Competive Exam Math 13

---

Q. What is the average of the first twelve multiples of 11 ?

Solution

First multiple = 11

12th multiple: $$11\times 12\; =\; 132$$

For equally spaced numbers: $$Average\; =\; First\; +\; Last\; /\; 2\; =\; 11+132\; /\; 2\; =\; 143/2\; =\; 71.5$$

Ans: 71.5

Trick

For the first n multiples of x: Average = x(n+1)/2 = 11(12+1)​/2 = 143/2 ​= 71.5

============================================

Q. What is the average of the first twelve multiples of 11 ?

A) 71.5   B) 69.5   C) 68.5   D) 70.5

Solution

For the first nn multiples of x:

Average = x(n+1)/2

Here, x = 11, n = 12 

11(12+1)/2 = 143/2=71.5

Ans: (A) 71.5

=======================================

Q. Find the average of all even numbers up to 100.

A) 50.5  B) 50  C) 49.5  D) 51

Solution

Even numbers up to 100 are: 2,4,6,…,100

For equally spaced numbers:

Average = First + Last / 2 = 2+100/2 = 102/2 = 51 

Ans: (D) 51

Trick:
For consecutive/equally spaced numbers: Average = First term + Last term/2

============================​

Q. The average of 7 numbers is 45. If 4 is subtracted from each number, what will be the new average ?

A) 41  B) 7  C) 37  D) 45

Trick

If the same number is subtracted from every value, the average also decreases by that number.

New Average = 45 − 4 = 41

Ans: (A) 41

Note:

• Add x to every number → Average increases by x


• Subtract x from every number → Average decreases by x


• Multiply every number by x → Average becomes x times


• Divide every number by x → Average becomes x times smaller

​============================================

================================

Q. The average of 29 numbers is 45. If each number is divided by 9, find the average of the new numbers.

Trick

If each number is divided by the same number, the average is also divided by that number.

New Average = 45/9 = 5

Ans: 5

Note:

• Add x to each number → Average increases by x


• Subtract x from each number → Average decreases by x


• Multiply each number by x → Average multiplies by x


• Divide each number by x → Average divides by x

================================

Q. What is the value of the expression ?

√(12345)² + 12345 + 12346

(A) 12345  (B) 12346  (C) 12347  (D) 12344

Short Trick:

12345 + 12346 = 2(12345) + 1

Therefore,

√(12345)²+12345 + 1

 = √(12345 + 1)² = 12346

Ans: (B) 12346

Shortcut: √a² + a + (a+1) ​= a + 1

​===================================

Q. What is the difference between -3 and -7 ?

(A) -10  (B) 4  (C) 10  (D) -4

Solution:

−3 − (−7) = −3 + 7 = 4

Ans: (B) 4

==================================