4: Captain's Age = 330 - (135 + 145) Step 5: Captain's Age = 330 - 280 = 50
Explanation:
Step 1: Total age of 11 players = 11 × 30 = 330 Step 2: Sum of first 5 players = 5 × 27 = 135 Step 3: Sum of next 5 players = 5 × 29 = 145 Step 4: Captain's Age = 330 - (135 + 145) Step 5: Captain's Age = 330 - 280 = 50
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