Math concepts made simple

Hyderabad: This article is in continuation to the last article on arithmetic that will aid you in your preparation for government recruitment exams. Here are some practice bits along with solutions on the Average topic. 1. There are Indians and Europeans in an Army of 12,000. The average height of Europeans is 5’ 10” and […]

Hyderabad: This article is in continuation to the last article on arithmetic that will aid you in your preparation for government recruitment exams. Here are some practice bits along with solutions on the Average topic.

1. There are Indians and Europeans in an Army of 12,000. The average height of Europeans is 5’ 10” and that of Indians is 5’ 9” and the average height of the entire Army is . Find out the number of Indians in the Army.

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1) 1800                  2) 1500                  c) 3000                  4) 2400
Ans: 3

2. A student finds the average of 10, 2 – digit numbers. If the digit of one of the numbers is interchanged, the average increases by 4.5. The difference between the digits of 2- digit number is?
1) 4                         2) 7                         3) 2                         4) 5
Ans: 4

3. The arithmetic mean of the following numbers
1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6, and 7,7,7,7,7,7,7?
1) 4                         2) 5                         3) 14                      4) 20
Ans: 2

Solution: (1×2 + 2×2 + 3×3 + …….. +
7×7)/ (1 + 2+ 3 + 4 + 5 + 6
+ 7)
= (12 + 22 + ……… 72)/ 28
= 140/28
= 5

4. If two consecutive terms are removed from a series 1,2…..n, then the average of remaining terms is , then the number of terms is?
1) 40                 2) 42                       3) 30                           4) 34
Ans: 3

Solution: Sum of terms cannot be fraction
So, the number of remaining terms should be divisible by 14
From given options,
1)  40 – 2 = 38
2) 42 – 2 = 40
3) 30 – 2 = 28 is divisible by 14
4) 34 – 2 = 32

 

5. The average of the first 1234_____ numbers is equal to 1234. Fill in the blank?
1) Even                 2) Odd
3) Prime               4) natural
Ans: 2

Solution: Average of first ‘n’ odd numbers = n
Average of first 1234 odd numbers = 1234

To be continued